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Physics 203
Lab Manual
PCC Rock Creek
Fellman
2
Table of Contents
General Instructions for Lab Reports……………………………………………………………..……3
Uncertainty Analysis and Propagation………………………………………………………………….4
Lab 1 Electrostatics………………..…………..……………………………………………………………… 6
Lab 2 Electric Field Mapping……….…………………………..……………..………………………….8
Lab 3 Use of Energy………….….………………………………………………………………….……….10
Lab 4 Introduction to Circuits…….…………………………………………………………………… 11
Lab 5 More Circuits (Kirchhoff’s Rules)……………….…………………………………………….. 13
Lab 6 RC Circuits………………………………………………………………………………………………. 15
Lab 7 Magnetic Fields………………..……………………………………………………………………… 16
Lab 8 The Wheatstone Bridge….……………………………………………………………………….19
Make-Up Lab Lenz’s Law in a Pipe…………………….………..………….………………………..20
Sample Lab Report A…………………………………………………………………………………………. 21
Sample Lab Report B…………………………………………………………………………………………..25
3
General Instructions for Lab Reports
For every lab completed, each person will be responsible for handing in a lab
report. These reports will be due one week from the day the exercise is completed, at
the beginning of class. Reports may be typed or handwritten as long as they are
neat, easy to follow, and contain the following elements:
Purpose - What you hope to accomplish through the exercise, in your own words.
Procedure - Brief procedural notes in your own words. It is not acceptable to simply
write “We followed the instructions in the lab handout.” Instead, your report should
outline the steps you followed in enough detail so that it would make sense to a
person who has never seen the lab instructions.
Data - All original data in a well organized format.
Uncertainties - The range of possible values associated with every measurement
you take. (Ex: 3.5 cm  .1 cm) These uncertainties are usually due to precision
limitations of measuring equipment and will also propagate through calculations. (See
uncertainty handout.) Remember: Every measurement we take in the lab has an
uncertainty associated with it.
Calculations - Include formulas, sample calculations, and results of all calculations.
Graphs - (When appropriate) With clearly labeled axes.
Diagrams - (When appropriate) Free body diagrams, electric circuit diagrams, etc.
Sketches of Equipment - (Always appropriate) Also include a basic diagram of the
experimental setup if applicable.
Comments - Your thoughts and observations throughout the process.
Results - Clear statement of results.
Conclusion - The most important part!!! Almost anything will do as long as it shows
that you thought about it. Examples: What did you learn? Did the results make
sense? If not, what are the possible reasons? Relate the concept to an everyday
experience. Relate it to something in the text. (Get the idea?) The conclusion should
be at least a paragraph.
** Note that with the exception of the purpose (at the beginning of the
report) and the conclusion (at the end), these elements should not each be
contained in a separate section of the report, but instead will flow naturally
throughout the report. Please see the sample lab reports at the end of this
booklet **
Once again, neatness is VERY important. A well organized, easy to read report
with moderately good results will receive a higher grade than a report with excellent
results that are hidden in scribble.
4
Uncertainty Analysis and Propagation
Every measurement has a range of uncertainty associated with it. This uncertainty
is usually a result of precision limitations of the instrument used to make the
measurement. Any calculations done using a measurement will also have a degree of
uncertainty. This is a measure of how confident you are in the result of your
calculation. The propagation of the uncertainties through various calculations has to
be carefully considered.
One way to proceed with the concept of uncertainty propagation is called the
“Worst Case Calculation”, and is shown in the following two examples.
Example #1
Length = 93.10 cm  .05 cm
Width = 3.540 cm  .003 cm
Area = L  W = (93.10 cm)(3.540 cm) = 329.6 cm 2
Worst cases:
L & W both largest possible value:
Area = (93.15 cm)(3.543 cm) = 330.0 cm2
L & W both smallest possible value:
Area = (93.05 cm)(3.537 cm) = 329.1 cm2
(+.4 cm2)
(-.5 cm2)
Report final result as: 329.6 cm2  .5 cm2
Example #2
Mass = 32.32 g  .01 g
Volume = 18.8 cm3  .1 cm3
Density = M / V = 32.32 g / 18.8 cm3 = 1.72 g/cm3
Worst cases:
Largest M / Smallest V:
Density = (32.33 g) / (18.7 cm3) = 1.73 g/cm3
Smallest M / Largest V:
Density = (32.31 g) / (18.9 cm3) = 1.71 g/cm3
Report final result as: = 1.72 g/cm3  .01 g/cm3
(+.01 g/cm3 )
(-.01 g/cm3 )
5
On the other hand, when your data consists of a number of measurements to be
averaged for a final result, the uncertainty can be reported as the standard deviation.
Example #3
You are measuring the range of a projectile. The experiment has been repeated 5
times, yielding 5 different distances: 3.41 m, 3.69 m, 3.33 m, 3.57 m, and 3.50 m.
First find the average:
_
x =  xi = (3.41+3.69+3.33+3.57+3.50)m = 3.50 m
n
5
Now find the standard deviation:
_
st. dev. =
 (xi - x )2
=
(n-1)
_
x
3.50 m
3.50 m
3.50 m
3.50 m
3.50 m
xi
3.41
3.69
3.33
3.57
3.50
m
m
m
m
m
_
(xi - x )
- .09 m
+.19 m
- .17 m
+.07 m
.00 m
.078 m2
4
=
.14 m
(xi - x )2
.0081 m2
.0361 m2
.0289 m2
.0049 m2
.0000 m2
.078 m2
(The standard deviation may also be obtained by using your calculator’s standard
deviation function.)
Report final result as: 3.50 m  .14 m
*******************************************************************
Notice the appropriate use of significant figures and decimal places in the three
examples above:
*Each final result has no more significant figures than any measurement involved in
the calculation.
*The smallest decimal place of the uncertainty matches the smallest decimal place of
the measurement or result.
6
Lab 1
Electrostatics
Today’s lab is qualitative in nature and is intended to give you practical experience in
electrostatics. It will also serve as good practice for writing properly detailed,
descriptive lab reports. Be sure to include all of the appropriate elements in your
report. Because this experiment is qualitative, most of your data and results will be in
the form of detailed comments and pictures complete with indications of the signs of
the various charged objects.
1) Pull a couple of strips of scotch tape quickly from a roll. Each one should be the
same length (about 15 cm long). Hold them up by their ends, then slowly bring
them side by side. What happens? What is the reason for their behavior? Do
they carry opposite or like charges?
2) One at a time, pass each of the strips of tape slowly and completely between your
fingers, then hold the two strips near each other again. Now what happens?
Why?
3) Fold over a couple of centimeters of the end of each strip. This gives you a nonsticky handle to work with. Carefully stick the two strips to each other so the
sticky side of one strip adheres to the dry side of the other. Now grasp the tabs
and rapidly peel the strips apart. Keep them distantly separated, then slowly bring
them together again. Now what happens? Do they carry opposite or like charges?
Were they charged before you pulled them apart? Where did the charge come
from? Does their total amount of charge change?
4) Neutralize both pieces of tape again by rubbing them, and then repeat the
previous step, this time with the sticky sides together. Does it work? Why or why
not?
5) We know that when rubbed against your hair, a balloon becomes negatively
charged (i.e. takes electrons from your hair). Now blow up two balloons of the
same color, and inflate them to the same size. Do not rub them against your
hair or clothing yet. Considering what happened in the previous step, do you
think that you can create static electricity by rubbing the two electrically neutral
balloons together? Why or why not? Try it.
6) Remember in step 1 you were able to recognize that the tape was charged, but
unable to identify whether it was positive or negative. Now, using a balloon,
devise an experiment to determine the sign of the charge on a piece of tape after
it is pulled from the roll.
7) Now using a similar method, determine which side of the tape tends to give up
electrons, and which side tends to steal them.
8) Paper is a reasonably good conductor compared to plastic tape. Explain why
masking tape does not work well for this activity.
9) Now, referring to the material presented in the lecture and textbook, use the clear
plastic rod, glass rod, fur, silk, and any other necessary materials to devise a
method of observing the attraction between the positively and negatively charged
rods. (Hints: This effect may require precise conditions to be noticeable, but you
will definitely know when you’ve got it. Make sure that you don’t accidentally
ground the rods by direct contact with your hands. Also, if you are trying to see
movement of one of the rods, consider their relative masses.) Be sure to show me
when you have found a way to observe this effect.
10) Now incorporate the black plastic rod in order to witness the repulsion between
like charges. Are the objects in this step charged negatively or positively?
7
11) What happens when you bring a neutral, metal object (not in direct contact with
your hand) close to a suspended charged object? Give a detailed explanation of
what is happening on an atomic level. What term describes this phenomenon?
Should your observation depend upon the type of charge on the suspended object?
12) What happens when you charge the clear plastic rod, then hold it close to a lightly
running stream of tap water? Why?
13) Steps 11 and 12 involved induction with materials known to be good conductors.
Interestingly, this can be observed even in materials that are not good conductors,
although the molecular interaction is slightly different in this case. Balance the
center of mass of a meter stick on the edge of your table so that the end on the
table just barely rises off of the surface. Now charge the clear plastic rod and
bring it slowly up under the lower end of the meter stick. Surprised? Explain how
this could happen even though the electrons in the wood are not free to move
throughout the material.
14) Rub a balloon against your hair so that it will stick to the wall. The wall is not a
good conductor, so the mechanism here is the same as in the previous step. Draw
a picture of the wall and balloon indicating as usual the role of the charges
involved.
15) I have read (however not yet verified) that different colored balloons retain charge
to a different extent because of the various dyes used. Design an experiment to
test this claim, and rate the different colors.
16) By now, you have no doubt discovered that if you touch a charged object with
your hand it discharges, and that if you use rubber gloves, it does not. This is
because your hand is a good conductor and the gloves are not. Devise a method
to rate, in order, the conductivities of the following four materials: paper, the table
top, your hands, and tap water.
17) An electrophorus sounds like a complex piece of equipment, but it’s actually just a
plastic square and an aluminum disk with an insulating handle. Charge the plastic
square by rapidly and repeatedly whipping the fur across its surface. Then place
the aluminum disk directly on top of it. While still in place, touch the top of the
aluminum with your fingers while touching another metal object (preferably a large
one) with your other hand. You should feel a very small spark. Now remove the
disk holding only its handle. The disk is now charged. Determine whether is
contains a positive or a negative charge.
18) In the previous step, does the disk still become charged if you skip touching it
with your fingers? Speculate on the reasons for this process, including an
explanation for the sign of the charge on the disk, and when you think you have an
answer check it with me.
8
Lab 2
Electric Field Mapping
The field mapping apparatus makes use of an electric potential between two
electrodes. This configuration creates a 2-dimensional electric field that can be
sustained for as long as it takes to map the equipotential surfaces (or in 2-D,
equipotential lines).
You will use an electric potential meter (commonly known as a volt meter or
Galvanometer) to find points on the paper that have no potential difference between
them. In other words, you are locating the positions of the equipotential lines.
General instructions for all maps:
1. Obtain a battery, galvanometer and a field mapping kit which contains:
a. Mapping board
b. U-shaped probe
c. 2 clear plastic templates
d. 5 plates with various designs
2. Turn the mapping board over and remove the 2 thumb screws. Center one of the
plate designs so that the design faces you and line it up with the screw holes.
Replace the thumb screws, turning until they touch the board.
3. Flip the board back over. Connect the battery to the two posts marked Battery.
4. Place a piece of graph paper on the surface, sliding the corners under the rubber
stoppers to hold it in place.
5. Select the design template containing the field configuration you have chosen.
Place the template on the two small metal projections along the top of the board.
Trace out only the appropriate design corresponding to the field plate you have
selected. Now remove the template.
6. Look carefully at the U-shaped probe. Slightly loosen the screw with the silver
knob near the open end of the probe so that the screw is just protruding
underneath. You can tighten this later if necessary. Also make sure the silver
support screw at the hinge end of the probe is screwed most of the way down. This
screw helps keep the probe level.
7. Bend the probe open slightly and slide the probe onto the board so that the ball
end is facing the underside of the board. Connect one lead from the Galvanometer
to the probe (black connector at the hinge end), and another lead the banana jack
numbered E1.
8. You are now ready to trace out your equipotential lines. Guide the probe with a
finger from one hand resting lightly on the sliver screw nob at the open end of the
probe, and use your other hand on the support leg to guide the probe around the
page. DO NOT APPLY PRESSURE to the probe and avoid squeezing the jaws of
the probe as this will cause unnecessary wear on the plates.
9
9. Move the probe till you find a null point (zero on the Galvanometer). This tells you
that this point is at the same potential as point E1. Record the location of this point
by putting your pencil through the circular hole at the end of the probe. Continue
this procedure until you have a sufficient number of points to draw an accurate
equipotential line.
10. Repeat the above procedure for all of the banana jacks E1 through E7. Since the
potential difference is the same across each similar resistor, the equipotential lines
will be spaced to show an equal potential drop between successive lines.

Repeat the above procedure for each of the 5 designs:
a. Parallel plate
b. Two point
c. Point and plate
d. Faraday Ice Pail (point and “bucket”)
e. Insulator and conductor in a field

You should now have 5 separate pages with equipotential lines for each
configuration. Add E-field lines to each diagram.
Remember:
o the electric field is perpendicular to the equipotential surfaces.
o the electric field lines will never cross one another.
o give the direction of your E-field lines.
o Label which pole is positive, and which is negative, on your sketches.

Now answer the following questions:
a. Why are the E-field lines near the conductor surfaces perpendicular to the
surface?
b. Why is this not the case near the insulator surfaces?
c. For the parallel plate and two point configurations look at the distance between
adjacent equipotential lines on a straight line between the electrodes. Explain
why the equipotential lines are evenly spaced (or not) by looking at the
equations for calculating potential (V) in each case.
10
Lab 3
Use of Energy
Part I
Most household appliances (lightbulbs, TV, microwave, hairdryer, alarm clock, etc.)
are either labeled with their wattage, or their current. If they are labeled with their
current, you can calculate the wattage using the relationship P = iV, and the fact that
household voltage is generally around 120 V.
Choose 10 appliances from around your home, and list the wattage for each one.
Then estimate the number of hours per month each is generally in use. This will allow
you to arrive at a figure for the number of kiloWatt hours of energy that is used by
each one. Refer to your own electric bill, or use the textbook’s value of $0.12 per
kWhr. Calculate the cost per month for each item. What percentage of your electric
bill does each of the 10 items account for?
Part II
You may have noticed that most packaged foods are labeled with their Calorie
content per serving. (1 Calorie = 4186 Joules of energy.) The Calories that we
consume are burned off at different rates by various activities. (See list below.)
Find the number of Calories per serving for 5 different foods, and calculate the amount
of time you would have to participate in various activities to burn them off.
Part III
Choose your favorite appliance from part I and your favorite food from part II. If
by some miracle you were able to run electrical appliances with the energy you
obtained from food, how many servings of this food would you have to eat to run this
appliance for 1 hour?
Activity & Calories/10 min. **
Aerobics (traditional at high intensity)
Gardening
Racquetball
Running (9 min/mile)
Shopping
Sitting (reading or watching TV)
Sleeping
Standing (light activity)
Volleyball
Walking (15 min/mile)
Walking upstairs
125 lbs
95
41
75
109
35
10
10
20
28
44
150
150 lbs
115
49
90
131
42
12
12
24
34
52
175
175 lbs 200 lbs
134
153
57
65
105
120
153
174
49
56
14
16
14
16
28
32
40
45
61
70
202
229
**More activities may be looked up at http://www.myfitnesspal.com/exercise/lookup
11
Lab 4
Introduction to Circuits
Today we will be using a multimeter to measure voltage, resistance, and current. The
multimeter is a very useful device that many of you have probably used outside of this
class. We will be utilizing it to explore the relationships between voltage, resistance,
and current in a circuit. This lab will also give you experience with the common color
band labeling system used for resistors, and finally experience working with building
circuits on a breadboard.
1) Measure and record the voltages of two different batteries. Use these values
rather than the labeled voltages in the calculations that follow. What happens if
you accidentally reverse the leads of the multimeter when measuring voltage?
2) Choose 5 mounted resistors, and for each one determine the resistance from the
color bands. Also record the uncertainty rating from the fourth band. Now
measure the resistance of each one using the multimeter. Are the values within
the acceptable range?
3) Choose two resistors of the same order or magnitude (the third band of the same
color). Using alligator clips, connect them in series and measure the resistance of
the combination. What is the rule for adding resistors in series (in other words,
finding the equivalent resistance)? Verify this with several other series
combinations.
4) Using two resistors of the same order of magnitude once again, this time measure
the resistance of a parallel combination. What is the rule for adding resistors in
parallel? Verify this with several other combinations also.
5) How do the rules for adding resistances differ from the rules for adding
capacitances?
6) Recall that increased resistance results in decreased current and vice versa. Using
an analogy between traffic on the freeway and current in a circuit, give a physical
explanation of why the equivalent resistance is greater or smaller for both types of
combination (series and parallel).
7) Construct a circuit consisting of a battery
and a resistor. Before measuring current,
always calculate the current you expect so
that you do not exceed the current
limitation of the multimeter. Also,
remember that you must break the circuit
to measure current. Failing to do either of
these things may blow a fuse in the meter!
Now measure the current. Do the
measured and calculated values agree
within the uncertainty?
8) Now construct another circuit, this time
containing two resistors (of roughly the
same order of magnitude) in series.
Measure the current at several different
places in the circuit. What can you
conclude about the current in a single-loop
circuit? With the circuit still connected,
measure the voltage across each resistor.
What is the sum of these two voltages?
How does this compare to the voltage of
the battery? What can you conclude about
12
the voltage across elements in a singleloop circuit?
9) Now construct one more circuit,
this time containing the same two
resistors in parallel. Measure the
current through the battery. Then
measure the current through the
first resistor, and finally the second
resistor. What is the sum of the
two resistor currents? How does
this compare with the current
through the battery? What can
you conclude about the currents in
a circuit with two loops?
With the circuit still connected, measure the voltage across each resistor. How do
each of these voltages compare to the voltage of the battery? What can you conclude
about the voltages across circuit elements in parallel?
10) Now that you have constructed several different circuits on a large scale using
mounted resistors, batteries and alligator clips, you should familiarize yourself with
the more common breadboard design, as we will be using this in the future. Obtain
one of the electronics kits (these are smaller and should be shared by two people
instead of four). Each kit should be accompanied by a power supply and a small box
of resistors and connecting wires.
Important: Don’t ever jam the multimeter leads into the little holes on the
breadboard!!!!! Instead, you will be measuring current and voltage by simply
touching the leads to the metal part of the connecting wire that is left slightly exposed
when the wire is plugged in.
First, familiarize yourself with the layout of the circuit board (i.e. which holes are
connected to each other). Do this by consulting the diagram on the board, and then
verify it yourself by using your multimeter’s continuity function (each meter is a little
different, so please ask for help if needed).
When the power supply is connected, the kit has its own voltage source. Instead of
using a battery, you will use the gnd and +V holes printed on the breadboard. The
voltage can be adjusted using the sliding +V knob.
To make sure that you understand the circuit board, reconstruct each of the three
types of circuits from today’s lab using the small resistors that fit into the breadboard
holes. Measure voltage and current in various locations until you are convinced that
the circuits you have constructed indeed match the circuit diagrams.
13
Lab 5
More Circuits (Kirchhoff’s Rules)
R1
a
R3
R2
R5
b
R4
1) Connect the circuit shown using 5 resistors and a voltage source. Record the
resistance values in a table like the one below.
Resistance ()
R1
R2
R3
R4
R5
Requiv
Voltage (V)
V1
V2
V3
V4
V5
Vbattery
Current (amps)
I1
I2
I3
I4
I5
Ibattery
2) With no current flowing (the voltage source disconnected), measure the total
resistance of the circuit between points a and b, and record this value in the data
table. Try to calculate the equivalent resistance. Why can’t this be done?
3) With the circuit connected to the voltage source and the current flowing, measure
the voltage across each of the resistors and record the values in the table. On
your circuit diagram, indicate which side of each of the resistors is at a higher
potential by placing a “+” at that side and a “-“ at the other. Also record the
measured voltage of the voltage source in the table.
4) Now measure the current through each of the resistors. Remember that you must
interrupt the circuit and place the multimeter in series to obtain your reading.
Record each of the individual currents, as well as the current flow through the
voltage source.
5) Referring to the data table and circuit diagram, show that the junction rule is
obeyed at each of the four junctions. Do this BEFORE the circuit is dismantled so
that if your data doesn’t yield good results, we can figure out why.
6) Now show that the loop rule is obeyed around the three independent loops in the
circuit. Do this part also BEFORE the circuit is dismantled.
14
7) Now build the circuit shown below, and label the 3 distinct currents on the
diagram.
R2
A
R1
R3
R4
B
8) This time calculate the expected values for the 3 different currents BEFORE
actually measuring them.
(Hint: You could start by calculating the equivalent resistance for the whole circuit,
using that value to solve for Ibattery, then finding VAB. After that, solving for the
remaining 2 currents should be easy.)
9) Now measure all 3 currents and verify that their values agree with your
calculations within experimental uncertainty.
15
Lab 6
RC Circuits
An RC circuit is one containing a DC voltage source, a resistor and a capacitor all in
series. At the instant when the circuit is first connected, the current flows as
expected. As charge begins to build on the capacitor, the current decays until the
capacitor is fully charged, at which point no current flows in the circuit. The time for
the current to decay to 37% (1/e) of its initial value is called the time constant, ,
where
 = RC .
1) Construct a series RC circuit using a capacitor and resistor of your choice (choose
their values such that the charging will take place over a long enough time interval
to measure accurately, but not longer than 30 seconds). Also, notice that some of
the capacitors are marked with a specific polarity. For these, make sure you
connect the negative end of the capacitor closest to the ground of the voltage
source.
2) Describe the way in which the current changes with time after the circuit is first
connected.
3) Now break the circuit by disconnecting one of the wires. When you reconnect it,
does the current return to its initial value? Why or why not? What would you
have to do to start the experiment from the beginning again?
4) After letting the circuit run long enough for the current to decrease to zero, what
must be the value of the charge on the capacitor?
5) Now practice discharging the capacitor by simply removing the voltage source from
the loop. Be sure that the resistor remains connected whenever you are
discharging the capacitor. Describe the way in which the current changes as the
capacitor is being discharged. How do you know when it is completely discharged?
6) Now consider your original (charging) circuit. Calculate the current that you would
expect in this circuit if the capacitor was not present. This should be close to the
initial current value. Verify that it is.
7) Calculate 37% of this initial current, and measure the time it takes for your circuit
to reach this value. Do several trials and average the results.
8) Now compare your results from the previous step to the theoretical value for the
time constant. Are your results consistent with theory? If not exact, what could
be the reason?
9) Using your experimental data, calculate the actual value of the capacitor. Does it
fall within the given uncertainty range?
10) Now test the value of the capacitor you just calculated by using it in an RC circuit
with a different resistor. Again, calculate 37% of the expected initial current, then
take the average of several measurements of the time required for the current to
decrease to this value, and compare this to the theoretical time constant for the
new circuit. This time your values should be very close.
11) Now repeat the process of experimentally determining the capacitance for two
other capacitors in your kit.
12) Finally, using one of your previous RC circuits, allow the capacitor to become fully
charged. Then carefully disconnect the circuit without discharging the capacitor,
and reassemble it without the voltage source. What should the initial current in
this new (discharging) circuit be? Is it?
13) How long do you think it takes for the current in this new circuit to decrease to
37% of its initial value? Make an educated guess, and test your answer.
16
Lab 7
Part A
Magnetic Fields
Magnetic Field Mapping
In this lab you will be taking measurements of both the magnitude and the direction of
various magnetic fields. In each case, there will be a large number of measurements
taken, so make sure that everyone in your group has a turn at using the equipment
and recording data.
1. First connect the Magnetic Field Sensor to the computer interface box. This needs
to be done at least 15 minutes before it is used to take any data, since thermal
equilibrium is required to obtain the most stable measurements. You will have plenty
to do in the meantime...
2. Place a single bar magnet in the center of a piece of blank paper, and trace around
its shape so that it doesn't get moved accidentally. Note that the magnet is marked
with either North and South poles, or simply a white dot to indicate North.
3. Before you begin taking measurements, make sure that you move all other
magnets as far away as possible! (The other end of the table should be fine.)
4. Place the compass anywhere on the paper, noting the direction it points at that
location. Lift up the compass and draw a very short line in this direction, where the
center of the compass had been. Repeat this process for roughly 30-40 randomly
spaced locations around the paper.
5. You will eventually be sketching in the long, curving lines of the magnetic field
using all of these short lines as a direction guide. Before this can be done, however,
you will need to take many more direction measurements, especially in those areas of
the page where the magnetic field is curving most noticeably. Continue drawing these
short lines until you are confident that you will have enough information to sketch in
the long, curving lines of the magnetic field.
6. Now, sketch in the magnetic field lines, keeping in mind that all of the lines should
originate at or very near the poles of the magnet. In addition, use arrows to
indicate the direction of the magnetic field. Your field lines should be dense enough
that they are spaced roughly an inch apart by the time they reach the edge of the
paper. Also, don't worry if your magnetic field lines fail to cover all the short lines.
Remember, the short lines were only placed there as direction guides.
7. After you are finished drawing magnetic field lines, use a ruler to draw a single,
straight line that goes directly through the center of the magnet, dividing North from
South, and dividing the paper in half. (Folding the paper first may help to locate the
exact center of the magnet.) We will be needing to reference this line later.
8. Now that you have a map showing the direction of the magnetic field, we will begin
taking measurements of its magnitude. First, make sure the switch on the magnetic
field sensor is set to axial. This means it will be measuring the strength of the
magnetic field that is parallel to the length of the probe. Also check to be sure that
the ‘range select’ on the sensor is set to ‘1x’ since that is the default value for the
software.
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9. Select to view data from the Magnetic Field Sensor using the 'Digits' display
option in the Data Studio software. Press the start button on the screen, then zero
the sensor by holding it as far as possible from any magnets or equipment, and
pressing the 'tare' button. Once the sensor has been zeroed, place it flat on the table
with the “Magnetic Field Sensor” label facing up for all measurements.
10. In order to begin taking magnetic field measurements, hold the very tip of the
sensor near the North pole of the magnet, and orient the probe so that it is parallel (or
more generally tangent) to the field line at that location. You can now move the
probe along the magnetic field lines and see how the strength of the magnetic field
varies across the entire page. Remember: the probe must always be held
tangent to a magnetic field line to record the correct value for magnetic field
strength at that location.
11. You will now be indicating the magnitude of the magnetic field on your previously
drawn map by adding colors to the field lines in order to represent magnetic field
strength:
Magnetic Field Magnitude (in gauss)
gauss)
40
to 400
15 to 40
5 to 15
0 to 5
-40 to -400
-15 to -40
-5 to -15
0 to -5
Color
Dark Red
Light Red
Orange
Yellow
Dark Blue
Light Blue
Medium Green
Light Green
These colors will
be on the
North
side of the page
These colors will
be on the
South
side of the page
12. Repeat the same mapping process (steps 2 through 11) to create a similar
magnetic field map for the larger horseshoe magnet.
13. Considering the magnetic field maps you have just made (the bar magnet and the
horseshoe magnet), comment on the most significant similarities as well as the most
significant differences between the two fields.
14. Now place two bar magnets end-to-end (North to South) on a blank piece of
paper, and use the compass as before to create a map of the magnetic field
surrounding the magnets (no colors necessary this time - we're just looking for the
shape of the field). Compare this to the field obtained earlier for a single bar magnet.
15. As a result of what you observed in the previous step, sketch (to scale) the
magnetic field that you would expect to find surrounding half of a bar magnet.
Part B Graphing Magnetic Field Strength vs. Distance
16. Close the 'Digits' display window, and select to view data using a 'Graph' display
for this section. The computer will now display a graph of Magnetic Field vs. time. By
18
moving the probe away from the magnet at a constant slow speed, you will be
obtaining graphs which can be interpreted as representing Magnetic Field vs distance.
17. Pull the sensor directly away from the North pole of a bar magnet at a constant,
slow speed. Does the strength of the magnetic field have a linear relationship with
distance?
18. Draw a sketch showing the shape of the graph.
19. How does the slope of the magnetic field graph change as you move the sensor
away from the magnet?
20. What does this change in slope tell you about the rate of change of the magnetic
field strength as you move relative to a magnet?
21. Now flip the magnet around, and pull the sensor directly away from its South pole
at a constant, slow speed.
22. How does the magnetic field graph change when the bar magnet is flipped?
23. Use these graphs to explain why the colors had to be assigned unequal magnetic
field ranges in order to utilize all colors more evenly in the magnetic field maps that
were created in Part A.
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Lab 8
The Wheatstone Bridge
The drawing below shows a diagram of a wheatstone bridge:
R1
a
Rx
b
G
R2
c
R3
d
Resistors R1, R2, and R3 have known values, and resistor Rx is an unknown. The G in
the middle stands for galvanometer, a device used for sensitive measurement of
current. The bridge is said to be balanced when the galvanometer reading is zero.
When this is the case, there is no current flowing through the galvanometer, and so
points b and d must be at the same potential.
1) If we let I1 be the current in the top branch of the circuit, and I2 be the current in
the middle branch, show that when the bridge is balanced, Kirchoff’s loop rule results
in the following two equations:
I1R1 = I2Rx
and
I1R2 = I2R3
2) Now show that after a little algebra, this becomes
R x / R 3 = R1 / R 2
So if the values of R1, R2, and R3 are known, the value for the unknown, Rx, can be
calculated.
3) Construct a wheatstone bridge circuit as shown in the diagram, with R 2 and R3
being standard resistors, R1 as a variable resistor, and Rx as a resistor of unknown
value.
4) Vary the value of R1 until the galvanometer reads zero.
5) Use the values of R1, R2, and R3 to calculate the value of Rx , and then check your
answer by measuring the unknown resistance directly.
6) Repeat the process for 3 other unknown resistors.
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Make up Lab
Lenz’s Law in a Pipe
1) Observe the manner in which the two objects fall through the pipe. Considering
that they are the same size and shape, what could be the reason for their differing
behavior? When you have the answer, write a detailed explanation complete with
diagrams. Do the forces change when the object is dropped with the other end
first? Why or why not?
2) Draw free-body diagrams for both objects (blue and gray) as they are falling
through the pipe.
3) What object is exerting the upward force on the gray object as it falls? What does
this mean in light of Newton’s 3rd law?
4) Keeping your answers to part 3 in mind, devise a method of measuring the upward
force on the gray object as it is falling. When you have figured it out, measure this
force.
5) Now suppose you were wondering whether the object fell through the pipe at
constant velocity, or accelerated as it fell. First let’s assume that it accelerates.
Measure the length of the pipe and the time it takes for the gray object to fall the
entire length of the pipe. Assuming that the acceleration is constant, calculate its
value (you may have to think back a few chapters). Now consider your free-body
diagram from part 2, and apply Newton’s 2nd law to arrive at a theoretical value for
the acceleration. Do they match? What does this mean?
6) Now let’s assume that it falls through the pipe at constant velocity. If this is the
case, what must be the sum of the forces on the object? Again, consult your free
body diagram of the gray object. Considering your data, does this seem like a
more probable case?
7) Can you detect a magnetic field outside of the pipe as the gray object travels
through it? If so, use this to verify your results.
21
Sample Lab Report A:
Lab 4: Tension and Newton’s 2nd Law
Purpose: The purpose of this lab is to study the effect of tension in different
situations. First we will consider the tension caused by a hanging mass that is
connected to another mass resting on a flat surface. Since the two masses are
connected using a string of negligible mass running over a frictionless pulley, and one
of the masses is resting on a frictionless surface, we will be able to neglect friction.
During the second part, we will again neglect friction, but this time the hanging mass
is connected to a mass resting on an inclined plane. We will attempt to find the sum
of the forces acting on the cart which is on the inclined plane.
Procedure, Data, Calculations, Diagrams:
m1
Part A: Tension and Weight
m2
1. Using the computer interface, we measured the acceleration of the air cart
pulled by three different hanging masses. The air cart represented in the
drawing by m1, is resting on a frictionless surface and is connected to the
hanging mass m2, by means of a frictionless pulley. The pulley is also
interfaced with the computer and will be used to measure the acceleration of
m1. We measured the acceleration for three different hanging masses (m 2) of
20, 40, and 60 grams. The following table is the result of these tests:
Hanging mass m2
Acceleration of m1 (in m/s2)
20g
40g
60g
.795
1.447
2.006
2. Here is a free body diagram for our hanging mass, m2:
aa forces acting on the hanging mass
The only
are gravity, which is pulling the hanging mass
toward the ground, and the tension of the
string which is pulling the mass upward. The
tension in the string is present because of the
mass it is attached to on the flat, frictionless
plane.
T
m2
m2g
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3. Newton’s second law tells us that the sum of the forces acting on an object in
any one direction is equal to its mass multiplied by its acceleration in that
direction. Since both forces acting on the hanging block are along the vertical
axis, we can apply Newton’s second law to it as follows:
(sum of forces down) = (mass)(acceleration down)
(m2g-T) = (m2)(a)
Then, we can rearrange it to solve for the tension:
T = m2g – m2a = m2(g-a)
Since we used three different masses which resulted in three different
accelerations, we have to solve for three different values of T:
T(20g) = (.020 kg)[(9.8m/s2) – (.795 m/s2)] = .180N
T(40g) = (.040 kg)[(9.8m/s2) – (1.447m/s2)] = .334N
T(60g) = (.060 kg)[(9.8m/s2) – (2.006m/s2)] = .468 N
4. Next we will draw a free body diagram for the air cart:
In this case, the cart is resting on a cushion of air,
Thus the air cushion is where the normal force
is coming from. Since there is no motion in the
vertical direction, it is safe for us to assume that
T
the normal force, FN, is equal to and in the
opposite direction as gravity. Therefore these
two forces cancel each other out. At the same time,
since there is no friction, any amount of force acting
in the horizontal direction will produce an acceleration
for the cart.
FN
m1
m1g
5. Applying Newton’s second law to the cart tells us that the sum of the forces
acting in the horizontal direction will be equal to the cart’s mass times the
cart’s acceleration in the horizontal direction. Since the only force acting in the
horizontal direction is the tension, T, of the string, we can set up a relationship
between T, m1 and a:
(sum of the forces in the x direction) = T = (m1)(a)
 m1 = T/a
Now we are ready to predict a value for m1 for each of our three trial cases:
m2
T(m2)
a(m 2)
m1=T/a
20 g
.180 N
.795 m/s2
226 g
40 g
.334 N
1.447 m/s2
231 g
60 g
.468 N
2.006 m/s2
233 g
Averaging these results for m1, we get a value of 230 g.
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6. We measured the actual mass of the cart on the digital scale to be
221 g, so our average was only off by about 4%.
Part B: Tilted Air Track
7. Now we will tilt the air track so that the pulley end of the track is highest:
m1
m2
8. Since the cart is no longer on a level plane, gravity will now have some
effect in pulling the air cart towards the ground, or the lower end of the air
track. Therefore, to balance the cart we must apply a force in the opposite
direction, which can be accomplished by hanging a mass from the other
end. We had to hang 15 g on the string for the cart to remain in
equilibrium. At this point, since there is no motion in any direction, the
sum of the forces acting on the cart is zero.
9. Now we will give the cart an initial velocity by gently pushing it down the
track. Since the sum of the forces is zero before the push, it must also be
zero after the push, and therefore the acceleration should be zero also.
Using the computer interface, we measured an acceleration for the cart of
.004 m/s2, which is very close to zero. We would also expect the cart to
have zero acceleration (constant velocity) after the push in consideration of
Newton’s first law, which states that an object in motion will continue in
straight line motion if no force acts.
10. Now we will sketch a free body diagram for the cart. I have included the
original direction of the force due to gravity, but only with a dotted line as it
is resolved into the directions of the tilted x and y axes for our calculations.
FN
T
m1
m1gsin
m2gsin
m1g
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Conclusion:
Looking at the two separate parts of this lab, I find a common link: Newton’s second
law of motion, which tells us that the force acting on an object in any direction is
equal to the object’s mass times the object’s acceleration in that direction. Sure, it
sounds pretty straightforward, but as this lab has shown, we run into different kinds of
obstacles when applying this law. So what I have learned by doing this lab is that in
applying Newton’s second law, we must also consider the angle at which the object is
moving, as well as any kinds of frictional forces that may be resisting the object’s
motion, not to mention all the uncertainties involved in the motion of everyday objects
that we have not even considered in this lab.
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Sample Lab Report B:
Introduction to Circuits
Purpose: To explore the relationship between voltage, resistance and current in a
circuit.
Procedures & Comments:
1. Using a multimeter, measure and record the voltage of two different batteries.
Voltages
Battery 1
Battery 2
1.502 V
1.513 V
Battery Pak (1&2
combined)
3.010 V
If the leads are reversed when measuring voltage, the multimeter will display
the same magnitude but will indicate that the voltage is negative.
2. A. From their color bands, determine and record the resistance and the uncertainty
rating for five different resistors.
B. Measure and record the resistance with the multimeter.
Resistor Color Guide
Band Color
Black
Brown
Red
Orange
Yellow
0
1
2
3
4
Band Color
Green
Blue
Purple
Gray
White
5
6
7
8
9
Uncertainty: Silver = 10% ; Gold =  5.0%
Resistor:
Resistor
1
2
3
1. Red, Purple, Black, Silver
2. Red, Red, Yellow, Silver
3. Red, Purple, Red, Silver
4. Orange, Orange, Red, Gold
5. Brown, Green, Yellow, Silver
Determined
Resistance, 
27X10^0
22X10^4
27X10^2
Determined
Uncertainty, %
10
10
10
Measured
Resistance, 
30.0X10^0
23.2X10^4
29.0X10^2
Actual
Difference, %
10.0
5.17
6.90
26
4
5
33X10^2
15X10^4
5
10
33.2X10^2
15.2X10^4
0.60
1.32
All of the measured values fall within the range given by the color
bands.
3. Using two resistors of the same order or magnitude (the third band of the same
color), connect them in series and measure and record the resistance of the
combination. Repeat twice again with different resistors.
Equivalent Resistance = R1 + R2
Resistors
3&4
2&5
4&5
Measured Resistance, 
6.23X10^3
3.83X10^5
1.55X10^5
Calculated Resistance, 
6.22X10^3
3.84X10^5
1.55X10^5
4. Using two resistors of the same order or magnitude (the third band of the same
color), connect them in parallel and measure and record the resistance of the
combination. Repeat twice again with different resistors.
1 / Equivalent Resistance = 1 / R1 + 1 / R2
Resistors
3&4
2&5
4&5
Measured Resistance, 
1.55X10^3
9.18X10^4
3.25X10^3
Calculated Resistance, 
1.55X10^3
9.18X10^4
3.25X10^3
5. Rules for adding Equivalent Resistances and Capacitances in Series and Parallel
Circuits:
Series
Resistance:
R=R1+R2+R3+…
Capacitance:1/C=1/C1+1/C2+1/C3+…
Parallel
1/R=1/R1+1/R2+1/R3+…
C=C1+C2+C3+…
6. A series circuit acts like a one-lane highway and therefore all of the
traffic must pass along the same path, which resists and slows
down flow.
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A parallel circuit acts like a freeway and therefore the traffic
can always take the path of least resistance, which allows it
to flow freely.
7. Construct a circuit consisting of a battery and a resistor and
measure the current.
Resistor 3
Measured
Calculated
Voltage, V
Resistance, 
3.00 V
2.90X10^3
V/R=I
Current, A
1.03X10^-3
1.03X10^-3
Measured and calculated answers agree.
8. Construct a circuit consisting of a battery and two resistors, with
roughly the same order of magnitude, in series and measure the
current.
Resistors 3 & 4
Measured
Across
Current, A
Voltage, V
Battery
Resistor 3
Resistor 4
4.80X10^-4
3.00
4.80X10^-4
1.40
4.80X10^-4
1.60
28
In series the current must be the same through all elements. The
voltage measured across resistor 3 and 4 equaled 1.40 V and 1.60 V
respectively. The sum of these two voltages equals 3.00 V, which is
the same as the voltage of the battery. In series the sum of the
voltages through all of the elements must equal the power
source.
9. Construct a circuit consisting of a battery and the two resistors used
in procedure 8 in parallel and measure the current through the battery,
the first resistor and the second resistor. Then measure the voltage
across each resistor.
Resistors 3 & 4
Measured
Across
Current, A
Voltage, V
Battery
Resistor 1
Resistor 2
1.93X10^-3
2.99
1.03X10^-3
2.99
9.00X10^-4
2.99
In parallel the voltage must be the same through all elements.
The current measured across resistor 3 and 4 equaled 1.03X10^-3 A
and 9.00X10^-4 A respectively. The sum of these two currents equals
1.93X10^-3 A, which is the same as the current through the battery. In
parallel the sum of the currents through all of the elements must
equal to the current through the power source.
Conclusion: The resistance of a resistor can be determined easily by deciphering its
color bands. These determined resistances, although not perfect, are quite accurate.
Using the multimeter to measure voltage, resistance and current is straight forward,
but one must take special consideration when measuring current not to damage to
meter. For series circuits, the equivalent resistance is equal to the sum of the
resistances of the resistors; and the reciprocal of the equivalent capacitance is equal
to the sums of the reciprocals of the capacitances of the capacitors. And for parallel
circuits just the reverse is true. The reciprocal of the equivalent resistance is equal to
the sum of the reciprocals of the resistances of the resistors; and the equivalent
capacitance is equal to the sum of the capacitances of the capcitors. In a series circuit
29
the current is the same through all of the elements in the circuit; and the sum of the
voltages through the elements in the circuit are equal to the voltage of the power
source.
And for parallel circuits, again just the reverse is true. The voltage is the same
through all of the elements in a circuit; and the sum of the currents through the
elements in the circuit are equal to the current through the power source. Whenever
possible all circuit lab work should be done on the breadboard. It is easier to handle
and is a much more efficient way to do experimentation.