Download PHYSICS LABORATORY MANUAL - İstanbul Ticaret Üniversitesi

Istanbul Commerce University
Engineering and Design Faculty
PHYSICS LABORATORY
MANUAL
Department_______________________
Name______________________________
2015-2016
Contents
İçindekiler
Contents ............................................................................................................................................. 2
MEAUSEREMENT .................................................................................................................................. 8
UNIT SYSTEMS / SI UNITS ..................................................................................................................... 8
MEASUREMENTS AND UNCERTAINITY ................................................................................................. 9
THE VERNIER CALIPER ......................................................................................................................... 11
GRAPHICAL REPRESENTATION OF DATA ............................................................................................ 13
EXPERIMENT 1: HOOKE’S LAW—MEASURING FORCES ...................................................................... 16
EXPERIMENT 2: ADDING FORCES RESULTANTS AND EQUILIBRANTS (PASCO) ................................... 19
EXPERIMENT 3: RESOLVING FORCES—COMPONENTS (PASCO)......................................................... 23
EXPERIMENT 4: TORQUE—PARALLEL FORCES (PASCO) ..................................................................... 27
EXPERIMENT 5: CENTER OF MASS (PASCO) ........................................................................................ 31
EXPERIMENT 6: SLIDING FRICTION (PASCO) ....................................................................................... 34
Experiment 7: Simple Harmonic Motion: Mass on a Spring ............................................................... 38
Experiment 8: Simple Harmonic Motion—the Pendulum .................................................................. 42
Experiment 9: Ballistic Pendulum ....................................................................................................... 46
Experiment 10: Conservation of Angular Momentum Using a Point Mass (PASCO) .......................... 55
Experiment 11: Rotational Inertia of Disk and Ring (PASCO) ............................................................. 57
Experiment 12: Conservation of Angular Momentum (PASCO) ......................................................... 64
Experiment 13: Projectile Motion....................................................................................................... 68
Experiment 14: Projectile Motion Using Photogates (PASCO) ........................................................... 73
Experiment 15: Polarization of Light .................................................................................................. 76
EXPERIMENT 16: Interference and Diffraction of Light ...................................................................... 85
Experiment 17 : Ohm's Law .............................................................................................................. 92
Experiment 18: Kirchoff’s Law ............................................................................................................ 98
EXPERIMENT 19: Emf and Internal Resistance ................................................................................. 103
EXPERIMENT 20: ............................................................................................................................... 106
CAPACITOR CHARGE-DECHARGE CHARACTERISTICS ........................................................................ 106
EXPERIMENT 21: FORCE VERSUS CURRENT (F = ILBSin) ................................................................. 110
Experiment 22: Transformer Basics I ................................................................................................ 115
Experiment 23: Ohm’s Law, RC and RL Circuits ................................................................................ 118
EXPERIMENT 24: RL, RC, RLC Circuts ................................................................................................ 127
2
Experiment 25. Oscilloscope ............................................................................................................. 131
Experiment 26. I-V Curves of Non linear Device ............................................................................... 134
Experiment 27: Radioactivity Simulation .......................................................................................... 137
3
GENERAL INSTRUCTIONS
1. You must arrive on time since instructions are given and announcements are made at the start of
class.
2. You will do experiments in a group but you are expected to bear your share of responsibility in
doing the experiments. You must actively participate in obtaining the data and not merely watch
your partners do it for you.
3. The assigned work station must be kept neat and clean at all times. Coats/jackets must be hung at
the appropriate place, and all personal possessions other than those needed for the lab should be
kept in the table drawers or under the table.
4. The data must be recorded neatly with a sharp pencil and presented in a logical way. You may
want to record the data values, with units, in columns and identify the quantity that is being
measured at the top of each column.
5. If a mistake is made in recording a datum item, cancel the wrong value by drawing a fine line
through it and record the correct value legibly.
6. Get your data sheet, with your name, ID number and date printed on the right corner, signed by
the instructor before you leave the laboratory. This will be the only valid proof that you actually did
the experiment.
7. Each student, even though working in a group, will have his or her own data sheet and submit his
or her own written report, typed, for grading to the instructor by the next scheduled lab session. No
late reports will be accepted.
8. Actual data must be used in preparing the report. Use of fabricated, altered, and other students’
data in your report will be considered as cheating.
9. Be honest and report your results truthfully. If there is an unreasonable discrepancy from the
expected results, give the best possible explanation.
10. If you must be absent, let your instructor know as soon as possible. Amissed lab can be made up
only if a written valid excuse is brought to the attention of your instructor within a week of the
missed lab.
11. You should bring your calculator, a straight-edge scale and other accessories to class. It might be
advantageous to do some quick calculations on your data to make sure that there are no gross
errors.
12. Eating, drinking, and smoking in the laboratory are not permitted.
13. Refrain from making undue noise and disturbance.
4
SEMESTER I
Student’s
NAME - SURNAME
NO :
DEPARTMENT :
DATE:
:
EXP NAME.:
INSTRUCTOR’S SIGNATURE
st
1 Week
2
nd
Week
rd
3 Week
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4 Week
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5 Week
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6 Week
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7 Week
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8 Week
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9 Week
10
th
Week
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SEMESTER II
Student’s
NAME - SURNAME
NO :
DEPARTMENT :
DATE:
:
EXP NAME.:
INSTRUCTOR’S SIGNATURE
st
1 Week
2
nd
Week
rd
3 Week
th
4 Week
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5 Week
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6 Week
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7 Week
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Week
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REPORT FORMAT
The laboratory report must include the following:
1. Title Page: This page should show only the student’s name, ID number, the name of the
experiment, and the names of the student’s partners.
2. Objective: This is a statement giving the purpose of the experiment.
3. Theory: You should summarize the equations used in the calculations to arrive at the results for
each part of the experiment.
4. Apparatus: List the equipment used to do the experiment.
5. Procedure: Describe how the experiment was carried out.
6. Calculations and Results: Provide one sample calculation to show the use of the equations.
Present your results in tabular form that is understandable and can be easily followed by the grader.
Use graphs and diagrams, whenever they are required.
It may also include the comparison of the computed results with the accepted values together with
the pertinent percentage errors. Give a brief discussion for the origin of the errors.
7. Conclusions: Relate the results of your experiment to the stated objective.
8. Data Sheet: Attach the data sheet for the experiment that has been signed by your instructor.
7
INTRODUCTION
The aim of the laboratory exercise is to give the student an insight into the significance of the
physical ideas through actual manipulation of apparatus, and to bring him or her into contact with
the methods and instruments of physical investigation.
Each exercise is designed to teach or reinforce an important law of physics which, in most cases, has
already been introduced in the lecture and textbook. Thus the student is expected to be acquainted
with the basic ideas and terminology of an experiment before coming to the laboratory.
The exercises in general involve measurements, graphical representation of the data, and calculation
of a final result. The student should bear in mind that equipment can malfunction and final results
may differ from expected values by what may seem to be large amounts. This does not mean that
the exercise is a failure. The success of an experiment lies rather in the degree to which a student has:
• mastered the physical principles involved,
• understood the theory and operation of the instruments used, and
• realized the significance of the final conclusions.
MEAUSEREMENT
UNIT SYSTEMS / SI UNITS
Sciences are built upon measurements. Measurements are expressed with numbers. This allows the
logic, precision and power of mathematics to be brought to bear on our study of nature.
Units of measurement are names which characterize the kind of measurement and the standard of
comparison to which each is related. So, when we see a measurement expressed as "7.5 feet" we
immediately recognize it as a measurement of length, expressed in the unit "foot" (rather than other
possible length units such as yard, mile, meter, etc.) Since many possible units are available for any
measurement it is essential that every measurement include the unit name. A statement such as "the
length is 7.5" is ambiguous, and therefore meaningless.
8
MEASUREMENTS AND UNCERTAINITY
Such comparisons come down to the question ”Is the difference between our value and that in the
text consistent with the uncertainty in our measurements?”.
The topic of measurement involves many ideas. We shall introduce some of them by means of
definitions of the corresponding terms and examples.
SENSITIVITY - The smallest difference that can be read or estimated on a measuring instrument.
Generally a fraction of the smallest division appearing on a scale. About 0.5 mm on our rulers. This
results in readings being uncertain by at least this much.
VARIABILITY - Differences in the value of a measured quantity between repeated measurements.
Generally due to uncontrollable changes in conditions such as temperature or initial conditions.
RANGE - The difference between largest and smallest repeated measurements. Range is a rough
measure of variability provided the number of repetitions is large enough. Six repetitions are
reasonable. Since range increases with repetitions, we must note the number used.
UNCERTAINTY - How far from the correct value our result might be. Probability theory is needed to
make this definition precise, so we use a simplified approach. We will take the larger of range and
sensitivity as our measure of uncertainty.
Example: In measuring the width of a piece of paper torn from a book, we might use a cm ruler with
a sensitivity of 0.5 mm (0.05 cm), but find upon 6 repetitions that our measurements range from 15.5
cm to 15.9 cm. Our uncertainty would therefore be 0.4 cm.
PRECISION - How tightly repeated measurements cluster around their average value. The
uncertainty described above is really a measure of our precision.
ACCURACY - How far the average value might be from the ”true” value. A precise value might not be
accurate. For example: a stopped clock gives a precise reading, but is rarely accurate.
Factors that affect accuracy include how well our instruments are calibrated (the correctness of the
marked values) and how well the constants in our calculations are known. Accuracy is affected by
systematic errors, that is, mistakes that are repeated with each measurement.
Example: Measuring from the end of a ruler where the zero position is 1 mm in from the end.
BLUNDERS - These are actual mistakes, such as reading an instrument pointer on the wrong scale.
They often show up when measurements are repeated and differences are larger than the known
uncertainty. For example: recording an 8 for a 3, or reading the wrong scale on a meter.
9
COMPARISON - In order to confirm the physical principles we are learning, we calculate the value of
a constant whose value appears in our text. Since our calculated result has an uncertainty, we will
also calculate a Uncertainty Ratio, UR, which is defined as
UNCERTAINTY
A value less than 1 indicates very good agreement, while values greater than 3 indicate
disagreement. Intermediate values need more examination. The uncertainty is not a limit, but a
measure of when the measured value begins to be less likely. There is always some chance that the
many effects that cause the variability will all affect the measurement in the same way.
Example: Do the values 900 and 980 agree?
If the uncertainty is 100, then U R = 80/100 = 0.8 and they agree,
but if the uncertainty is 20 then U R = 80/20 = 4 and they do not agree.
10
THE VERNIER CALIPER
A vernier is a device that extends the sensitivity of a scale. It consists of a parallel scale whose
divisions are less than that of the main scale by a small fraction, typically 1/10 of a division. Each
vernier division is then 9/10 of the divisions on the main scale. The lower scale in Fig. 2 is the vernier
scale, the upper one, extending to 120 mm is the main scale.
The left edge of the vernier is called the index, or pointer. The position of the index is what is to be
read. When the index is beyond a line on the main scale by 1/10 then the first vernier line after the
index will line up with the next main scale line. If the index is beyond by 2/10 then the second vernier
line will line up with the second main scale line, and so forth.
If you line up the index with the zero position on the main scale you will see that the ten divisions on
the vernier span only nine divisions on the main scale. (It is always a good idea to check that the
vernier index lines up with zero when the caliper is completely closed. Otherwise this zero reading
might have to be subtracted from all measurements.)
Note how the vernier lines on either side of the matching line are inside those of the main scale. This
pattern can help you locate the matching line.
The sensitivity of the vernier caliper is then 1/10 that of the main scale. Keep in mind that the
variability of the object being measured may be much larger than this. Also be aware that too much
pressure on the caliper slide may distort the object being measured.
11
MICROMETER
12
GRAPHICAL REPRESENTATION OF DATA
In order to understand a physical problem, one usually studies the dependence of one quantity upon
another. Whereas sometimes such a dependence is obtained theoretically, at times it must be arrived
at experimentally. The experimental determination involves obtaining experimentally a series of
values of one quantity corresponding to the various arbitrary values of the other and then subjecting
the data to some kind of analysis. One of the most convenient and useful means of treating the
experimental data is by graphical analysis.
Graphs are an important technique for presenting scientific data. Graphs can be used to suggest
physical relationships, compare relationships with data, and determine parameters such as the slope
of a straight line.
There is a specific sequence of steps to follow in preparing a graph. (See Figure 1 )
1.
Arrange the data to be plotted in a table.
2.
Decide which quantity is to be plotted on the x-axis (the abscissa), usually the independent
variable, and which on the y-axis (the ordinate), usually the dependent variable.
3.
Decide whether or not the origin is to appear on the graph. Some uses of graphs require the
origin to appear, even though it is not actually part of the data, for example, if an intercept is to be
determined.
4.
Choose a scale for each axis, that is, how many units on each axis represent a convenient
number of the units of the variable represented on that axis. (Example: 5 divisions = 25 cm)
Scales should be chosen so that the data span almost all of the graph paper, and also make it easy to
locate arbitrary quantities on the graph. (Example: 5 divisions = 23 cm is a poor choice.) Label the
major divisions on each axis.
5.
Write a label in the margin next to each axis which indicates the quantity being represented
and its units.Write a label in the margin at the top of the graph that indicates the nature of the graph,
and the date the data were collected. (Example: "Air track: Acceleration vs. Number of blocks,
12/13/05")
6.
Plot each point. The recommended style is a dot surrounded by a small circle. A small cross or
plus sign may also be used.
7.
Draw a smooth curve that comes reasonably close to all of the points. Whenever possible we
plot the data or simple functions of the data so that a straight line is expected. A transparent ruler or
the edge of a clear plastic sheet can be used to "eyeball" a reasonable fitting straight line, with equal
numbers of points on each side of the line. Draw a single line all the way across the page. Do not
simply connect the dots.
8.
If the slope of the line is to be determined, choose two points on the line whose values are
easily read and that span almost the full width of the graph. These points should not be original data
points. Remember that the slope has units that are the ratio of the units on the two axes.
9.
The uncertainty of the slope may be estimated as the larger uncertainty of the two end points,
13
14
GENERAL LINEAR RELATIONSHIP
A straight line plot of y versus x indicates that the relationship is linear and is of the form
y = mx + b
where b is the intercept on the y-axis (the value of y when x = 0) and m is the slope of the line.
Graphics
I- Linear Graphics:
y = mx + A
II-Power
III- Exponential
y = K.xm
Y = K.amx
Logy = LogK + m.logx
a = e “special case”
y = K.emx
Lny = LnK + mx
Lny – x grafiğinin eğimi m
y
y
y=k.xm
y=mx + A
0<m<1
m>1
y=mx
y=mx - A
m<0
x
x
15
EXPERIMENT 1: HOOKE’S LAW—MEASURING FORCES
EQUIPMENT NEEDED:
– Experiment Board
– Spring Scale
– Mass Hanger (1)
– Masses
Introduction
The concept of force is defined in Newton’s second law as F = ma; Force = Mass x Acceleration.
Using this law, a force can be determined by measuring the acceleration it produces on a body of
known mass. However, this method is rarely practical. A more convenient method is to compare the
unknown force with an adjustable force of known magnitude. When both forces are applied to an
object, and the object is not accelerated, the unknown force must be exactly opposite in both
magnitude and direction to the known force.
With this statics system, there are two methods of measuring and applying forces. One method is to
hang the calibrated masses. For a mass m, gravity pulls it downward with a magnitude
2
F = mg, where g is the acceleration caused by gravity (g= 9.8 m/s downward, toward the center of
the Earth). The Spring Balance provides a second method of applying and measuring forces. In this
experiment you will use the known forces provided by the calibrated masses to investigate the
properties of the Spring Balance.
Setup
Hang the Spring Balance on the Experiment Board. Be sure the spring hangs vertically in the plastic
tube. With no weight on the Spring Balance, adjust the zeroing screw on the top of the Spring
Balance until the indicator is aligned with the 0 m mark on the centimeter scale of the Balance as
shown in Figure 1.1a
Procedure

Hang a Mass Hanger with a (.02 kg) Mass from the Spring Balance. Measure the spring
displacement on the scale as shown in Figure 1.1b. Record this value in the appropriate space in
Table 1.1. Be sure to include the mass of the Mass Hanger (.005 kg) in the total mass.

By hanging additional masses from the Mass Hanger, adjust the total mass hanging from the
Spring Balance to each of the values shown in the table. For each value, record the spring
displacement.
16

Using the formula F = mg, determine the total weight in newtons for each set of masses that
was used. Record your results in the table. (To get the correct force in newtons, you must use the
mass values in kilograms.)
NOTE: When using hanging weights to measure force, a unit for mass is often used as if it were a
unit of weight. Remember, there is a difference between weight and mass. That is: Weight = Mass x
(the Acceleration due to gravity).
Weight is a force that depends on mass and gravity. If the gravitational constant changes—on the
moon, for example—the weight changes as well, but the mass remains the same.
Calculations
À On a separate sheet of paper, construct a graph of Weight versus Spring Displacement with Spring
Displacement on the x-axis (see Figure 1.2). Draw the line that best fits your data points. The slope of
the graph is the spring constant for the spring used in the Spring Balance.
Measure the spring constant from your graph. Be sure to include the units (newtons/meter).
Spring Constant = _____________ (newtons/meter)
Questions
The linear relationship between force and displacement in springs is called Hooke’s Law. If Hooke’s
Law were not valid, could a spring still be used successfully to measure forces? If so, how?
In what way is Hooke’s Law a useful property when calibrating a spring for measuring forces?
Table 1.1
n
Mass (kg)
Weight (N)
1
2
3
4
5
6
7
17
Spring Displacement
(m)
18
EXPERIMENT 2: ADDING FORCES RESULTANTS AND
EQUILIBRANTS (PASCO)
EQUIPMENT NEEDED:
– Experiment Board – Spring Balance
– Degree Scale – Force Ring
– Pulleys (3) – Mass Hangers (3)
– Masses – String
Theory
In Figure 2.1, spaceships x and y are pulling on an asteroid with forces indicated by vectors Fx and
Fy. Since these forces are acting on the same point of the asteroid, they are called concurrent forces.
As with any vector quantity, each force is defined both by its direction, the direction of the arrow, and
by its magnitude, which is proportional to the length of the arrow. (The magnitude of the force is
independent of the length of the tow rope.)
The total force on the asteroid can be determined by adding vectors Fx and Fy. In the illustration,
theparallelogram method is used. The diagonal of the parallelogram defined by Fx and Fy is Fr, the
vector indicating the magnitude and direction of the total force acting on the asteroid. Fr is called
the resultant of Fx and Fy.
Another useful vector is Fe, the equilibrant of Fx and Fy. Fe is the force needed to exactly offset the
combined pull of the two ships. Fe has the same magnitude as Fr, but is in the opposite direction. As
19
you will see in the following experiment, the equilibrant provides a useful experimental method for
finding the resultant of two or more forces.
Setup
Set up the equipment as shown in Figure 2.2. The Mass Hanger and mass provide a gravitational
force of F = mg downward. However, since the Force Ring is not accelerated, the downward force
must be exactly balanced by an equal and opposite, or equilibrant, force. This equilibrant force, Fe, is
of course provided by the Spring Balance.
Procedure

What is the magnitude and direction of F, the gravitational force provided by the mass and
Mass Hanger (F = mg)?
F: Magnitude = _______________ .
Direction = ___________________ .

Use the Spring Balance and the Degree Plate to determine the magnitude and direction of Fe.
Fe: Magnitude = __________________ .
Direction = ___________________ .
Now use pulleys and hanging masses as shown in Figure 2.3 to set up the equipment so that two
known forces, F1 and F2, are pulling on the Force Ring. Use the Holding Pin to prevent the ring from
being accelerated. The Holding Pin provides a force, Fe, that is exactly opposite to the resultant of F1
and F2.
Adjust the Spring Balance to determine the magnitude of Fe. As shown, keep the Spring Balance
vertical and use a pulley to direct the force from the spring in the desired direction. Move the Spring
Balance toward or away from the pulley to vary the magnitude of the force. Adjust the pulley and
Spring Balance so that the Holding Pin is centered in the Force Ring.
NOTE: To minimize the effects of friction in the pulleys, tap as needed on the Experiment Board each
time you reposition any component. This will help the Force Ring come to its true equilibrium
position.
Record the magnitude in newtons of F1, F2, and Fe; the value of the hanging masses, M1, and M2
(include the mass of the mass hangers); and alsoq1, q2, and qe, the angle each vector makes with
respect to the zero-degree line on the degree scale.
F1:
M1 = ___________(kg) Magnitude = ______________(N) Angle = ____________
F2:
M2 = ___________ (kg) Magnitude = ______________ (N) Angle = ____________
Fe: Magnitude = ______________(N) Angle = ____________
Use the values you recorded above to construct F1, F2, and Fe on a separate sheet of paper. Choose
an appropriate scale (such as 2.0 cm/newton) and make the length of each vector proportional to the
magnitude of the force. Label each vector and indicate the magnitude of the force it represents.
On your diagram, use the parallelogram method to draw the resultant of F1 and F2. Label the
resultant Fr. Measure the length of Fr to determine the magnitude of the resultant force and record
this magnitude on your diagram.
20
Does the equilibrant force vector, Fe, exactly balance the resultant vector, Fr. If not, can you suggest
some possible sources of error in your measurements and constructions? Vary the magnitudes and
directions of F1 and F2 and repeat the experiment.
21
22
EXPERIMENT 3: RESOLVING FORCES—COMPONENTS (PASCO)
EQUIPMENT NEEDED:
– Experiment Board – Degree Scale
– Force Ring – Pulleys (3)
– Mass Hangers (3) – Masses
– String
Theory
In Experiment 2, you added concurrent forces vectorially to determine the magnitude and direction
of the combined force. In this experiment, you will do the opposite; you will find two forces which,
when added together, have the same effect as the original force. As you will see, any force vector in
the x-y plane can be expressed as the sum of a vector in the x direction and a vector in the y
direction.
Set Up.
As shown, determine a force vector, F, by hanging a mass from the Force Ring over a pulley. Use the
Holding Pin to hold the Force Ring in place. Set up the Spring Balance and a pulley so the string from
the balance runs horizontally from the bottom of the pulley to the Force Ring. Hang a second Mass
Hanger directly from the Force Ring. Now pull the Spring Balance toward or away from the pulley to
adjust the horizontal, or “xcomponent” of the force. Adjust the mass on the vertical Mass Hanger to
adjust the vertical or “y-component” of the force. Adjust the x and y components in this way until the
Holding Pin is centered in the Force Ring. (Notice that these x and y components are actually the x
and y components of the equilibrant of F, rather than of F itself.)
NOTE: The hanging masses allow the mass to be varied only in 10 gram increments. Using an
additional Mass Hanger as a mass allows adjustments in 5 gram increments. Paper clips are
convenient for more precise variation. Weigh a known number of clips with the Spring Balance to
determine the mass per clip.
Procedure
Record the magnitude and angle of F. Measure the angle as shown in Figure 3.1.
Magnitude =_________________ Angle = _______________ .
Record the magnitude of the x and y components of the equilibrant of F.
23
x-Component = ______________ y-Component = _____________ .
What are the magnitudes of Fx and Fy, the x and y components of F?
Fx = ______________ Fy =______________ .
Change the magnitude and direction of F and repeat the experiment.
Record the angle of F, and the magnitudes of F, Fx, and Fy.
F: Magnitude = ______________ Angle = _______________ .
Fx = _______________________ Fy = __________________
Why use components to specify vectors? One reason is that using components makes it easy to add
vectors mathematically. Figure 3.2 shows the x and y components of a vector of length F, at an angle
q with the x-axis. Since the components are at right angles to each other, the parallelogram used to
determine their resultant is a rectangle.
Using right triangle AOX, the components of F are easily calculated: the x-component equals F cos q;
the y-component equals F sin q. If you have many vectors to add, simply determine the x and y
components for each vector.
Add all the x-components together and add all the y-components together. The resulting values are
the x and y components for the resultant.
Set up the equipment as in the first part of this experiment, using a pulley and a hanging mass to
establish the magnitude and direction of a force vector. Be sure the x-axis of the Degree Plate is
horizontal
Record the magnitude and angle of the force vector, F, that you have constructed.
Magnitude =_________________ Angle = _______________ .
Calculate Fx and Fy, the magnitudes of the x and y components of
F (Fx = F cos q; Fy = F sin q).
Fx = _______________________ Fy = __________________
Now set up the Spring Balance and a hanging mass, as in the first part of this experiment (Figure 3.1).
Using the values you calculated in question 6, position the Spring Balance so it pulls the Force Ring
horizontally by an amount Fx. Adjust the hanging mass so it pulls the Force Ring vertically down by
an amount Fy.
Questions

Is the Force Ring at equilibrium in the center of the Degree Plate? Generally it is most useful to
find the components of a vector along two perpendicular axes, as you did above. However, it is not
necessary that the x and y axes be perpendicular. If time permits, try setting up the equipment to find
24
the components of a vector along nonperpendicular axes. (Use pulleys to redirect the component
forces to non-perpendicular directions.)

What difficulties do you encounter in trying to adjust the x and y components to resolve a
vector along non-perpendicular axes?
25
26
EXPERIMENT 4: TORQUE—PARALLEL FORCES (PASCO)
EQUIPMENT NEEDED:
– Experiment Board – Balance Beam
– Pivot – Mass Hangers (3)
– Masses – Tape
Theory
In Experiment 2, you found resultants and equilibrants for concurrent forces—forces that act upon
the same point. In the real world, however, forces are often not concurrent. In Figure 4.1, for example,
two spaceships are pulling on different points of an asteroid. Two questions might be asked: À Which
direction will the asteroid be accelerated in?
Will the asteroid rotate?
If both tow ropes were attached to point A, the resultant would be the force vector shown, Fr. In fact,
Fr does point in the direction in which the asteroid will be accelerated (this idea will be investigated
further in later experiments).
However, what of question 2. Will the asteroid rotate? In this experiment you will begin to investigate
the types of forces that cause rotation in physical bodies. In doing so, you will encounter a new
concept—torque.
27
Setup
Using a magic marker pen, draw a horizontal line on the Experiment Board. (The Inclined Plane can
be used as a level and a straightedge to ensure a truly horizontal line.) Then set up the equipment as
shown in Figure
4.2. Adjust the beam in the pivot retainer until the beam is perfectly balanced on the pivot. Use your
horizontal line as a reference.
NOTE: To prevent the pivot point from sliding, place a piece of thin tape against either edge of the
pivot retainer. Add additional small pieces of tape, if needed, to rebalance the beam.
Slide a plastic retainer with a hook onto each end of the beam, then hang a Mass Hanger from each
hook as shown in Figure 4.3. Position one Mass Hanger approximately half way between the pivot
point and the end of the beam. Slide the other Mass Hanger on the beam until the beam is perfectly
balanced.
Procedure
À Measure d1 and d2, the distances of each Mass Hanger from the pivot point (see Figure 4.3).
d1 = ___________________
d2 = ___________________ .
Add a 50-gram mass to each Mass Hanger. Á Is the beam still balanced? Add an additional 20-gram
mass to one Mass Hanger. Â Can you restore the balance of the beam by repositioning the hanger?
Place 75 grams of mass on one Mass Hanger (M1 in Figure 4.4) and position it approximately half
way between the pivot and the end of the beam, as shown.
Place various masses on the other Mass Hanger (M2), and slide it along the beam as needed to
rebalance the beam. At each balanced position, measure the mass (M) hanging from each Mass
Hanger and the distance (d) between the Mass Hanger and the pivot point, as shown in the
illustration. Take measurements for at least 5 different values of M2 and record your results in Table
4.1. Be sure to include the units of your measurements. Vary M1 and repeat your measurements.
Tablo 4.1
M1 (kg)
F1 (N)
d1
(m)
1 = (d1 x
F1)
M2 (kg)
F2 (N)
d2 (m)
2= (d2 x
F2)
NOTE: For accurate results, include the mass of the Mass Hangers (5 grams) and of the plastic
retainers and hooks (2.2 grams) when determining M 1 and M2.
Use the formula F = Mg, where g is the acceleration due to gravity, to determine the gravitational
forced produced by the hanging masses in each case. Then perform the calculations shown in the
table to determine t1 and t2; that is,
28
1 = F1 d1, and 2 = F2
d2. Record your calculated values for each balanced position of the beam.
The quantity 1 = F1 d1 is called the torque of the force
F1 about the pivot point of the balance beam.
Questions
1.
From your results, what mathematical relationship must hold between 1 and 2 in order for
the beam to be balanced? There is an additional force on the beam, besides F1 and F2. The pivot
pulls up on the beam—otherwise, of course, the beam would accelerate downward.
2.
What torque is produced about the pivot point of the balance beam by the upward pull of the
pivot? If you have time, try adding a third Mass Hanger with masses (M3) to the balance beam, on
the same side of the beam as M2.
3.
What relationship must hold between 1 , 2 , and 3 in order for the beam to be balanced?
29
30
EXPERIMENT 5: CENTER OF MASS (PASCO)
EQUIPMENT NEEDED:
– Experiment Board – Pivot
– Planar Mass – Balance Beam
– Mass Hanger (1) – 50-gram Mass
– String
Theory
Gravity is a universal force; every bit of matter in the universe is attracted to every other bit of matter.
So when the balance beam is suspended from a pivot point, every bit of matter in the beam is
attracted to every bit of matter in the Earth.
Fortunately for engineers and physics students, the sum of all these gravitational forces produces a
single resultant. This resultant acts as if it were pulling between the center of the Earth and the center
of mass of the balance beam. The magnitude of the force is the same as if all the matter of the Earth
were located at the center of the Earth, and all the matter of the balance beam were located at the
center of mass of the balance beam. In this experiment, you will use your understanding of torque to
understand and locate the center of mass of an object.
Setup
Hang the Balance Beam from the pivot as shown in Figure 6.1. As in Experiment 4, use the Inclined
Plane as a level and straightedge to draw a horizontal reference line. Adjust the position of the
Balance Beam in the pivot so that the beam balances horizontally.
Since the Balance Beam is not accelerated, the force at the pivot point must be the equilibrant of the
total gravitational force acting on the beam. Since the beam does not rotate, the gravitational force
and its equilibrant must be concurrent forces.
Experiment
À Why would the Balance Beam necessarily rotate if the resultant of the gravitational forces and the
force acting through the pivot were not concurrent forces? Think of the Balance Beam as a collection
of many small hanging masses. Each hanging mass is pulled down by gravity and therefore provides
a torque about the pivot point of the Balance Beam.
What is the relationship between the sum of the clockwise torques about the center of mass and the
sum of the counterclockwise torques about the center of mass? Explain.
31
On the basis of your answer to question 1, use a pencil to mark the center of mass of the balance
beam. Then attach a Mass Hanger to each end of the beam. Hang 50 grams from one hanger, and
100 grams from the other, as shown in Figure 6.2. Now slide the beam through the pivot retainer
until the beam and masses are balanced and the beam is horizontal. The pivot is now supporting the
beam at the center of mass of the combined system (i.e. balance beam plus hanging masses).
Calculate the torques, t1, t2, and t3, provided by the forces F1, F2, and F3 acting about the new pivot
point, as shown in the illustration. Be sure to indicate whether each torque is clockwise (cw) or
counterclockwise (ccw).
1 = ________________2 =_______________3 = _______________ .
Are the clockwise and counterclockwise torques balanced? Remove the 50 gram mass and Mass
Hanger. Reposition the beam in the pivot to relevel the beam. Recalculate the torques about the
pivot point. Are the torques balanced?
Hang the Planar Mass from the Holding Pin of the Degree Plate as shown in Figure 6.3. Since the
force of the Pin acting on the mass is equilibrant to the sum of the gravitational forces acting on the
mass, the line of the force exerted by the Pin must pass through the center of mass of the Planar
Mass. Hang a piece of string with a hanging mass from the Holding Pin. Tape a piece of paper to the
Planar Mass as shown. Mark the paper to indicate the line of the string across the Planar Mass. Now
hang the Planar Mass from a different point. Again, mark the line of the string. By finding the
intersection of the two lines, locate the center of mass of the Planar Mass. Hang the Planar Mass
from a third point.
Does the line of the string pass through the center of mass?
Would this method work for a three dimensional object? Why or why not?
32
33
EXPERIMENT 6: SLIDING FRICTION (PASCO)
EQUIPMENT NEEDED:
– Experiment Board – Inclined Plane
– Friction Block – Spring Balance
– Pulley (1) – Mass Hangers (2)
– Masses – String
Theory
In most physical systems, the effects of friction are not easily predicted, or even measured. The
interactions between objects that cause them to resist sliding against each other seem to be due in
part to microscopic irregularities of the surfaces, but also in part to interactions on a molecular level.
However, though the phenomena is not fully understood, there are some properties of friction that
hold for most materials under many different conditions. In this experiment you will investigate some
of the properties of sliding friction the force that resists the sliding motion of two objects when they
are already in motion.
Procedure
Use the Spring Scale to determine W, the magnitude of the weight of the Friction Block.
W = __________________ .
Set up the equipment as shown in Figure 9.1. Use the built-in plumb bob to ensure that the Inclined
Plane is level. Adjust the position of the pulley so that the string is level with the surface of the
Inclined Plane. Adjust the mass on the Mass Hanger until, when you give the Friction Block a small
push to start it moving, it continues to move along the Inclined Plane at a very slow, constant speed.
34
If the block stops, the hanging mass is too light; if it accelerates, the mass is too large. The weight of
the hanging mass that is just sufficient to provide a constant slow speed is Ff, the force of the sliding
friction of the Friction Block against the Inclined Plane.
Three variables can be varied while measuring Ff.
They are: Normal Force (W + Mg)—Place masses of weight W on top of the Friction Block to adjust
the normal force between the block and the Inclined Plane.
Contact Material—Using sides A and B of the Friction Block, wood is the material in contact with the
Inclined Plane. Using side C, only the two strips of teflon tape contact the
Inclined Plane.
Contact Area (A, B, C)—Adjust the area of contact between the Friction Block by having side A, B, or
C of the Friction Block in contact with the Inclined Plane. (NOTE: Using side C, the contact area is the
surface area of the two strips of teflon tape.)
Adjust the mass on top of the Friction Block to each of the values shown in Table 9.1. At each value
of M, adjust the hanging mass to determine the magnitude of Ff. Perform this measurement using
side A, B, and C of the Friction Block. For each measurement, calculate the ratio between the
magnitude of the sliding friction (Ff) and the magnitude of the normal force (W + Mg). This ratio is
called the coefficient of friction, m.
M(kg)
W+Mg
(N)
0
Ff = mg
A
=
B
C
A
B
C
NOTE: You will need to adjust the hanging mass in small increments. Paper clips are convenient for
this purpose. Weigh a large number of paper clips on the Spring Balance and divide by the number
of clips to determine the weight per clip.
Based on your measurements:
Questions
1.
Does the value of sliding friction between two objects depend on the normal force between
the two objects? If so, what is the relationship between normal force and sliding friction?
35
2.
Does the value of sliding friction between two objects depend on the area of contact between
the two objects?
3.
Does the value of sliding friction between two objects depend on the materials that are in
contact?
36
37
Experiment 7: Simple Harmonic Motion: Mass on a Spring
EQUIPMENT NEEDED:
– Experiment Board – Spring Balance
– Mass Hanger – Masses
– Stopwatch
Theory
Figure 10.1 shows a mass hanging from a spring. At rest, the mass hangs in a position such that the
spring force just balances the gravitational force on the mass. When the mass is below this point, the
spring pulls it back up. When the mass is above this point, gravity pulls it back down. The net force
on the mass is therefore a restoring force, because it always acts to accelerate the mass back toward
its equilibrium position.
In Experiment 1 you investigated Hook’s Law, which states that the force exerted by a spring is
proportional to the distance beyond its normal length to which it is stretched (this also holds true for
the compression of a spring).
This idea is stated more succinctly in the mathematical relationship: F = -kx;
where F is the force exerted by the spring, x is the displacement of the end of the spring from its
equilibrium position, and k is the constant of proportionality, called the spring constant (see
Experiment
1). Whenever an object is acted on by a restoring force that is proportional to the displacement of
the object from its equilibrium position, the resulting motion is called Simple Harmonic Motion.
When the simple harmonic motion of a mass (M) on a spring is analyzed mathematically using
Newton’s Second Law (the analysis requires calculus, so it will not be
shown here), the period of the motion (T) is found to be:
38
In this experiment, you will experimentally test the validity of this equation.
Experiment
À Measure k, the spring constant for the spring in the Spring Balance (see Experiment 1).
k = _______________(newtons/meter).
Set up the equipment as shown in Figure 10.1, with 120 grams on the Mass Hanger (125 grams total
mass, including the hanger). Be sure that the Spring Balance is vertical so that the rod hangs straight
down through the hole in the bottom of the balance. This is important to minimize friction against
the side as the mass oscillates.
Now pull the rod down a few centimeters. Steady the mass, then let go of the rod. Practice until you
can release the rod smoothly, so that the mass and the rod oscillate up and down and there is no
rubbing of the rod against the side of the hole.
Set the mass oscillating. Measure the time it takes for at least 10 full oscillations to occur. (Measure
the time for as many oscillations as can be conveniently counted before the amplitude of the
oscillations becomes too small.) Record the mass, the time, and the number of oscillations counted in
Table 10.1. Divide the total time by the number of oscillations observed to determine the period of
the oscillations. (The period is the time required for one complete oscillation). Record this value in
the table.
Repeat the measurement 5 times. Calculate the period for each measurement. Then add your five
period measurements together and divide by 5 to determine the average period over all five
measurements.
Use the equation given at the beginning of this Experiment to calculate a theoretical value for the
period using each mass value. (Since the spring constant is in units of newtons/m, your mass values
used in the equation must be in kg.) Enter this value in the table.
39
1.
Does your theoretical value for the period accurately predict your experimental value? Repeat
the experiment using masses of 175 and 225 grams (including the mass of the Mass Hanger).
2.
Does the equation for the period of an oscillating mass provide a good mathematical model
for the physical reality?
40
41
Experiment 8: Simple Harmonic Motion—the Pendulum
EQUIPMENT NEEDED:
– Experiment Board – Pivot
– Mass Hanger – Masses
– String
Theory
Simple harmonic motion is not restricted to masses on springs. In fact, it is one of the most common
and important types of motion found in nature. From the vibrations of atoms to the vibrations of
airplane wings, simple harmonic motion plays an important role in many physical phenomena. A
swinging pendulum, for example, exhibits behavior very similar to that of a mass on a spring. By
making some comparisons between these two phenomena, some predictions can be made about the
period of oscillations for a pendulum.
Figure 11.1 shows a pendulum with the string and mass at an angle q from the vertical position. Two
forces act on the mass; the force of the string and the force of gravity. The gravitational force, F =
mg, can be resolved into two components; Fx and Fy. Fy just balances the force of the string and
therefore does not accelerate the mass. Fx is in the direction of motion of the mass, and therefore
does accelerate and decelerate the mass.
Using the two congruent triangles in the diagram, it can be seen that Fx = mg sinq, and that the
displacement of the mass from its equilibrium position is an arc whose distance, x, is approximately L
tanq. If the angle q is reasonably small, then it is very nearly true that sinq = tanq. Therefore, for
small swings of the pendulum, it is approximately true that Fx = mgtanq = mgx/L. (Since Fx is a
restoring force, the equation could be stated more accurately as Fx = -mgx/L.) Comparing this
equation with the equation for a mass on a spring (F = -kx), it can be seen that the quantity mg/L
plays the same mathematical role as the spring constant. On the basis of this similarity, you might
speculate that the period of motion for a pendulum is just:
T  2
L
g
g=
4 2 L
T2
42
where m is the mass, g is the acceleration due to gravity, and L is distance from the pivot point to the
center of mass of the hanging mass. In this experiment, you will test the validity of this equation.
M (kg)
L (m)
Total t (s)
T, Period
(s)
M1
M2
M3
L (m)
t (s)
Period (s)
(10 T)
T =t/10
(g’)
1
2
3
Experiment
Hang a Mass Hanger from the pivot as shown in Figure 11.1. Set the mass swinging, but keep the
angle of the swing reasonably small. Measure the time it takes for at least 30 full oscillations to occur.
In Table 11.1, record the mass, the distance L, the time, and the number of oscillations counted.
Divide the total time by the number of oscillations observed to determine the period of the
oscillations. (The period is the time required for one complete oscillation). Record this value in the
table. Repeat the measurement 5 times. Calculate the period for each measurement. Then add your
five period measurements together and divide by 5 to determine the average period over all five
measurements Repeat your measurements using a different mass.
Use the equation given at the beginning of this Experiment to calculate a theoretical value for the
period in each case (g = 9.8 N/m; be sure to express L in meters when you plug into the equation).
Enter this value in the table.
Does the period of the oscillations depend on the mass of the pendulum?
43
Does your theoretical value for the period accurately predict your experimental value? Repeat the
experiment using a significantly different string length.
Does the equation for the period of an oscillating mass provide a good mathematical model for the
physical reality?
44
45
Experiment 9: Ballistic Pendulum
EQUIPMENT
INCLUDED
1
Rotary Motion Sensor
PS-2120
1
Mini Launcher
ME-6825A
2
Photogate Heads
ME-9498A
1
Photogate Mounting Bracket
ME-6821A
1
Digital Adapter
PS-2159
1
Mini Launcher Ballistic Pendulum
ME-6829
1
Large Table Clamp
ME-9472
1
Steel Rod
ME-8736
NOT INCLUDED, BUT REQUIRED
1
PASPORT Interface
1
DataStudio Software
CI-6870
INTRODUCTION
A ballistic pendulum is used to determine the muzzle velocity of a ball shot out of a Projectile
Launcher. The laws of conservation of momentum and conservation of energy are used to derive the
equation for the muzzle velocity.
THEORY
The ballistic pendulum has historically been used to measure the launch velocity of a high speed
projectile. In this experiment, a projectile launcher fires a steel ball (of mass mball) at a launch velocity,
vo. The ball is caught by a pendulum of mass mpend. After the momentum of the ball is transferred to
the catcher-ball system, the pendulum swings freely upwards, raising the center of mass of the
system by a distance h. The pendulum rod is hollow to keep its mass low, and most of the mass is
concentrated at the end so that the entire system approximates a simple pendulum. During the
collision of the ball with the catcher, the total momentum of the system is conserved. Thus the
momentum of the ball just before the collision is equal to the momentum of the ball-catcher system
immediately after the collision:
46
mballvo = Mv
(1)
where v is the speed of the catcher-ball system just after the collision, and
M = mball + mpend
(2)
During the collision, some of the ball's initial kinetic energy is converted into thermal energy. But
after the collision, as the pendulum swings freely upwards, we can assume that energy is conserved
and that all of the kinetic energy of the catcher-ball system is converted into the increase in
gravitational potential energy.
1
2
Mv2  Mgh
(3)
2
where g =9.8 m/s , and the distance h is the vertical rise of the center of mass of the pendulum-ball
system.
47
Combining equations 2.1 through 2.3 (eliminating v) yields
vo 
mball  mpend
mball
(4)
2gh
SETUP
1. Attach the ballast mass to the bottom of the catcher.
2. Set up the mini launcher, bracket, table clamp, mounting rod, and Rotary Motion Sensor as
shown in Figure 1. The exact position of the Rotary Motion Sensor is not important yet. Note that the
side of the Rotary Motion Sensor without the model number on the label is facing you. (If the Rotary
Motion Sensor is mounted the other way, it will measure negative
displacement.)
3.
Slide the three-step pulley onto the Rotary Motion Sensor
shaft with the largest pulley facing out.
4.
Attach the pendulum to the Rotary Motion Sensor using
the hole near the end of the pendulum. See Figure 2.
__
_________
Figure 1: Launcher and Rotary Motion
Sensor mounted on rod
Figure 2: Mounting Pendulum on Rotary Motion Sensor
5.
Adjust the position of the Rotary Motion Sensor so the
pendulum is aligned with the launcher as shown in Figure 3.
Figure 3: Aligning Pendulum with Launcher
6.
Connect the Rotary Motion Sensor to the PASPORT interface.
48
7.
Open the DataStudio file called "Ballistic Pend1.ds".
PROCEDURE
1.
To load the launcher, swing the pendulum out of the way, place the ball in the end of the
barrel and, using the pushrod included with the launcher, push the ball down the barrel until the
trigger catches in the third position.
2.
Return pendulum to its normal hanging position.
3.
Start data collection.
4.
Launch the ball so that it is caught in pendulum.
5.
After the pendulum has swung out and back, stop data collection.
6.
If the statistics are not already selected on the graph, turn on the statistics and select
Maximum. Record the maximum angular displacement in the table.
7.
Repeat steps 1 through 6 several times.
8.
Look at the table to find the average maximum displacement, θmax.
Find the Mass and Center of Mass
1.
Fire the ball one more time (without recording data). Stop the pendulum near the top of its
swing so it does not swing back and hit the launcher (this will prevent the ball from falling out or
shifting).
2. Remove the pendulum from the Rotary Motion Sensor.
3.
Remove the screw from the pendulum shaft.
4.
With the ball still in the catcher, place the
pendulum at the edge of a table with the pendulum
shaft perpendicular to the edge and the counterweight
hanging over the edge. Push the pendulum out until it
just barely balances on the edge of the table. The
balance point is the center of mass. (See Figure 4)
Figure 4: Balancing the Pendulum
5.
Measure the distance, r, from the center of rotation (where the pendulum was attached to the
Rotary Motion Sensor) to the center of mass.
6.
Remove ball from the catcher.
7.
Measure the mass of the pendulum (without the ball).
8.
Measure the mass of the ball.
49
Figure 5: Finding Height
ANALYSIS
1.
Use your value of θmax, the distance r, and Equation 5 to calculate the maximum height (h) that
the center of mass rises as the pendulum swings up (see Figure 5).
h = r (1 - cos (θmax))
2.
(5)
Use your value of h and Equation 4 to calculate the launch velocity of the ball.
Verifying the Initial Speed of the Ball Using Photogates
1.
Remove the Rotary Motion Sensor plug from the interface. The pendulum should be removed
from the Rotary Motion Sensor so it does not hang in front of the launcher.
2.
Open the DataStudio file called "Ballistic Pend2".
3.
Attach two photogates to the photogate bracket. To mount the bracket to the launcher, slide
the bracket into bottom T-slot of the barrel. Slide the bracket back until the photogate is as close to
the barrel as possible without blocking the beam. Tighten the thumb screw to secure the bracket in
place.
4.
Plug the Digital Adapter into the interface. Plug the photogate which is closest to the projectile
launcher into Port #1 of the Digital Adapter. Plug the second photogate into Port #2 of the Digital
Adapter.
5.
Load the ball and cock the launcher to the third position before starting to record. Start
recording and shoot the ball. The software learns the order of the photogates from this first shot so
you can load and cock the launcher for future shots without registering erroneous data. Repeat 5
times for the same launch speed, stop recording.
6.
From the table, record the average speed of the ball. Also choose Standard Deviation and
record this value as the uncertainty in the initial speed.
7.
Compare this initial speed with the result from the ballistic pendulum part of the experiment
by calculating the percent difference.
50
51
QUESTION
The theory for this experiment ignores the rotational inertia of the pendulum. Because the pendulum
is not really a simple pendulum (a point mass on a massless rod), a systematic error is introduced.
Does this simplistic analysis tend to give a launch velocity that is too high or too low?
52
APPENDIX: XPLORER GLX CONFIGURATIONS
If you are using an Xplorer GLX in stand-alone mode (without DataStudio), the following instructions
explain how to configure the Xplorer GLX files.
Measuring the Pendulum Swing
1.
Plug the Rotary Motion Sensor into the GLX.
2.
Go to SENSORS and change the Sample Rate to 100 Hz.
3.
In the Graph window, select Angular Position vs. time. Press the Check button on the GLX to
edit the graph. Navigate to the (rad) units on the vertical axis using the arrow buttons. Change the
units to (deg).
4.
Open the Table window (F2) and choose Edit (F3) and then New Data Column (1). Press the
check button to edit: Rename the column Max Angle and choose the Data Properties. Edit the
Measurement Unit to read "deg" and press OK (F1) to accept the changes. On the Statistics menu
(F1), select Average (3) and Standard Deviation (4).
5.
Open the Data Files window on the main menu and name the file "ballistic pend1" and save it.
Return to the Graph window. The GLX is now ready to record data.
Measuring the Muzzle Speed of the Ball Using Photogates
1.
Plug the Digital Adapter into the GLX. Plug the photogate which is closest to the projectile
launcher into Port #1 of the Digital Adapter. Select "Time of Flight" from the timer list on the GLX.
Choose the Time of Flight to be Visible and the Initial Velocity to be Not Visible.
2.
Plug the second photogate into Port #2 of the Digital Adapter.
3.
Open the Calculator window (F3) and make the following calculation:
speed = 0.1/[Time Of Flight(s)]
This will calculate the initial speed of the ball by dividing the separation of the photogates
(0.1m) by the Time of Flight between the two photogates. This calculation is used instead of the
standard Initial Velocity measurement because it allows multiple shots to be fired in one run.
4.
Open the Table window (F2) and choose speed in the first column. Press the check button to
select "speed" and choose the Data Properties. Edit the Measurement Unit to read m/s and press OK
(F1) to accept the changes. On the Statistics menu (F1), select Average (3) and Standard Deviation (4).
5.
Go to the Data Files window and save the file as "ballistic pend2.glx".
6.
Return to the Table window. The GLX is now ready to record data.
53
54
Experiment 10: Conservation of Angular Momentum Using a Point Mass
(PASCO)
EQUIPMENT REQUIRED
- Smart Pulley Timer Program
- Rotational Inertia Accessory (ME-8953)
- Rotating Platform (ME-8951)
- Smart Pulley
- balance
Purpose
A mass rotating in a circle is pulled in to a smaller radius and the new angular speed is predicted
using conservation of angular momentum.
Theory
Angular momentum is conserved when the radius of the circle is changed.
where Ii
speed is given by:
i is the initial angular speed. So the final rotational
where  is the angular acceleration which is equal to a/r and  is the torque caused by the weight
hanging from the thread which is wrapped around the base of the apparatus.
where r is the radius of the cylinder about which the thread is wound and T is the tension in the
thread when the apparatus is rotating.
Applying Newton’s Second Law for the hanging mass, m, gives (See Figure 4.1)
Solving for the tension in the thread gives:
Once the linear acceleration of the mass (m) is determined, the torque and the angular acceleration
can be obtained for the calculation of the rotational inertia
55
56
Experiment 11: Rotational Inertia of Disk and Ring (PASCO)
EQUIPMENT REQUIRED
- Precision Timer Program - mass and hanger set
- Rotational Inertia Accessory (ME-9341) - paper clips (for masses < 1 g)
- Smart Pulley - triple beam balance
- calipers
Purpose
The purpose of this experiment is to find the rotational inertia of a ring and a disk experimentally and
to verify that these values correspond to the calculated theoretical values.
Theory
Theoretically, the rotational inertia, I, of a ring about its center of mass is given by:
where M is the mass of the ring, R1 is the inner radius of the ring, and R2 is the outer radius of the
ring. See Figure 5.1.
The rotational inertia of a disk about its center of mass is given by:
where M is the mass of the disk and R is the radius of the disk. The rotational inertia of a disk about
its diameter is given by:
57
To find the rotational inertia experimentally, a known torque is applied to the object and the
resulting angular acceleration is measured. Since  = I
where  is the angular acceleration which is equal to a/r and  is the torque caused by the weight
hanging from the thread which is wrapped around the base of the apparatus.
= rT
where r is the radius of the cylinder about which the thread is wound and T is the tension in the
thread when the apparatus is rotating.
Applying Newton’s Second Law for the hanging mass, m, gives (See Figure 5.3)
Solving for the tension in the thread gives:
T=mg–a
Once the linear acceleration of the mass (m) is determined, the torque and the angular acceleration
can be obtained for the calculation of the rotational inertia
Setup
Remove the track from the Rotating Platform and place the disk directly on the center shaft as shown
in Figure 5.4. The side of the disk that has the indentation for the ring should be up.
Place the ring on the disk, seating it in this indentation.
Mount the Smart Pulley to the base and connect it to a computer.
Run the Smart Pulley Timer program.
58
Procedure
Measurements for the Theoretical Rotational Inertia
Weigh the ring and disk to find their masses and record these masses in Table 5.1.
Measure the inside and outside diameters of the ring and calculate the radii R1 and R2. Record in
Table 5.1.
Measure the diameter of the disk and calculate the radius R and record it in Table 5.1.
Measurements for the Experimental Method
Accounting For Friction
Because the theory used to find the rotational inertia experimentally does not include friction, it will
be compensated for in this experiment by finding out how much mass over the pulley it takes to
overcome kinetic friction and allow the mass to drop at a constant speed. Then this “friction mass”
will be subtracted from the mass used to accelerate the ring.
To find the mass required to overcome kinetic friction run “Display Velocity”: <V>-Display
Velocity <RETURN>; <A>-Smart Pulley/Linear String <RETURN>; <N>-Normal Display
<RETURN>.
59
Put just enough mass hanging over the pulley so that the velocity is constant to three significant
figures. Then press <RETURN> to stop displaying the velocity. Record the friction mass in
Table 5.2.
Finding the Acceleration of Ring and Disk
To find the acceleration, put about 50 g over the pulley and run “Motion Timer”: <M>-Motion
Timer <RETURN> Wind the thread up and let the mass fall from the table to the floor, hitting
<RETURN> just before the mass hits the floor.
Wait for the computer to calculate the times and then press <RETURN>. To find the acceleration,
graph velocity versus time: <G>-Graph Data <RETURN>; <A>-Smart Pulley/Linear String <RETURN;>
<V>-Velocity vs. Time <R>-Linear Regression <SPACEBAR> (toggles it
on) <S>-Statistics <SPACEBAR> <RETURN>.
The graph will now be plotted and the slope = m will be displayed at the top of the graph. This
slope is the acceleration. Record in Table 5.2.
Push <RETURN> and <X> twice to return to the Main Menu.
Measure the Radius
Using calipers, measure the diameter of the cylinder about which the thread is wrapped and
calculate the radius. Record in Table 5.2.
Finding the Acceleration of the Disk Alone
Since in Finding the Acceleration of Ring and Disk the disk is rotating as well as the ring, it is
necessary to determine the acceleration, and the rotational inertia, of the disk by itself so this
rotational inertia can be subtracted from the total, leaving only the rotational inertia of the ring.
To do this, take the ring off the rotational apparatus and repeat Finding the Acceleration of
Ring and Disk for the disk alone.
NOTE: that it will take less “friction mass” to overcome the new kinetic friction and it is only
necessary to put about 30 g over the pulley in Finding the Acceleration of Ring and Disk.
60
Disk Rotating on an Axis Through Its Diameter
Remove the disk from the shaft and rotate it up on its side. Mount the disk vertically by inserting the
shaft in one of the two “D”-shaped holes on the edge of the disk. See Figure 5.5.
WARNING! Never mount the disk vertically using the adapter on the track. The adapter is too short
for this purpose and the disk might fall over while being rotated.
Repeat steps Measure the Radius and Finding the Acceleration of the Disk Alone to determine
the rotational inertia of the disk about its diameter. Record the data in Table 5.2.
Calculations
1.
Record the results of the following calculations in Table 5.3.
2.
Subtract the “friction mass” from the hanging mass used to accelerate the apparatus to
determine
3.
the mass, m, to be used in the equations.
4.
Calculate the experimental value of the rotational inertia of the ring and disk together.
5.
Calculate the experimental value of the rotational inertia of the disk alone.
6.
Subtract the rotational inertia of the disk from the total rotational inertia of the ring and disk.
This will be the rotational inertia of the ring alone.
7.
Calculate the experimental value of the rotational inertia of the disk about its diameter.
8.
Calculate the theoretical value of the rotational inertia of the ring.
9.
Calculate the theoretical value of the rotational inertia of the disk about its center of mass and
about its diameter.
10.
Use a percent difference to compare the experimental values to the theoretical values.
61
62
63
Experiment 12: Conservation of Angular Momentum (PASCO)
EQUIPMENT REQUIRED
- Smart Pulley Timer Program - balance
- Rotational Inertia Accessory (ME-8953)
- Rotating Platform (ME-8951)
- Smart Pulley Photogate
Purpose
A non-rotating ring is dropped onto a rotating disk and the final angular speed of the system is
compared with the value predicted using conservation of angular momentum.
Theory
When the ring is dropped onto the rotating disk, there is no net torque on the system since the
torque on the ring is equal and opposite to the torque on the disk. Therefore, there is no change in
angular momentum. Angular momentum is conserved.
where Ii is the initial
i is the initial angular speed. The initial rotational
inertia is that of a disk
and the final rotational inertia of the combined disk and ring is
2
2
2
If = (1/2)M1R + (1/2)M2(r1 +r2 )
So the final rotational speed is given by
Setup
Level the apparatus using the square mass on the track
64
Assemble the Rotational Inertia Accessory as shown in Figure 7.1. The side of the disk with the
indentation for the ring should be up.
Mount the Smart Pulley photogate on the black rod on the base and position it so it straddles the
holes in the pulley on the center rotating shaft.
Run the Smart Pulley Timer program.
Procedure
Select <M>-Motion Timer <RETURN>.
Hold the ring just above the center of the disk. Give the disk a spin using your hand. After about 25
data points have been taken, drop the ring onto the spinning disk See Figure 7.2.
Continue to take data after the collision and then push <RETURN> to stop the timing.
When the computer finishes calculating the times, graph the rotational speed versus time. <A>Data Analysis Options <RETURN> <G>-Graph Data <RETURN> <E>-Rotational Apparatus
<RETURN> <V>-Velocity vs. Time <RETURN>
After viewing the graph, press <RETURN> and choose <T> to see the table of the angular
velocities. Determine the angular velocity immediately before and immediately after the collision.
Record these values in Table 7.1.
Weigh the disk and ring and measure the radii. Record these values in Table 7.1.
Analysis
Calculate the expected (theoretical) value for the final angular velocity and record this value in Table
7.1.
Calculate the percent difference between the experimental and the theoretical values of the final
angular velocity and record in Table 7.1.
Questions
Does the experimental result for the angular speed agree with the theory?
What percentage of the rotational kinetic energy lost during the collision? Calculate this and
record the results in Table 7.1.
65
66
67
Experiment 13: Projectile Motion
Equipment Needed
Item Item
Projectile Launcher and plastic ball Plumb bob and string
Meter stick Carbon paper
White paper Sticky tape
Purpose
The purpose of this experiment is to predict and verify the range of a ball launched at an angle. The
initial speed of the ball is determined by shooting it horizontally and measuring the range of the ball
and the height of the Launcher.
Theory
To predict where a ball will land on the floor when it is shot from the Launcher at some angle above
the horizontal, it is first necessary to determine the initial speed (muzzle velocity) of the ball. That can
be determined by shooting the ball horizontally from the Launcher and measuring the vertical and
horizontal distances that the ball travels.
The initial speed can be ued to calculate where the ball will land when the ball is shot at an angle
above the horizontal.
Initial Horizontal Speed
For a ball shot horizontally with an initial speed, v0, the horizontal distance travelled by the ball is
given by
x = v0t,
where t is the time the ball is in the air. (Neglect air friction.)
The vertical distance of the ball is the distance it drops in time t given by .
The initial speed can by determined by measuring x and y. The time of flight, t, of the ball can be
found using and the initial horizontal speed can be found using .
Initial Speed at an Angle
To predict the horizontal range, x, of a ball shot with an initial speed, v0, at an angle, , above the
horizontal, first predict the time of flight from the equation for the vertical motion:
where y0 is the initial height of the ball and y is the position of the ball when it hits the floor. In other
words, solve the quadratic equation for t and then use x = v0 cost where v0 cos is the horizontal
component of the initial speed.
68
Setup
1. Clamp the Projectile Launcher to a sturdy table or other horizontal surface. Mount the Launcher
near one end of the table.
2. Adjust the angle of the Projectile Launcher to zero degrees so the ball will by launched
horizontally.
Item Item
Projectile Launcher and plastic ball Plumb bob and string Meter stick Carbon paper White paper
Sticky
Part A: Determining the Initial Horizontal Speed of the Ball
1. Put a plastic ball in the Projectile Launcher and use the ramrod to cock it at the long range
position. Fire one shot to locate where the ball hits the floor. At that point, tape a piece of white paer
to the floor. Place a piece of carbon paper (carbon-side down) on top of the white paper and tape it
in place. • When the ball hits the carbon paper on the floor, it will leave a mark on the white paper.
2. Fire ten shots.
3. Measure the vertical distance from the bottom of the ball as it leaves the barrel to the floor.
Record this distance in the Data Table.
The “Launch Position of Ball” in the barrel is marked on the label on the side of the Launcher.
4. Use a plumb bob to find the point on the floor that is directly beneath the release point on the
barrel. Measure the horizontal distance along the floor from the release point to the leading edge of
the piece of white paper. Record the distance in the Data Table.
5. Carefully remove the carbon paper and measure from the leading edge of the White paper to each
of the ten dots. Record these distances in the Data Table and find the average. Calculate and record
the total horizontal distance (distance to paper plus average distance from edge of paper to dots).
6. Using the vertical distance, y, and the total horizontal distance, x, calculate the time of flight, t, and
the initial horizontal speed of the ball, v0. Record the time and speed in the Data Table.
Part B: Predicting the Range of a Ball Shot at an Angle
1. Adjust the angle of the Projectile Launcher to an angle between 30 and 60 degrees. Record this
angle in the second Data Table.
2. Using the initial speed and vertical distance from the first part of this experiment, calculate the
new time of flight and the new horizontal distance based on the assumption that the ball is shot at
the new angle you have just selected. Record the predictions in the second Data Table.
3. Draw a line across the middle of a white piece of paper and tape the paper on the floor so that the
line on the paper is at the predicted horizontal distance from the Projectile Launcher. Cover the white
paper with carbon paper (carbon side down) and tape the carbon paper in place.
4. Shoot the ball ten times.
5. Carefully remove the carbon paper. Measure the distances to the ten dots and record the
distances in the second Data Table.
69
Data Table A: Determine the Initial Speed
Vertical distance = _____________ Horizontal distance to edge of paper = _________________
Calculated time of flight = ________________ Initial speed = _____________
Data Table B: Predict the Range
Angle above horizontal = _____________ Horizontal distance to edge of paper = _________________
Calculated time of flight = ________________ Predicted range = _____________
70
71
72
Experiment 14: Projectile Motion Using Photogates (PASCO)
Equipment Needed
Item Item
Projectile Launcher and plastic ball Plumb bob and string
Photogate Head ME-9498A (2) Photogate Mounting Bracket ME-6821A
PASCO Interface or Timer* PASCO Data acquisition software*
Meter stick Carbon paper
White paper Sticky tape
Purpose
The purpose of this experiment is to predict and verify the range of a ball launched at an angle.
Photogates are used to determine the initial speed of the ball.
Theory
To predict where a ball will land on the floor when it is shot from the Launcher at some angle above
the horizontal, it is first necessary to determine the initial speed (muzzle velocity) of the ball. The
speed can be determined by shooting the ball and measuring a time using photogates. To predict
the range, x, of the ball when it is shot with an initial speed at an angle, , above the horizontal, first
predict the time of flight using the equation for the vertical motion:
where y0 is the initial height of the ball and y is the position of the ball when it hits the floor. Solve
the quadratic equation to find the time, t. Use x = (v0 cos  t) to predict the range.
Setup
1. Clamp the Projectile Launcher to a sturdy table or other horizontal surface. Mount the Launcher
near one end of the table.
2. Adjust the angle of the Projectile Launcher to an angle between 30 and 60 degrees and record the
angle.
3. Attach the photogate mounting bracket to the Launcher and attach two photogates to the
bracket. Check that the distance between the photogates is 0.10 m (10 cm).
4. Plug the photogates into an interface or a timer.
Procedure
Part A: Determining the Initial Speed of the Ball
1. Put a plastic ball in the Projectile Launcher and use the ramrod to cock it at the long range
position.
2. Setup the data acquisition software or the timer to measure the time between the ball blocking
the two photogates.
3. Shoot the ball three times and calculate the average of these times. Record the data in the Data
Table.
4. Calculate the initial speed of the ball based on the 0.10 m distance between the photogates.
Record the value.
73
Part B: Predicting the Range of a Ball Shot at an Angle
1. Keep the angle of the Projectile Launcher at the original angle above horizontal.
2. Measure the vertical distance from the bottom of the ball as it leaves the barrel to the
floor. Record this distance in the second Data Table.
• The “Launch Position of Ball” in the barrel is marked on the label on the side of the
Launcher.
3. Use the vertical distance, the angle, and the initial speed to calculate the time of flight.
Record the value.
4. Use the time of flight, t, angle, , and initial speed, v0, to predict the horizontal distance (range, x
= (v0 cos  t). Record the predicted range.
5. Draw a line across the middle of a white piece of paper and tape the paper on the floor so the line
is at the predicted horizontal distance. Cover the white paper with carbon paper and tape the carbon
paper in place.
6. Use a plumb bob to find the point on the floor that is directly beneath the release point on the
barrel. Measure the horizontal distance along the floor from the release point to the leading edge of
the piece of white paper. Record the distance in the Data Table.
7. Shoot the ball ten times.
8. Carefully remove the carbon paper and measure from the leading edge of the white paper to each
of the ten dots. Record these distances in the Data Table and find the average. Calculate and record
the total horizontal distance (distance to paper plus average distance from edge of paper to dots).
Angle above horizontal = ______________ Horizontal distance to edge of paper = _______________
Calculated time of flight = _________________ Predicted range = ________________
74
75
Experiment 15: Polarization of Light
EQUIPMENT INCLUDED
1
Polarization Analyzer
OS-8533A
1
Basic Optics Bench (60 cm)
OS-8541
1
Aperture Bracket
OS-8534
1
Red Diode Laser
OS-8525A
1
Light Sensor
CI-6504A
1
1
1
Rotary Motion Sensor
NOT INCLUDED, BUT REQUIRED:
ScienceWorkshop 500 Interface
DataStudio Software
CI-6538
CI-6400
CI-6870
INTRODUCTION
Laser light (peak wavelength = 650 nm) is passed through two polarizers. As the second polarizer
(the analyzer) is rotated by hand, the relative light intensity is recorded as a function of the angle
between the axes of polarization of the two polarizers. The angle is obtained using a Rotary Motion
Sensor that is coupled to the polarizer with a drive belt. The plot of light intensity versus angle can
be fitted to the square of the cosine of the angle.
THEORY
A polarizer only allows light which is vibrating in a particular plane to pass through it. This plane
forms the "axis" of polarization. Unpolarized light vibrates in all planes perpendicular to the direction
of propagation. If unpolarized light is incident upon an "ideal" polarizer, only half of the light
intensity will be transmitted through the polarizer.
Figure 1: Light Transmitted through Two Polarizers
Picture from: http://micro.magnet.fsu.edu/optics/lightandcolor/polarization.html
76
The transmitted light is polarized in one plane. If this polarized light is incident upon a second
polarizer, the axis of which is oriented such that it is perpendicular to the plane of polarization of the
incident light, no light will be transmitted through the second polarizer. See Fig.1.
However, if the second polarizer is oriented at an angle not perpendicular to the axis of the first
polarizer, there will be some component of the electric field of the polarized light that lies in the
same direction as the axis of the second polarizer, and thus some light will be transmitted through
the second polarizer.
Polarizer #1
Polarizer #2
Eo

E

E
Unpolarized
E-field
Figure 2: Component of the Electric Field
If the polarized electric field is called E0 after it passes through the first polarizer, the component, E,
after the field passes through the second polarizer which is at an angle  with respect to the first
polarizer is E0
tric field,
the light intensity transmitted through the second filter is given by
I  I o cos 2 
(1)
77
THEORY FOR 3 POLARIZERS
Figure 3: Electric Field Transmitted through Three Polarizers
Unpolarized light passes through 3 polarizers (see Fig.3). The first and last polarizers are oriented at
o
90


   from the second
2

the first polarizer. Therefore, the third polarizer is rotated an angle 
polarizer. The intensity after passing through the first polarizer is I1 and the intensity after passing
through the second polarizer, I2 , is given by
I 2  I1 cos 2  .
The intensity after the third polarizer, I3 , is given by


I 3  I 2 cos 2      I1 cos 2 
2


 cos  2    
(2)
2



cos     cos cos   sin  sin  , gives
1




cos     cos cos   sin sin   sin  . Therefore, since cos  sin   sin 2  ,
2
2
2
2

Using the trigonometric identity,
I3 
I1 2
sin (2 )
4
(3)
Because the data acquisition begins where the transmitted intensity through Polarizer 3 is a
  45o  
o
from
(4)
78
SET UP
Figure 4: Equipment Separated to Show Components
1.
Mount the aperture disk on the aperture bracket holder.
2.
Mount the Light Sensor on the Aperture Bracket and plug the Light Sensor into the interface
(See Fig.5).
Figure 5: ScienceWorkshop 500 Interface with Sensors
3.
Rotate the aperture disk so the translucent mask covers the opening to the light sensor (see
Fig.6).
Figure 6: Use Translucent Mask
4.
Mount the Rotary Motion Sensor on the polarizer bracket. Connect the large pulley on the
Rotary Motion Sensor to the polarizer pulley with the plastic belt (see Fig.7).
5.
Plug the Rotary Motion Sensor into the interface (see Fig 5).
79
6.
Figure 7: Rotary Motion Sensor Connected to Polarizer with Belt
Place all the components on the Optics Track as shown in Fig.8.
Figure 8: Setup with Components in Position for Experiment
SOFTWARE SET UP
Start DataStudio and open the file called "Polarization".
PROCEDURE FOR 2 POLARIZERS
In the first two procedure steps, the polarizers are aligned to allow the maximum amount of light
through.
1.
Since the laser light is already polarized, the first polarizer must be aligned with the laser's axis
of polarization. First remove the holder with the polarizer and Rotary Motion Sensor from the track.
Slide all the components on the track close together and dim the room lights. Click START and then
rotate the polarizer that does not have the Rotary Motion Sensor until the light intensity on the
graph is at its maximum. You may have to use the button in the upper left on the graph to expand
the graph scale while taking data to see the detail.
2.
To allow the maximum intensity of light through both polarizers, replace the holder with the
polarizer and Rotary Motion Sensor on the track, press Start, and then rotate polarizer that does have
the Rotary Motion Sensor until the light intensity on the graph is at its maximum (see Fig. 9).
80
Figure 9: Rotate the Polarizer That Has the Rotary Motion Sensor
3.
If the maximum exceeds 4.5 V, decrease the gain on the switch on the light sensor. If the
maximum is less than 0.5 V, increase the gain on the switch on the light sensor.
4.
Press Start and slowly rotate the polarizer which has the Rotary Motion Sensor through 180
degrees. Then press Stop.
ANALYSIS
1.
Click on the Fit button on the graph. Choose the User-Defined Fit and write an equation
(Acos(x)^2) with constants you can adjust to make the curve fit your data.
3
4
2.
Try a cos
Does the equation that best fits your data match theory? If not, why not?
81
PROCEDURE FOR 3 POLARIZERS
NOTE: This section is optional if you do not have a third polarizer. Perhaps another lab group may have
one you can share.
1.
Now repeat the experiment with 3 polarizers. Place one polarizer on the track and rotate it
until the transmitted light is a maximum.
2.
Then place a second polarizer on the track and
rotate it until the light transmitted through both
polarizers is a minimum.
3.
Then place a third polarizer on the track
between the first and second polarizers. Rotate it until
the light transmitted through all three polarizers is a
maximum (see Fig.10).
Figure 10: Setup with a Third Polarizer (#2) between
the Rotary Motion Sensor and the Light Sensor
4.
Press Start and record the Intensity vs. angle for 360 degrees as you rotate the third polarizer
that has the Rotary Motion Sensor.
5.
Select your data from 2 polarizers and from 3 polarizers. What two things are different for the
Intensity vs. Angle graph for 3 polarizers compared to 2 polarizers?
6.
Click on the Fit button and select the User-Defined Fit. Double-click the User-Defined Fit box
on the graph and enter the equation that you had for two polarizers. Then change the equation until
it matches your data for the 3 polarizers.
QUESTIONS
1.
For 3 polarizers, what is the angle between the middle polarizer and the first polarizer to get
the maximum transmission through all 3 polarizers? Remember: In the experiment, the angle of the
middle polarizer automatically reads zero when you start taking data but that doesn't mean the
middle polarizer is aligned with the first polarizer.
2.
For 3 polarizers, what is the angle between the middle polarizer and the first polarizer to get
the minimum transmission through all 3 polarizers?
82
83
84
EXPERIMENT 16: Interference and Diffraction of Light
EQUIPMENT
1
1
1
1
1
1
1
INCLUDED:
Basic Optics Track, 1.2 m
Basic Optics Slit Accessory
Basic Optics Diode Laser
Aperture Bracket
Linear Translator
Light Sensor
Rotary Motion Sensor
OS-8508
OS-8523
OS-8525A
OS-8534
OS-8535
CI-6504A
CI-6538
NOT INCLUDED, BUT REQUIRED:
1
ScienceWorkshop 500 or 750 Interface
1
DataStudio
CI-6400
CI-6870
INTRODUCTION
The distances between the central maximum and the diffraction minima for a single slit are measured
by scanning the laser pattern with a Light Sensor and plotting light intensity versus distance. Also,
the distance between interference maxima for two or more slits are measured. These measurements
are compared to theoretical values. Differences and similarities between interference and diffraction
patterns are examined.
THEORY
Diffraction
When diffraction of light occurs as it passes through a slit, the angle to the minima (dark spot) in the
diffraction pattern is given by
(1)
where "a" is the slit width, θ is the angle from the center of the pattern to the a minimum,
is the
wavelength of the light, and m' is the order (1 for the first minimum, 2 for the second minimum,
...counting from the center out).
85
In Figure 1, the laser light pattern is shown just below the
computer intensity versus position graph. The angle theta
is measured from the center of the single slit to the first
minimum, so m' equals one for the situation shown in the
diagram.
Figure 1: Single-Slit Diffraction
Double-Slit Interference
When interference of light occurs as it passes through two slits, the angle from the central maximum
(bright spot) to the side maxima in the interference pattern is given by
(m=1,2,3, …)
(2)
where "d" is the slit separation, θ is the angle from the center of
th
the pattern to the m maximum,
is the wavelength of the
light, and m is the order (0 for the central maximum, 1 for the
first side maximum, 2 for the second side maximum ...counting
from the center out).
In Figure 2, the laser light pattern is shown just below the
computer intensity versus position graph. The angle theta is
measured from the midway between the double slit to the
second side maximum, so m equals two for the situation shown
in the diagram.
Figure 2: Double-Slit Interference
SET UP
86
Figure 3: Mounting the Slits
1.
Mount the Single Slit disk to the optics bench: Each of the slit disks is mounted on a ring that
snaps into an empty lens holder. The ring should be rotated in the lens holder so the slits at the
center of the ring are vertical in the holder (see Figure 3). Then the screw on the holder should be
tightened so the ring cannot rotate during use. To select the desired slits, just rotate the disk until it
clicks into place with the desired slit at the center of the holder.
NOTE: All slits are vertical EXCEPT the comparison slits that are horizontal. The comparison slits are
purposely horizontal because the wide laser diode beam will cover both slits to be compared. If you
try to rotate these slits to the vertical position, the laser beam may not be large enough to illuminate
both slits at the same time.
87
2.
Mount the Rotary Motion Sensor on the rack of the Linear Translator and mount the Linear
Translator to the end of the optics track (see Figure 4). Mount the Light Sensor with the Aperture
Bracket (set on slit #6) in the Rotary Motion Sensor rod clamp.
Figure 5: Adjusting the Laser
Figure 4: Scanner with Light Sensor
3.
To complete the alignment of the laser beam and the slits, place the Diode Laser on the bench
at one of the bench. Put the slit holder on the optics bench a few centimeters from the laser, with the
disk-side of the holder closest to the laser (see Figure 5). Plug in the Diode Laser and turn it on.
CAUTION: Never look into the laser beam.
4.
Adjust the position of the laser beam from left-to-right and up-and-down until the beam is
centered on the slit. Once this position is set, it is not necessary to make any further adjustments of
the laser beam when viewing any of the slits on the disk. When you rotate the disk to a new slit, the
laser beam will be already aligned. Since the slits click into place, you can easily change from one slit
to the next, even in the dark. When the laser beam is properly aligned, the diffraction pattern should
be centered on the slits in front of the light sensor (see Figure 6). You may have to raise or lower the
light sensor to align the pattern vertically.
88
Figure 6: Aligning the Light Sensor
5.
Begin with the Light Sensor gain switch set on x10 and if the intensity goes off scale, turn it
down to x1.
6.
Plug the Rotary Motion Sensor into Channels 1 and 2 on the
ScienceWorkshop 500 interface and plug the Light Sensor into Channel A.
7.
Open the DataStudio file called "Diffraction".
FAMILIARIZATION WITH THE PATTERNS
1.
Start with the Single Slit Set. Rotate the wheel to
the 0.16 mm single slit.
2.
Look at the pattern produced by each selection on
the Single Slit wheel. Draw a diagram of each slit and the
corresponding diffraction pattern.
3.
Repeat Steps 2 and 3 for the Multiple Slit wheel.
Align the wheel on the 0.08/0.50 double slit.
SINGLE SLIT PROCEDURE
Figure 7: Complete Setup
1.
Replace the Multiple Slit wheel with the Single Slit wheel and set it to the 0.04 mm single slit.
89
2.
Before starting to record data, move the Light Sensor to one side of the laser pattern. You can
mark your scan starting point using the black clamp on the linear translator.
3.
Turn out the room lights and click on the START button. Then slowly turn the Rotary Motion
Sensor pulley to scan the pattern. Click on STOP when you have finished the scan. If you make a
mistake, simply do the scan again. You may have to change the gain setting on the light sensor (1x,
10x, 100x) depending on the intensity of the pattern. You should try to use slit #4 on the mask on the
front of the light sensor. Sketch each graph or, if a printer is available, print the graph of the
diffraction pattern.
4.
Determine the slit width using Equation (1):
(a)
Measure the distance between the first minima on each side of the central maximum
using the Smart Cursor in the computer program and divide by two.
(b)
the laser wavelength is given on the laser label.
(c)
Measure the distance between the slit wheel and the mask on the front of the light
sensor.
(d)
Solve for "a" in Equation (1). Measure at least two different minima and average your
answers. Find the percent difference between your average and the stated slit width on the wheel.
Note that the stated slit width is given to only one significant figure so the actual slit width is
somewhere between 0.035mm and 0.044mm.
DOUBLE SLIT PROCEDURE
1.
Replace the single slit disk with the multiple slit disk. Set the
multiple slit disk on the double slit with slit separation 0.25 mm (d)
and slit width 0.04 mm (a).
2.
Set the Light Sensor Aperture Bracket to slit #4.
3.
Before starting to record data, move the Light Sensor to one side of the laser pattern, up
against the linear translator stop.
4.
Turn out the room lights and click the START button. Then slowly turn the Rotary Motion
Sensor pulley to scan the pattern. Click STOP when you have finished the scan. You may have to
change the gain setting on the light sensor (1x, 10x, 100x) depending on the intensity of the pattern.
To get the most detail, use the smallest slit possible on the Light Sensor mask.
5.
Use the magnifier to enlarge the central maximum and the first side maxima. Use the Smart
tool to measure the distance between the central maximum and the first side maxima.
6.
Measure the distance between the central maximum and the second and third side maxima.
Also measure the distance from the central maximum to the first minimum in the DIFFRACTION (not
interference) pattern.
7.
Determine the slit separation using Equation (2):
90
(a)
Measure the distance between the slit wheel and the mask on the front of the light
sensor.
(b)
Solve for "d" in Equation (2). Determine "d" using the first, second, and third maxima
and find the average "d". Find the percent difference between your average and the stated slit
separation on the wheel.
8.
Determine the slit width using Equation (1) and the distance between the central maximum
and the first minimum in the diffraction pattern (not interference pattern). Is this the slit width given
on the wheel?
9.
Repeat Steps 2 through 8 for the interference patterns for the double slits (a/d = 0.04/0.50
mm).
QUESTIONS
1.
What physical quantity is the same for the single slit and the double slit?
2.
How does the distance from the central maximum to the first minimum in the single-slit
pattern compare to the distance from the central maximum to the first diffraction minimum in the
double-slit pattern?
3.
What physical quantity determines where the amplitude of the interference peaks goes to
zero?
4.
In theory, how many interference maxima should be in the central envelope for a double slit
with d = 0.25 mm and a = 0.04 mm?
5.
How many interference maxima are actually in the central envelope?
91
Experiment 17 : Ohm's Law
Purpose
The main purpose of this experiment is to review the measurement of voltage (V), current (I), and
resistance (R) in dc circuits. In the first part, you will measure the internal resistance of a battery and
examine the relationship between V and I in a resistor which obeys Ohm's law. In second part of the
lab, you will measure the resistance of some electrical devices that do not obey Ohm’s law.
References
Halliday, Resnick and Krane, Physics, Vol. 2, 4th Ed., Chapters 32, 33
Purcell, Electricity and Magnetism, Chapter 4
Taylor, An Introduction to Error Analysis, Second Edition
Equipment
Digital multimeters
Resistor board with 4, 5 10, and 20 ohm resistors
6-volt battery
knife switch
10 V Power Supply
diode board with switching diodes, LED and 40 ohm resistor
Introduction
This section contains background material on current, voltage and resistance that you should already
know from your prior physics classes, including high-school physics, Physics 174, and Physics 272. A
few days before your lab class starts, at the latest, take a quick look over this introduction. If you find
you are already familiar with the material, then skip to the next section and go over the experiment.
You probably will need to read the section on diodes, since this is usually not covered in beginning
physics classes. If you are not familiar with the other material in the introduction, then you have
missed or forgotten some very important and basic physics and you need to give this introduction a
thorough and careful reading. You also should dig out your Physics 272 text, or one of the references
above, and read over chapters on dc circuits.
Voltage
When an electric charge moves between two points that have an electric potential difference
between them, work is done on the charge by the source that is creating the potential. The amount
of work that is done is equal to the decrease in the potential energy of the charge. The difference in
potential energy is equal to the product of the difference in the electrical potential between the
points and the magnitude of the electric charge. In the SI system of units, the unit of electrical
potential difference is the volt (written as V). For this reason, almost everyone who work with circuits
say "voltage difference" instead of "electrical potential difference". Voltages are measured using a
voltmeter. Voltage differences are always measured between two points, with one lead of the
voltmeter connected to one point and the second lead connected to another point. On the other
hand, diagrams of circuits almost always show the voltage at individual locations in the circuit. If the
voltage is given at one point, then this means that the second point was at "ground" potential or
92
"zero volts" and this ground point is labeled on a circuit schematic using a special symbol (see Figure
1.2).
Current
The rate at which charge passes through a surface is called the electrical current. Current is
measured in Ampères, commonly called amps, with units written as A. One amp of current is defined
as one Coulomb of charge passing through a cross-sectional area per second. Since an electron has
-19
18
a charge of -1.609x10 C, This is equivalent to about 6×10 electrons passing per second. Current is
measured using an ampermeter which is placed in a circuit so that the current flows into the positive
terminal of the ammeter and out the negative terminal. Since the current flows through the ammeter,
and we do not want the ammeter to disrupt the current that is ordinarily flowing through a circuit, an
ammeter has a low resistance. Never connect an ammeter directly across a battery (or other voltage
source), since this will result in a large current flowing through the ammeter, possibly damaging it or
the battery. Note that in contrast a voltmeter has a high resistance.
Resistance and Ohm's Law
When current is driven through an ordinary electrically conducting material, such as a metal or
semiconductor at room temperature, it encounters resistance. You can think of resistance as a sort
of frictional drag. In a sample made of a good conductor, the current is directly proportional to the
potential difference, i.e.
I
1
V
R
This relationship is called Ohm's Law and is usually written:
V=IR
In this relationship, I is the current flowing through the sample. The potential difference V is the
difference in voltage between one end of the sample (where the current enters) to the other end
(where the current leaves). Finally, R is the resistance of the sample. In the SI system of units,
In many materials the resistance does not change with the amount of voltage applied or the current
passing through it, over a large range of both parameters, so it is a constant to a very good
approximation. The resistors used in this lab are made of thin metal films or carbon (a
semiconductor). You should find that they obey Ohm’s Law very well. Metals are examples of good
conductors. They have a high density of electrons that are relatively free to move around, so that
connections made with metal tend to have a low resistance. In an electrical insulator, the electrons
are more tightly bound and cannot move freely. In a semiconductor, most of the electrons are
tightly bound, but there is a small fraction (compared to a metal) that are free to conduct current.
The small density of carriers in semiconductors makes them more resistive than metals, and much
more conducting than insulators. It also gives them many other unusual properties, some of which
we will see in this lab.
Batteries and EMF
There are a variety of ways to generate a voltage difference. Batteries produce an electrical potential
difference through chemical reactions. If the plus (+) and minus (-) leads of a battery are connected
across a resistor, a current will flow out of the positive terminal of the battery (which has a more
positive potential than the negative terminal), through the resistor and into the negative terminal. In
other words, the positive current flows from the positive to the negative terminal of the battery.
Inside the battery, chemical reactions drive a current flow from the more negative region to the more
positive region. As a result, a battery can be thought of as a charge pump that is trying to push
positive charge out of the + terminal and suck positive charge into the - terminal.
In physics and EE textbooks, one also encounters the terms electromotive force or EMF. The term
EMF comes from the idea that a force needs to be exerted on charges to move them through a wire
(to overcome the resistance of the piece of wire to the flow of the current). The battery can be
93
thought of as the source of this force. However, the EMF of a battery is just the voltage difference
generated across the terminals of the battery and is measured in volts. So EMF is not actually a force,
despite its name. In Physics 276, we will not make distinctions between the EMF, the voltage
difference, and the electrical potential difference, but use these terms interchangeably.
Part of this experiment is to measure the EMF and internal resistance of a battery. When a current
flows inside a battery it is also encounters resistance and the battery is said to have an internal
resistance. Batteries with low internal resistance, such as the 12 V lead-acid batteries commonly
found in cars, can deliver a lot of current. They need to be treated with caution; shorting together the
terminals of a battery (or other voltage source) with a low internal resistance could lead to melted
wires, a fire, or the battery exploding. On the other hand, batteries with high internal resistance
cannot deliver much current and show significant loss of voltage when current is supplied.
Electrical Symbols
Components used in electrical experiments have standard symbols. Those required in this
experiment are shown in Fig. (1.2). You should understand what each symbol represents and use
them when drawing schematics of your own circuits.
electrical
ground
(V=0)
Figure 1.2. Some common symbols used in electrical circuits.
Figure 1.3 Simple circuit with a battery and two resistors showing direction of positive current flow I.
Electrical Circuits
An electrical circuit is formed by using wires to connect together resistors, batteries, switches, or
other electrical components into one or more connected closed loops. Where three or more wires
meet, the current will split between the different paths. However each new path for current flow that
is created at these junctions must rejoin another channel at some other point, so that all loops close.
All loops that are created must be closed so that current can flow.
Kirchhoff's Rules
There are two very useful rules for analyzing electrical circuits and finding the currents and voltages
94
at different points in a circuit.
Rule 1: In going round a closed loop the total change in voltage must be zero.
Rule 2: The current flowing into any junction where wires meet is equal to the current flowing out of
the junction.
For example, applying the first rule to Fig.1.3 and assuming that the conductors joining the
components have zero resistance, we find the potential differences between the lettered points in
the circuit are given by:
V A  VB  V AB  0 VBC  IR
VCD  0 VDE  Ir
VEF  0 VFG  
Summing all the differences we get:
VAA  IR  Ir    0
which can be rewritten:
  I (R  r) .
As another example, we can apply rule 2 to Fig. 1.3. Considering the nodes at points P and Q in
the circuit, we get
At P:
Current in = I
Current out = I1 + I2
At Q:
Current in = I1 and I2
Current out = I
Both points yield the equation I = I1 + I2.
P
Q
Figure I-3
95
(a)
(b)
O
O'
Figure I-4: (a) Connecting resistors R1 and R2 in series produces a resistance R
Connecting resistors R1 and R2 in series produces a resistance R
96

R1 R2
.
R1  R2
 R1  R2 . (b)
97
Experiment 18: Kirchoff’s Law
OBJECTIVES




To calculate expected voltages and currents for each component using Kirchhoff’s Laws.
To measure the actual voltage and current for each component.
To compare the expected and actual values of the voltages and currents
To determine if the circuit obeys Kirchhoff’s Laws.
V1
V2
V3
V4
Vtotal

Circuit
EWB
Simulation
I = E/Rtot
I1
I2
I3
Circuit
EWB
Simulation
98
I1+I2+I3
99
SERIES AND PARALLEL RESISTORS
In Physics II, you measured the resistance of two resistors when they were connected in series (see
Fig. 1.4 a) and in parallel (see Fig. 1.4 b). For the series connection, one finds R  R1  R2 , i.e. the
resistance adds. For the parallel connection, one finds R

R1 R2
.
R1  R2
These elementary results can be derived by applying Kirchoff's rules. For example, consider the series
connected resistors. Since current is conserved, the current I in R1 must be the same as the current I
in R2.
Hence the voltage drop across R1 is V1  IR1 and the voltage drop across R2 is V2  IR2 . Thus we
can write V1
 V2  I ( R1  R2 ) .
This is equivalent to writing
V  IR where V  V1  V2 and R  R1  R2 , i.e. two resistors
connected in series are equivalent to one resistor whose value is equal to their sum. This argument
can be generalized to n resistors in series, and one finds
R  i Ri .
Next, consider the parallel connected resistors. The potential difference V between O and O ’ must
be the same whether we go along OABO ’ or OCDO ’. Also conservation of current requires that
I  I1  I 2 , where:
I1  V R1
is the current through R1 and
I 2  V R2
is the current through R2. Substituting these expressions for I1 and I2 into our equation for I gives:
 1
1 
 .
I  V  
 R1 R2 
V  IR where R  R1 R2 ( R1  R2 ) . This argument can be generalized
n
1
1
 .
to n resistors connected in parallel and one finds
R i 1 Ri
This is equivalent to writing
Diodes
Not everything obeys Ohm's law, i.e. current is not necessarily proportional to voltage. In this lab you
will also measure the characteristics of a common type of electrical device called a diode. A diode
consists of a junction of an “n-type” semiconductor and a "p-type" semiconductor. The current in ntype semiconductors is carried by negative charges (the electrons), while in p-type semiconductors
the current is best thought of as being carried by positive charges (called "holes" that are due to
missing electrons). When n and p materials are brought together, a few electrons will drift from n to
p and some holes will drift from p to n. This charge transfer between n and p regions generates an
internal electrical potential at the junction which opposes further transfer of electrons and holes
between the two sides. It is possible to drive current from p to n (i.e. holes from the p region to n and
electrons from the n region to the p) only if this potential “barrier” is overcome by applying a
sufficiently large voltage difference across the diode. For current to flow, the p region must be
positive with respect to the n. Applying a positive voltage to n and a negative voltage to p produces
only a very small “leakage current”. Thus the diode acts like a one-way valve with low resistance to
current flowing in the direction of the arrow, and high resistance to current flowing in the opposite
direction. If too much voltage is applied in either direction, the diode will be destroyed.
The symbol for a diode is shown in Fig. 1.1 (a). The tip of the triangle points in the direction that
current can flow with low resistance. The characteristics of an IN914 switching diode are shown in
Table 1.1. This is one of the diodes that you can measure in the lab. A light emitting diode (LED) has
100
also been provided. In an LED, the current flow causes emission of light with a fairly well-defined
wavelength or color. LEDs are efficient, reliable and long-lived, provided you don't apply too much
voltage across them. A red, yellow or green LED can typically withstand about 3 V and about 5V for a
blue LED.
(a)
(b)
anode
cathode
b
a
I
(c)
Figure 1.1: (a) Electrical symbol for a diode. (b) When Vb > Vg+Va, current flows through the diode,
from b (the p-type region or anode) to a (the n-type region or cathode). Here Vg is the threshold
voltage that needs to be reached before significant forward conduction occurs. When Vb < Vg+Va the
flow of current is blocked. In particular, when Vb<Va, the device is said to be "reverse biased" and
only a very small leakage current will flow. (c) Sketch of the physical layout of an 1N914 switching
diode. The dark black band is on the cathode.
Table 1.1 Some electrical characteristics of the IN914 switching diode.
Peak Reverse Voltage
75 V
Average Forward Rectified Current
75 mA
Peak Surge Current, 1 Second
500 mA
Continuous Power Dissipation at 25°C
250 mW
Operating Temperature Range
-65 to 175°C
Reverse Breakdown Voltage
100 V
Static Reverse Current
25 nA
Static Forward Voltage
1 V at 10 mA
Capacitance
4 pF
Typical threshold voltage
0.6 V
101
102
EXPERIMENT 19: Emf and Internal Resistance
Purpose: to find internal resistance of a battery.
Teori: Real batteries are constructed from materials which possess non-zero resistivities. It follows
that real batteries are not just pure voltage sources. They also possess internal resistances.
Incidentally, a pure voltage source is usually referred to as an emf (which stands for electromotive
force). Of course, emf is measured in units of volts. A battery can be modeled as an emf
connected
in series with a resistor , which represents its internal resistance.
Suppose that such a battery is used to drive a current through an external load resistor
, as
shown in Fig. 1. Note that in circuit diagrams an emf
is represented as two closely spaced parallel
lines of unequal length. The electric potential of the longer line is greater than that of the shorter one
by
volts. A resistor is represented as a zig-zag line.
Figure 1: A battery of emf
Thus, the voltage
and internal resistance
resistance
.
of the battery is related to its emf
103
connected to a load resistor of
and internal resistance
via
Table 1: Datas
R = V/I
(ohm)
R (ohm)
I (A)
V (volt)
Draw a graphic V viceversa I, and find the internal resistance of the battery.
104
105
EXPERIMENT 20:
CAPACITOR CHARGE-DECHARGE CHARACTERISTICS
Goal
1.)Understand the working principles of the capacitor
2.)Investigate the charge and decharge characteristics of capacitor
Theory
Basicly a capacitor can be built by placing two metal conductive plate face to face in a small distance.
Then the plates are connected to a voltage source and when the potential is applied one of the
plates are charged +Q ,while other is –Q. The voltage difference between two plates are
approximately V applied potential. Capacitance is the ratio of the charge to the potential difference
between the plates. It is shown by “C” and in SI unit system its value is Farad (F).
Capacitance of the capacitor:
C: Capasitance
Q: net charge
V: potential difference between the
plates
E0: electric constant
A: plate area
D: distance between plates
106
107
108
109
EXPERIMENT 21: FORCE VERSUS CURRENT (F = ILBSin)
INTRODUCTION
Procedure
If you're using a quadruple-beam balance:

Set up the apparatus as shown in figure 1.1.

Determine the mass of the magnet holder and magnets with no current flowing. Record this
value in the column under “Mass” in Table 1.1.

Set the current to 0.5 amp. Determine the new “mass” of the magnet assembly. Record this
value under “Mass” in Table 1.1.

Subtract the mass value with the current flowing from the value with no current flowing.
Record this difference as the “Force.”

Increase the current in 0.5 amp increments to a maximum of 5.0 amp, each time repeating
steps 2-4.
If you're using an electronic balance:

Set up the apparatus as shown in figure 1.1.

Place the magnet assembly on the pan of the balance. With no current flowing, press the TARE
button, bringing the reading to 0.00 grams.

Now turn the current on to 0.5 amp, and record the mass value in the “Force” column of Table
1.1.

Increase the current in 0.5 amp increments to a maximum of 5.0 amp, each time recording the
new “Force” value.
Data Processing
Plot a graph of Force (vertical axis) versus Current (horizontal axis).
Analysis
What is the nature of the relationship between these two variables? What does this tell us about how
changes in the current will affect the force acting on a wire that is inside a magnetic field?
110
111
Experiment 21/B: Force versus Length of Wire
Procedure

Set up the apparatus as in Figure 2.1.

Determine the length of the conductive foil on the Current Loop. Record this value under
“Length” in Table 2.1.
If you are using a quadruple-beam balance:
 With no current flowing, determine the mass of the Magnet Assembly. Record this value on the line
at the top of Table 2.1.
Set the current to 2.0 amps. Determine the new “mass” of the Magnet Assembly. Record this value
under “Mass” in Table 2.1.
Subtract the mass that you measured with no current flowing from the mass that you measured with
the current flowing. Record this difference as the “Force.”
Turn the current off. Remove the Current Loop and replace it with another. Repeat steps 2-5.
If you are using an electronic balance:

Place the magnet assembly on the pan of the balance. With no current flowing, press the TARE
button, bringing the reading to 0.00 grams.

Now turn the current on, and adjust it to 2.0 amps. Record the mass value in the “Force”
column of Table 2.1.

Turn the current off, remove the Current Loop, and replace it with another. Repeat steps 2-4.
Data Processing
Plot a graph of Force (vertical axis) versus Length (horizontal axis).
Analysis
What is the nature of the relationship between these two variables? What does this tell us about how
changes in the length of a current-carrying wire will affect the force that it feels when it is in a
magnetic field?
112
113
114
Experiment 22: Transformer Basics I
Introduction
When an alternating current passes through a coil of wire, it produces an alternating magnetic field.
This is precisely the condition needed for the electromagnetic induction to take place in a second coil
of wire. In this lab you will investigate several of the factors influencing the operation of a
transformer.
Equipment Needed - Supplied
1. The four coils from the PASCO SF-8616 Basic Coils Set
2. The U-shaped Core from the PASCO SF-8616 Basic Coils Set
3. Optional: the additional coils from the PASCO SF-8617 Complete Coils Set
Equipment Needed - Not Supplied
1. Low voltage ac power supply 0-6 VAC, 0-1 amp such as PASCO Model SF-9582
2. AC voltmeter 0-6 VAC
3. Banana connecting leads for electrical connections
Procedure
1. Set up the coils and core as shown in Figure 1. In the diagram, the coil to the left will be referred to
as the primary coil, and the one to the right will be the secondary coil. Note that we are putting in an
alternating current to the primary at one voltage level, and reading the output at the secondary.
2. With the 400-turn coil as the primary and the 400-turn coil as the secondary, adjust the input
voltage to 6 volts a.c. Measure the output voltage and record your results in Table 1.1.
3. Repeat step 2 after inserting the straight cross piece from the top of the U-shaped core. Record
your results. (See Figure 2.)
4. Repeat step 2 after placing the coils on the sides of the open U-shaped core. Record your results.
5. Finally, repeat step 2 after placing the cross piece over the U-shaped core. Record your results.
115
6. Using the core configuration which gives the best output voltage compared to input voltage, try all
combinations of primary and secondary coils. Use a constant input voltage of 6.0 volts a.c. Record
your data in Table 1.2.
Analysis
1. Which core configuration gives the maximum transfer of electromagnetic effect to the secondary
coil? Develop a theory to explain the differences between configurations.
2. From your data in table 1.2, for a primary having a constant number of turns, graph the resulting
output voltage versus the number of turns in the secondary. What type of mathematical relationship
exists between numbers of turns of wire and the resulting output voltage? Is the data ideal? Why or
why not?
3. Consider further improvements to your transformer. What additional changes might you make to
increase the transfer from one coil to the other?
116
117
Experiment 23: Ohm’s Law, RC and RL Circuits
OBJECTIVES
1. To explore the measurement of voltage & current in circuits
2. To see Ohm’s law in action for resistors
3. To explore the time dependent behavior of RC and RL Circuits
PRE-LAB READING
INTRODUCTION
When a battery is connected to a circuit consisting of wires and other circuit elements like resistors
and capacitors, voltages can develop across those elements and currents can flow through them. In
this lab we will investigate three types of circuits: those with only resistors in them and those with
resistors and either capacitors (RC circuits) or inductors (RL circuits). We will confirm that there is a
linear relationship between current through and potential difference across resistors (Ohm’s law: V =
IR). We will also measure the very different relationship between current and voltage in a capacitor
and an inductor, and study the time dependent behavior of RC and RL circuits.
The Details: Measuring Voltage and Current
Imagine you wish to measure the voltage drop across and current through a resistor in a circuit. To
do so, you would use a voltmeter and an ammeter – similar devices that measure the amount of
current flowing in one lead, through the device, and out the other lead. But they have an important
difference. An ammeter has a very low resistance, so when placed in series with the resistor, the
current measured is not significantly affected (Fig. 1a). A voltmeter, on the other hand, has a very
high resistance, so when placed in parallel with the resistor (thus seeing the same voltage drop) it will
draw only a very small amount of current (which it can convert to voltage using Ohm’s Law V = V
=I
R
meter meter
R
), and again will not appreciably change the circuit (Fig. 1b).
meter
Figure 1: Measuring current and voltage in a simple circuit. To measure current through the
resistor (a) the ammeter is placed in series with it. To measure the voltage drop across the resistor (b)
the voltmeter is placed in parallel with it.
The Details: Capacitors
Capacitors store charge, and develop a voltage drop V across them proportional to the amount of
charge Q that they have stored: V = Q/C. The constant of proportionality C is the capacitance
(measured in Farads = Coulombs/Volt), and determines how easily the capacitor can store charge.
Typical circuit capacitors range from picofarads (1 pF = 10
-6
-12
-3
F) to millifarads (1 mF = 10 F). In this
lab we will use microfarad capacitors (1 μF = 10 F).
RC Circuits
Consider the circuit shown in Figure 2. The capacitor (initially uncharged) is connected to a voltage
source of constant emf . At t = 0, the switch S is closed.
118
Figure 2 (a) RC circuit (b) Circuit diagram for t > 0
In class we derived expressions for the time-dependent charge on, voltage across, and current
through the capacitor, but even without solving differential equations a little thought should allow us
to get a good idea of what happens. Initially the capacitor is uncharged and hence has no voltage
drop across it (it acts like a wire or “short circuit”). This means that the full voltage rise of the battery
is dropped across the resistor, and hence current must be flowing in the circuit (V = IR). As time goes
R
on, this current will “charge up” the capacitor – the charge on it and the voltage drop across it will
increase, and hence the voltage drop across the resistor and the current in the circuit will decrease.
This idea is captured in the graphs of Fig. 3.
Figure 3 (a) Voltage across and charge on the capacitor increase as a function of time while (b) the
voltage across the resistor and hence current in the circuit decrease.
After the capacitor is “fully charged,” with its voltage essentially equal to the voltage of the battery,
the capacitor acts like a break in the wire or “open circuit,” and the current is essentially zero. Now we
“shut off” the battery (replace it with a wire). The capacitor will then release its charge, driving current
through the circuit. In this case, the voltage across the capacitor and across the resistor are equal,
and hence charge, voltage and current all do the same thing, decreasing with time. As you saw in
class, this decay is exponential, characterized by a time constant t, as pictured in fig. 4.
Figure 4 Once (a) the battery is “turned off,” the voltages across the capacitor and resistor, and
hence the charge on the capacitor and current in the circuit all (b) decay exponentially. The time
constant τ is how long it takes for a value to drop by e.
119
The Details: Inductors
Inductors store energy in the form of an internal magnetic field, and find their behavior dominated
by Faraday’s Law. In any circuit in which they are placed they create an EMF ε proportional to the
time rate of change of current I through them: ε = L dI/dt. The constant of proportionality L is the
inductance (measured in Henries = Ohm s), and determines how strongly the inductor reacts to
current changes (and how large a self energy it contains for a given current). Typical circuit inductors
range from nanohenries to hundreds of millihenries. The direction of the induced EMF can be
determined by Lenz’s Law: it will always oppose the change (inductors try to keep the current
constant)
RL Circuits
If we replace the capacitor of figure 2 with an inductor we arrive at figure 5. The inductor is
connected to a voltage source of constant emf . At t = 0, the switch S is closed.
Figure 5 RL circuit. For t<0 the switch S is open and no current flows in the circuit. At t=0 the switch
is closed and current I can begin to flow, as indicated by the arrow.
As we saw in class, before the switch is closed there is no current in the circuit. When the switch is
closed the inductor wants to keep the same current as an instant ago – none. Thus it will set up an
EMF that opposes the current flow. At first the EMF is identical to that of the battery (but in the
opposite direction) and no current will flow. Then, as time passes, the inductor will gradually relent
and current will begin to flow. After a long time a constant current (I = V/R) will flow through the
inductor, and it will be content (no changing current means no changing B field means no changing
magnetic flux means no EMF). The resulting EMF and current are pictured in Fig. 6.
Figure 6 (a) “EMF generated by the inductor” decreases with time (this is what a voltmeter hooked in
parallel with the inductor would show) (b) the current and hence the voltage across the resistor
increase with time, as the inductor ‘relaxes.’
After the inductor is “fully charged,” with the current essentially constant, we can shut off the battery
(replace it with a wire). Without an inductor in the circuit the current would instantly drop to zero, but
the inductor does not want this rapid change, and hence generates an EMF that will, for a moment,
keep the current exactly the same as it was before the battery was shut off. In this case, the EMF
generated by the inductor and voltage across the resistor are equal, and hence EMF, voltage and
current all do the same thing, decreasing exponentially with time as pictured in fig. 7.
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Figure 7 Once (a) the battery is turned off, the EMF induced by the inductor and hence the voltage
across the resistor and current in the circuit all (b) decay exponentially. The time constant τ is how
long it takes for a value to drop by e.
The Details: Non-Ideal Inductors
So far we have always assumed that circuit elements are ideal, for example, that inductors only have
inductance and not capacitance or resistance. This is generally a decent assumption, but in reality no
circuit element is truly ideal, and today we will need to consider this. In particular, today’s “inductor”
has both inductance and resistance (real inductor = ideal inductor in series with resistor). Although
there is no way to physically separate the inductor from the resistor in this circuit element, with a
little thought (which you will do in the pre-lab) you will be able to measure both the resistance and
inductance.
APPARATUS
1. Science Workshop 750 Interface
In this lab we will again use the Science Workshop 750 interface to create a “variable battery” which
we can turn on and off, whose voltage we can change and whose current we can measure.
2. AC/DC Electronics Lab Circuit Board
We will also use, for the first of several times, the circuit board pictured in Fig. 8. This is a general
purpose board, with (A) battery holders, (B) light bulbs, (C) a push button switch, (D) a variable
resistor called a potentiometer, and (E) an inductor. It also has (F) a set of 8 isolated pads with spring
connectors that circuit components like resistors and capacitors can easily be pushed into. Each pad
has two spring connectors connected by a wire (as indicated by the white lines). The right-most pads
also have banana plug receptacles, which we will use to connect to the output of the 750.
Figure 8 The AC/DC Electronics Lab Circuit Board, with (A) Battery holders, (B) light bulbs, (C) push
button switch, (D) potentiometer, (E) inductor and (F) connector pads
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4. Resistors & Capacitors
We will work with resistors and capacitors in this lab. Resistors (Fig. 8a) have color bands that indicate
their value (see appendix A if you are interested in learning to read this code), whereas capacitors
(Fig. 8b) are typically stamped with a numerical value.
Figure 10 Examples of a (a) resistor and (b) capacitor. Aside from their size, most resistors look the
same, with 4 or 5 colored bands indicating the resistance. Capacitors on the other hand come in a
wide variety of packages and are typically stamped both with their capacitance and with a maximum
working voltage.
GENERALIZED PROCEDURE
This lab consists of five main parts. In each you will set up a circuit and measure voltage and current
while the battery periodically turns on and off. In the last two parts you are encouraged to develop
your own methodology for measuring the resistance and inductance of the coil on the AC/DC
Electronics Lab Circuit Board both with and without a core inserted. The core is a metal cylinder
which is designed to slide into the coil and affect its properties in some way that you will measure.
Part 1: Measure Voltage Across & Current Through a Resistor
Here you will measure the voltage drop across and current through a single resistor attached to the
output of the 750.
Part 2: Resistors in Parallel
Now attach a second resistor in parallel to the first and see what happens to the voltage drop across
and current through the first.
Part 3: Measuring Voltage and Current in an RC Circuit
In this part you will create a series RC (resistor/capacitor) circuit with the battery turning on and off
so that the capacitor charges then discharges. You will measure the time constant in two different
ways (see Pre-Lab #5) and use this measurement to determine the capacitance of the capacitor.
Part 4: Measure Resistance and Inductance Without a Core
The battery will alternately turn on and turn off. You will need to hook up this source to the coil and,
by measuring the voltage supplied by and current through the battery, determine the resistance and
inductance of the coil.
Part 5: Measure Resistance and Inductance With a Core
In this section you will insert a core into the coil and repeat your measurements from part 1 (or
choose a different way to make the measurements).
Answer these questions on a separate sheet of paper and turn them in before the lab
1. Measuring Voltage and Current
In Part 1 of this experiment you will measure the potential drop across and current through a single
resistor attached to the “variable battery.” On a diagram similar to the one below, indicate where you
will attach the leads to the resistor, the battery, the voltage sensor , and the current sensor . For the
battery and sensors make sure that you indicate which color lead goes where, using the convention
that red is “high” (or the positive input) and black is “ground.” Reread the pre-lab description of this
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board carefully to understand the various parts. When you draw a resistor or other circuit element it
should go between two pads (dark green areas) with each end touching one of the spring clips (the
metal coils). Do NOT just draw a typical circuit diagram. You need to think about how you will
actually wire this board during the lab. RECALL: ammeters must be in series with the element they are
measuring current through, while voltmeters must be in parallel.
2. Resistors in Parallel
In Part 2 you will add a second resistor in parallel with the first. Show where you would attach this
second resistor in the diagram you drew for question 1, making sure that the ammeter continues to
measure the current through the first resistor and the voltmeter
measures the voltage across the first resistor.
3. Measuring the Time Constant τ
As you have seen, current always decays exponentially in RC circuits with a time constant τ: I = I
0
exp(-t/τ).
We will measure this time constant in two different ways.
(a) After measuring the current as a function of time we choose two points on the curve (t ,I ) and (t ,
1 1
2
I ). What relationship must we choose between I and I in order to determine the time constant by
2
2
1
subtraction: τ = t – t ? Should we be able to find a t that satisfies this for any choice of t ?
2
1
2
1
(b) We can also plot the natural log of the current vs. time, as shown at right. If we fit a line to this
curve we will obtain a slope m and a y-intercept b. From these fitting parameters, how can we
calculate the time constant?
(c) Which of these two methods is more likely to help us obtain an accurate measurement of the time
constant? Why?
Part 3: Measuring Voltage and Current in an RC Circuit
3A: Using a Single Resistor
1. Create a circuit with the first resistor and the capacitor in series with the battery
2. Connect the voltage sensor (still in channel A) across the capacitor
3. Record the voltage across the capacitor V and the current sourced by the battery I (Press the green
“Go” button above the graph). During this time the battery will switch between putting out 1 Volt
and 0 Volts.
Question 4:
Using the two-point method (which you calculated in Pre-Lab #3a), what is the time constant of this
circuit? Using this time constant, the resistance you measured in Question 1 and the typical
expression for an RC time constant, what is the capacitance of the capacitor?
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Table: For RC circuit, discharge
t(s)
0
15
30
45
60
V
(volt)
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75
90
105
120
125
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EXPERIMENT 24: RL, RC, RLC Circuts
INTRODUCTION
In this experiment the impedance Z, inductance L and capacitance C in alternating current circuits will
be studied.
The parameters of the circuit will be varied to produce the condition called resonance.
The inductive and capacitive reactance are defined as follows:
Inductive Reactance = XL = 2pifL
Capacitive Reactance = XC =
1 .
2fC
XL
Z
The impedance in a series AC
XL  XC
circuit is found by adding the
individual reactances and
resistance as vectors as shown
XC
R
in Figure 1.
Fig. 1
VL = IXL
Vtotal = IZ
VL  VC
Voltages are all equal to the
current I, times the individual
or combined reactances. They
can be calculated from a
VC = IXC
VR = IR
diagram which has the same
form as that shown in Figure 2.
Fig. 2
As the frequency is varied from low to high, a minimum value of total impedance Z is found when X L
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= XC, or f =
1
. The value of Z at this resonance frequency is Z = R. If the applied voltage is
2 LC
kept constant, then when Z is a minimum, I will be at a maximum, so both Z and I have the general
form as shown in Figure 3.
Z
I
f
f
Fig. 3
I
Imax
Small R
0.707 Imax
The width of the curves in the
above is of great importance in
Larger R
such devices as radio and TV
receivers (we only want one
channel at a time), and is
f1 fo f2
measured by the ratio of the
width to the center frequency, as
shown in Figure 4.
Fig. 4
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f
When the peak is narrow, the circuit
is said to have a high Q, where the
fo
quality Q is defined as: Q =
.
f2  f1
Z for f = f 2
XL  XC = R
Z for f = f o (Z = R)
A high Q corresponds to a small
Z for f = f 1
value of the total series resistance
45o
(coil resistance plus any other
45o
resistance). Q can also be shown to
X
be given by Q = L , where
R
XL =
XC  XL = R
oL, with fo being the
resonant frequency. Figure 5
Locus of points as f varies
indicates the relationship between Z,
R, XL and XC as f varies from f1 to fo
to f2.
Fig. 5
L (H)
R
XL
(ohm)
teorik
Z
VR (volt)
I=VR/R
1
2
3
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den=Vtop/I
Z teo= X L 2  R 2
C
(farad)
Xc
R (ohm)
teorik
VR (volt)
1
2
3
130
I=VR/R
Z den=Vtop/I
Z teo= X C 2  R 2
Experiment 25. Oscilloscope
Objective
To familiarize with the use of oscilloscope and the measurement of DC and AC voltages,
amplitude, period and frequency. To learn the method of measuring high resistance through
measurement of RC constant.
Apparatus
Oscilloscope, probes, variable DC power supply, and function generator.
Theory
The oscilloscope is a unique and probably the most important test instrument of an
electrical engineer or any scientist working with electronic devices. The basic component of the
oscilloscope is the cathode ray tube (CRT), as illustrated in Figure 1.
Electrons from a heated cathode or filament are accelerated through a potential difference
into a focusing element to become a well collimated and focused beam. The electron beam enters
into two sets of parallel deflection plates. The first pair of parallel plates is more sensitive and used
for the signal channel. It causes vertical deflection. The second pair of plates causes horizontal
deflection and is usually used for time sweeping. The electron beam coming out of the deflection
plates heats the CRT screen with fluorescent coating and make a bright spot at certain position
determined by the voltages applied across the two pairs of deflection plates. If both voltages are
varying in time, the electron beam will trace a two dimensional curve on the screen.
Figure 2 shows one of such a two dimensional curve, a sinusoidal wave function. The horizontal
movement of the electron beam is controlled by a voltage that increases as a linear function of time.
This voltage is sometimes called the sawtooth voltage or ramp voltage. The curve traced by the
electron beam on the screen is actually the waveform as a function of time of the signal applied
across the vertical deflection plates. The time measurement (horizontal axis) is determined by the
frequency of the sweeping voltage provided by a built-in sawtooth waveform generator, while the
voltage measurement (vertical axis) is determined by the amplification of the internal amplifier. Both
the sawtooth generator and the amplifiers are accurately calibrated by the manufacturer so that the
user can read the time and signal voltages directly from the knob settings on the front panel of the
oscilloscope.
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In Figure 2, the time interval between points o and b is called the period because the waveform
repeats itself again from the point b on. The maximum signal is called the amplitude of the
waveform, which is measured from the time axis, which is supposedly at the vertical center of the
waveform, to the peak of it. The period is usually very short (from a few nanoseconds to a few
milliseconds for most measurements), and the whole curve of Figure 2 would cause a fluorescent
flash for as long as the fluorescence lasts, which is about a second or so, too fast for any practical
measurement. In order display a static waveform, the electronics is designed such that the electron
beam keeps on repeating the same track on the screen. This requires that the electron beam always
starts at the same point of the waveform. Namely, the horizontal sweep waveform and the signal
waveform have to be synchronized. There are controls on the front panel for adjusting the trigger
level and polarity to achieve stable synchronization. If the signals are not synchronized, the waveform
will be seen running on the screen.
Procedure
1. Turn on the power switch. (It could be quite a challenge to find one for some models!)
You may need to wait for seconds to see something shown on the screen. Find the "Intensity" knob
and adjust the intensity such that the figure on the screen is bright enough for you to see, but not
too bright to burn up the screen. The problem is more serious if you see only a single dot on screen.
Reduce the intensity immediately when this happens. Get help from your instructor if you are
completely lost.
2. Adjust the "Focusing" knob to obtain the finest trace on the screen. The better focused
beam is usually brighter. You need to reduce the intensity accordingly to protect the screen.
3.
Set the time scan to the scale of 10 ms per division. Set the "Input" switch of both channels to
"Ground". Adjust the "X position" knob so that the horizontal sweep line is centered on the screen.
This is the time axis.
4. Adjust "Y position" knobs to see which channel is used. If the knob controls the Y
position of the sweep line, that channel is used. Make sure Channel One is used and adjust the Y
position so that the sweep line is centered vertically.
Apply a few volts of DC voltage to Channel One input, using a BNC probe. Notice the
change of the vertical position of the time axis. Set the Y sensitivity knob to the more sensitive scale,
but not too sensitive to send the sweep line off screen, for more accurate measurement.
Record the DC voltage as read from the screen. This is how you measure the voltage of a
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waveform or pulse.
Now switch the polarity of the input voltage. What happens to the sweep line?
Switch the "Input" from "DC" to "AC". What happens to the sweep line? Why?
5. Connect the output of the function generator to the input of channel One. Turn on the
function generator. Set the waveform to sinusoidal wave and the frequency to kHz range. Try to
obtain a few periods of a stable sine wave on the screen by adjusting the time base and the
triggering level. Make sure the triggering source is set at Channel One. This is probably the most
challenging part of the experiment. If you have great difficulties in obtaining a stable waveform after
reasonable effort, get some help from your instructor.
6. Measure the period and the amplitude of the sine wave. Record the numbers.
7. Now change the sensitivity of the y axis and measure the amplitude again. Do you get
the same voltage? Which scale setting gives you the best measurement ?
8. Change the time base to the adjacent settings. You may need to readjust the triggering to stabilize
the waveform. What happens to the waveform ? Measure the period again. Do you get the same
value for the period ?
9. Now switch the waveform from sinusoidal to square wave. There is a switch on the
waveform generator for choosing the waveforms. Measure the pulse height, the period and the pulse
width of the squarewave. Record the data.
10.
Repeat step 9 with a sawtooth waveform.
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Experiment 26. I-V Curves of Non linear Device
Objective:
To study the method of obtaining the characteristics of a non linear device, and to learn the
rectifying feature of the diodes.
Apparatus:
diode, adjustable DC power supply, resistor (200 ohms or so), computer and interface, voltage and
current sensors.
Theory:
Resistors and capacitors that we studied in the previous experiments are called linear devices
because the voltage across such a device is linearly proportional to the current passing through it.
However, many devices that play important roles in electronics are non linear devices.
Indeed, physics would be dull and life most unfulfilling if all physical phenomena were linear. As a
matter of fact, a linear device is linear only under certain conditions and within certain limits, as we
saw in the experiment of temperature dependence of resistance. In this experiment we will study one
of the simplest but not the least important non linear device -- a diode, and obtain the I-V curve of it.
A diode is made of two pieces of semiconductors, an n-type semiconductor and a p-type
semiconductor, in direct contact. The n-type semiconductor is electron-rich while the p-type is holerich. The region in which the semiconductor change from p-type to n-type is called a junction.
This junction creates a potential barrier that favors the current to run one way and impede it to run
the opposite way. When the positive terminal of a battery is connected to the p side of the junction,
the current can easily pass through and the diode is said to be forward biased. If the positive terminal
of the battery is connected to the n side, however, it is very difficult for the current to pass and the
diode is said to be reverse biased. The direction of bias is usually marked on the casing of the devise
or by the asymmetrical shape of the casing itself.
Figure 1 shows the characteristics of a typical diode. It is a plot of the current versus the
voltage. When the voltage is forward biased, the voltage across the diode is very small, about 0.5
volts for the germanium diode and about 0.7 volts for the silicon diodes. (The voltage drop across a
diode is more important than its resistance in most applications.) The working current of a diode
changes dramatically, ranging from less than one mA to more than a kA, depending on its
application. When the diode is re
for
avalanche breakdown voltage. If the reverse voltage exceeds the avalanche voltage, the current
would increase dramatically like the snow current running down hill in an avalanche, and it usually
kills the diode. It is therefore to stay safely below the avalanche voltage in your applications. The
breakdown voltage is listed in the semiconductor catalogue books and should be on the data sheets
attached to the purchased diode.
There is, however, a special type of diodes known as Zener diodes capable of recovering
from the avalanche if the current is kept too great. It is used to provide voltage references because
the avalanche voltage across a Zener diode is relatively stable within a great range of current. The
maximum allowed operating current of a Zener diode is specified in the catalogue books or the data
sheets.
The most important application for the regular diodes is rectification. A rectifier is a device that turns
an AC voltage into a DC voltage, which we will study in the next experiment.
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Procedures
1. Construct a circuit shown in Figure 2 and set up the computer system for the I-V Curve
2. Turn on the power supply and give a voltage of about one volt. If the current is practically zero,
then reverse the diode to forward bias it. The forward current should be a few mA depending on the
resistance of the resistor.
4.
Whence the diode is forward biased, then start from zero voltage and gradually increase to 5
Volts. The data should be automatically collected and a curve shown on the screen.
5.
Try to fit the curve into an exponential function and get the parameters. Include not only the
straight part, but almost the whole length of the curve in your curve fitting.
6. Now reverse the diode so that it is reverse biased. Repeat steps 3 and 4. Remember to
keep the voltage below 5 V. The current should be practically zero since the current sensor is not
sensitive enough to detect a current less than 1 mA. Get a hard copy of the plot, but you do not have
to do curve fitting for the reverse biased data.
7. Make a plot manually to combine the forward biased and the reverse biased data and
make a single plot. This is characteristics curve of the diode.
135
Questions
1. How well does the data fit to the exponential function ?
2. Can you come up with an idea to make use of the characteristics of the diode?
136
Experiment 27: Radioactivity Simulation
th
References: Modern Physics, (Tipler & Llewellyn, 4 ed.) Chapter 11, pp. 522–5377.
Introduction
The nuclei of many artificially created and of a few naturally occurring isotopes are unstable and
spontaneously change into other nuclei by the emission of α−particles, β−particles and γ−ray
photons in the process of radioactive decay. The rate at which decays occur, or number of decays per
unit time, is called the activity of the radioactive source. The half-life of a radioactive substance is the
time required for its activity to be reduced by one half. The intensity of the radiation detected
depends on the distance between the detector and the source (via the inverse square law) as well as
the activity of the source itself.
The probability of nuclear decay is determined by the interactions among the various components
within the nucleus, and because the forces among the nuclear par-ticles are so strong, external forces
do not usually play a role. Consequently, the prob-ability of decay is independent of external
circumstances, such as the number of other nuclei present, and the number of nuclei of the original,
or parent, isotope is a decreas-ing function of time. For example, if 100 million nuclei were present in
a sample, we might expect 100 of them to decay in the next second. If only 50 million nuclei were
pre-sent, we would then expect 50 to decay in the next second. At each moment, the activ-ity of the
source, A, is proportional to the number of parent nuclei, N, remaining at that time:
where λ is called the decay constant. The negative sign indicates that the number of parent nuclei
decrease with time. Integration of equation (4.1) leads to the result that
where is the initial value of . Moreover, since the activity of the sample is propor-tional to N, we can
also write 0NN
where is the initial activity. The half-life, 0A21t, of a radioactive isotope can be derived from equation
(4.3) by setting A/A0
NOT: Because of the statistical nature of radioactive decay, there is an uncertainty inherent in every
count that is obtained. Repeated counts, under identical conditions, follow a Pois-son distribution.
Furthermore, the standard deviation of the Poisson distribution is equal to the square root of the
average number of counts. Consequently, the error in any sin-gle count is taken as the square root of
that count. Therefore, it is advantageous to maximize the number of counts in order to reduce the
137
error. To illustrate this, note that if 100 counts were obtained, the uncertainty would be 10 counts —
or 10%. If 10,000 counts were obtained, the uncertainty would be 100 counts — only 1 per cent.
Units: An activity of one disintegration per second is called a becquerel (Bq). An older unit of activity
10
still in use is the curie (Ci), equal to 3.7 x 10 disintegrations per second. A common subunit is the
-5
microcurie: 1 μCi = 37,000 Bq and 1 Bq = 2.7 x 10 μCi.
M) tube connected to a pulse counter. A G–M tube is a cylindrical tube with a thin mem-brane on
one end containing a low-pressure gas. A wire through the central axis of the tube is held at a high
positive potential. When ionizing radiation enters the tube, the electrons freed through ionization are
attracted to the positively charged central wire. As they move toward the wire, the electrons ionize
other atoms through collisions, thus freeing more electrons which are also attracted to the central
wire and which in turn ion-ize other atoms. The resulting cascade of electrons produces a small
electrical pulse that is amplified and counted by a scalar–timer.
T
N
Log N
0
1
2
3
4
5
6
7
8
9
10
11
12
Simulations
http://phet.colorado.edu/en/simulation/alpha-decay
http://visualsimulations.co.uk/software.php?program=radiationlab
138
139
REFERENCES
-
Serway, Fen ve Mühendislik için Fizik I
Serway, Fen ve Mühendislik için Fizik II
H. Resnick, Fiziğin Temelleri I
H. Resnick, Fiziğin Temelleri II
İ. Eşme, Fiziksel Ölçmeler ve Değerlendirilmesi
www.pasco.com
http://www.yok.gov.tr/egitim/ogretmen/kitaplar/kimya/unite12.doc
http://fzk.fef.marmara.edu.tr/
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