Download Physics II Lab Packet

Department of Science, Engineering and Architecture.
Division of Business, Math, Science, Technology (BMST) BMST AVP: Stacey Moegenburg LRC 221
PHY 101 - General Physics Il
PHY 101: General Physics II
LAB
Professor: Michael Morgante, BSCE, MEE, P.E.
[email protected]
(845) 497-4000 ext. 311
Physics Lab Reports
Most lab reports in College Physics will be informal reports written by hand in a laboratory
research book. There will be an occasional formal typed lab report required as well. This is an
outline of the sections in a typical lab report.
Title:
Short and precise; should accurately depict experiment done.
Abstract (do only for formal typed reports):
A one paragraph concise summary of the experiment.
Purpose:
Give a rational explanation as to why you are conducting the experiment.
Hypothesis:
State your hypothesis. This should be an educated guess as to what you believe your
investigation will show.
Theoretical Background:
Provide a summary of the relationships, including mathematical equations, which are relevant to
the experiment.
Materials and Equipment
Provide a concise list of any materials and equipment that is needed to carry out the experiment.
Procedure
Give a detailed step-by-step description of how this experiment was conducted. Another scientist
should be able to perform your lab using your method.
Data collected
 Data table (Produce a labeled table of your results, including units of measurements).
 Calculations – show any calculations that you used in the interpretation o your data.
 Graphs – provide any labeled with units, suitably scaled graphs to help with the data you
collected.
 Diagrams – provide relevant diagrams, correctly labeled. It is especially important to
include force diagrams if appropriate.
Analysis
 Summarize data trends – give a brief explanation of the observations, trends/links in the
results.
 Explain how errors could have occurred during the experiment and what steps could be
taken to minimize their effects. If necessary, provide a statistical analysis of the accuracy
of your data. Please avoid using the term “human error”, which is imprecise and lacking
in specificity.
Conclusion
Give a full explanation of the outcome of your experiment, noting if the purpose was fulfilled using
this procedure. Was your hypothesis validated – why or why not? Explain concisely what you
achieved by performing this experiment. Reflect on what this experiment did to further your
knowledge either scientifically or personally. Include suggestions for further investigation.
2
Example Lab Report
Newton’s Second Law
Joe Physics
1st Period
Hypothesis
Newton’s Second Law can be used to describe the motion of a cart that is
accelerated on a low-friction cart track by a hanging mass.
Theory
Newton’s Second Law is summarized by the equation F = ma, where F is the net
force on a system in Newtons, m is the total mass of the system in kg, and a is the
acceleration in m/s 2. If this law holds, then x = xo + vot + ½ at2, where x and xo are the
final and initial positions, respectively, t is the time, vo the initial velocity, and a the
acceleration. If the cart is released from rest, the equation simplifies to x = xo + ½ at2.
Equipment
cart track
mass hanger
Pasco Science Workshop 500
laptop computer
motion sensor
cart
masses
pulley
string
magazines (to level cart track)
Procedure
1. Level cart track with magazines. Do this by setting cart in center of track and
placing magazines under one end or the other until cart does not roll by itself.
2. Place pulley on one end of the cart track.
3. Place cart on track. Connect cart to mass hanger with a string. The string must
be of a length appropriate to go over the pulley, and must allow the mass hanger
to reach all the way to the floor. A length of about 1.2 m is good.
4. Set up the Pasco Science Workshop 500 and the laptop computer as
established in prior experiments. Attach the motion sensor to an analog port of
the 500.
5. Measure the mass of the cart.
6. Put 50 g of mass on mass hanger, drape string over pulley, and hold cart so
that it does not move. The mass hanger should be suspended well above the
ground.
7. Start collecting position data with the motion sensor.
8. Release the cart, and allow it to accelerate down the ramp.
Motion sensor
Pulley
String
Cart
Cart track
Mass hanger
Computer
3
Pasco 500
Data
Cart mass: 500 g
Hanging mass: 50 g
Data point
time
measured position
predicted position
1
2
3
4
5
0.000
0.100
0.200
0.300
0.400
0.000
0.004
0.011
0.026
0.046
0.000
0.003
0.013
0.029
0.052
Analysis
The data can be shown to best be fit by an equation of the form x = x o + vot + ½
(0.654) t2, which suggests constant acceleration. The exact equation deviates somewhat
from the theoretical equation, in which the acceleration is 0.654 m/s 2, as determined by
the Newton’s Laws analysis of the experimental setup. However, agreeme nt is close
enough to verify the suitability of Newton’s Second Law to the experimental situation.
Position vs Time
measured position
x = 0.2806t2 + 0.0025t
R2 = 0.999
predicted position
Poly. (measured
position)
0.06
position (m)
0.05
0.04
0.03
0.02
0.01
Results 0.00
0.0
0.1
0.2
0.3
time (s)
4
0.4
0.5
The hypothesis has been verified. Newton’s Second Law is predictive of behavior
of a cart on a low-friction cart track when the cart is accelerated by a hanging mass.
Conclusion or Discussion
It is apparent that Newton’s Second Law is predictive, but does not provide an
exact fit of the experimental data. Certain problems have been ignored; among these are
the rotational inertia of the pulley and the friction of the pulley with its axle, the friction of
the cart’s wheels on their axles, and possibly the resistance of the air as the mass falls
and the cart accelerates. It is possible that even closer agreement between theory and
experiment could be achieved if rotational inertia of the pulley, and its impact on
acceleration, were considered. Also, more trials could have been performed had time
permitted this.
5
Lab Rubric
A. Criteria: Designs Experiment Student demonstrates knowledge and skills
necessary to perform scientific inquiry.
Standards and Benchmarks: SC11.3.1; SC11.3.2; SC11.8.4; and SC11.l.X
Level 4
The experimental design
meets all requirements of
a Level 3,
AND
Considers current
research and
understanding of the
question being
addressed.
Level 3
Level 2
The experimental design
includes:
An hypothesis with
cause/effect relationship which
addresses the question being
studied;




Choice of controls
Consideration of sample
Observations and/or
measurements that are
sufficient to address the
question being asked and
are reproducible
A description of the
procedures and materials
to be used.
All aspects of the experimental
design are logically related to
each other, to provide a
defensible experiment.
6
The experimental design is
incomplete, but the design is
sufficient for providing
information on the question
being asked.
(Check all elements missing
or incomplete.)





An hypothesis with
cause/effect relationship
which addresses the
question being studied
Choice of controls
Consideration of sample
size
Observations and/or
measurements that are
sufficient to address the
question being asked and
are reproducible
A description of the
procedures and materials
to be used.
Level 1
The experiment is
completed without an
explanation of the
design;
OR
Design is inadequate
for answering any
aspects of the
question;
B. Criteria: Conducts the Experiment Student demonstrates knowledge and skills
necessary to perform scientific inquiry. Standards and Benchmarks: SCI 1.3.1; 11.3.2;
SCI 1.8.4; and SCI 1.1.X
Level 4
Meets all of Level 3
requirements;
AND
Based upon findings
from the original
experiment, there is
evidence that an
experiment was
conducted to address a
new question directly
linked to the findings of
the original question;
OR
An additional and
related
experiment is conducted
to
further extend
understanding
and/or to implement a
modified
experimental design.
OR
A new experimental
design is
proposed that exhibits
deeper
understanding of
concepts and/or extends
thinking beyond original
conclusions.
Level 3
Level 2
The experiment was
implemented,
including:
Relevant observations and/or
measurements are missing or
are not defensible;
 Appropriate
observations
and/or
measurements
collected using
consistent
methods so that
measurements
are repeatable.
 Controls
implemented to
examine one
variable at a
time.
OR
Controls were not implemented
to examine one variable at a
time;
AND
Any explanations in
changes of the
design that address
the original question
are documented
with appropriate
observations and/or
measurements.
7
Level 1
The experiment was
attempted but is incomplete.
C. Criteria: Representation - Tables, graphs, models, diagrams, or other
appropriate representations. Student uses representations to communicate and apply
scientific concepts, in lab reports and technical writing.
Standards and Benchmarks: SCI 1.5.2; SCI 1.5.3
Level 4
Level 3
Representations
are accurate
and appropriate,
meeting
requirements of
Level 3, and
include other
elements, such
as:
 Data set is
displayed in
multiple
ways to
provide
additional
information
or a different
perspective
 Data is
represented
multiple
ways to
make a point
 Data is
represented
multiple
ways to
show a trend
 Additional
representati
on(s) used
to explain a
concept,
solve a
problem, or
as an
extension of
the situation.
Any tables, graphs, models, or
diagrams are appropriate for
representing the observations,
measurements, or concepts.
There may be some flaws, but the
flaws do not negatively impact the
understanding or use of the data,
diagram, model, etc.
Conventions of representation to
consider:
 Data tables have accurate
titles, correct values, and
labels
 Graphs have appropriate titles;
correct scaling; independent
and dependent variables
labeled correctly; and values
accurately plotted.
 Models and diagrams are
labeled.
Level 2
Tables, graphs, models, or
diagrams used have a
significant flaw(s) that
negatively impacts the
understanding or use of the
representation, such as:




.
8
Data is collected in tables,
but not organized or
correctly labeled and titled
The graph selected is not
appropriate for representing
the situation
Graphs contain errors or
inconsistencies in scaling,
labeling, or plotting
The diagram or model is
unclear (no labels, titles,
explanation).
Level 1
An attempt is made to
organize or graph data
(observations and/or
measurements), or to
use a diagram or
model, but the
representation chosen
cannot be used to
effectively
communicate the
concept for the given
situation;
OR
Tables, graphs,
diagrams, or models
are missing or have
errors in the
conventions
throughout;
D. Criteria: Conclusions - Student demonstrates knowledge and skills necessary to
perform scientific inquiry.
Standards and Benchmarks: SCI 1.3.1; SCI 1.3.2; SCI 1.3.3; and SC11.1.X
Level 4
Meets all
requirements of
Level 3:
AND
Demonstrates an indepth understanding
or extensive
knowledge of the
concepts by using
the conclusions to
do any of the
following:
 make further
predictions
 ask/address
additional
questions
 generalize
scientific
concepts
 provide scientific
explanations of
question studied
or an application
related to the
findings compare
the conclusion to
other research
and models and
appropriately
address
deficiencies.
Level 3
Level 2
Level 1
Conclusions drawn address
the hypothesis and are
supported with relevant
observations or
measurements. All aspects
of the experiment are
addressed.
Conclusions drawn address the
hypothesis, but are not fully or
consistently supported by
observations and/or
measurements;
Conclusions drawn do
not address the
hypothesis;
OR
AND
Observations and measurements
are summarized, but no
conclusion s are drawn;
Conclusions drawn
address hypothesis, but
are inconsistent or in
conflict with observations
and measurements.
If applicable, results are
evaluated to determine if
they are reasonable and
there is evidence that an
attempt was made to
determine the source of
error.
OR
Not all elements of the
experiment are addressed in the
conclusions;
OR
Observations and measurements
are used to support the
conclusions, but the observations
and measurements may be
inappropriate.
9
OR
F. Criteria: Communicates Results Student communicates and applies scientific
principles. (Note: This criterion assesses communication, not conceptual understanding.)
Standards and Benchmarks: SCI 1.5.3 and SCI 1. 5.2
Level 4
Meets requirements
of Level 3,
AND
Explanations are
strengthened by the
use of
such things as:
 Graphic
organizers
 Diagrams
 A keying system
 Cross-referencing
 Additional Tables,
Models, Graphs
Level 3
Scientific terms are
accurately and
appropriately applied in
report.
The application of
grammar and conventions
do not get in the way of
understanding the results
of the experiment.
Level 2
Inconsistent use of accurate
and appropriate scientific
terms throughout the report.
The application of grammar
and conventions get in the
way of completely
understanding the experiment
or results.
Level 1
Scientific vocabulary used,
but inaccurate throughout
the report or not used when
the opportunity exists;
OR
Used common terms instead
of appropriate scientific
terminology.
The application of grammar
and conventions make it
hard to follow the
explanations and/or the
results of the experiment.
10
Spring Lab
Purposes: To measure the force constant, to calculate and measure the period, and to examine
the sinusoidal behavior of a spring.
Theory: Hooke’s Law states that the restoring force of a spring is related to the displacement
from equilibrium as follows: F = -kx, where F is the force, k is the force constant, and x is the
displacement. The period of a spring is calculated by T = 2m/k.
Equipment: meter stick
set of masses
stopwatch or Photogate timer
mass hanger
ring stand with clamp
Part A: Simple Harmonic Motion
Method:
1. You’ll collect graphs of position, velocity and acceleration (dependent variables) as a
function of time (independent variable).
2. Closely examine the similarities and differences of the resulting graphs. You may need to
adjust the axes to get a better view. If you do not get clear sinusoidal functions on all
three graphs, you may need to adjust the position of the photogate or re-do the
stopwatch measurements.
Analysis: Find the period of the spring from the graphs created with the data you gather.
Compare with the period measured with the stopwatch versus data collected below. Compare
position, velocity and acceleration graphs. Specifically, how do the times at which maximum force
(acceleration), maximum displacement, and maximum velocity compare? Do all three maximums
occur simultaneously? If not, can you see a pattern that you can explain?
Part B: The Force Constant
Method:
1. Place mass hanger on spring hung vertically.
2. Measure the distance the spring has elongated.
3. Add 20 to 50 grams to the mass hanger and measure the distance again.
4. Repeat step 3 until 4 or 5 data points have been obtained.
Data:
Point number
Total Mass on
Spring (kg)
Total Weight on
Spring (N)
Elongation (m)
1
2
Etc.
Analysis: Plot total weight (y-axis) against distance of the mass hanger bottom from the tabletop
(x-axis). Fit the data points with a best-fit straight line. The absolute value of the slope of the line
is the force constant, k, of the spring.
Part C: The Period
Method: Using the force constant determined in part A, predict the period the spring should have
when it is holding 10-g total mass. Set the spring in motion and experimentally determine the
actual period.
Analysis: Compare the predicted and actual periods. Determine percent difference.
11
Standing Waves Lab
Purpose: To observe standing waves on a stretched string and to verify the formula
relating the wave speed to the tension and mass per length of the string.
Materials:
String vibrator, string, set of slotted weights, weight holder, pulley and clamp, meter
stick, analytical balance.
Theory:
Standing waves are produced by the interference of two waves of the same wavelength, speed of propagation and amplitude, travelling in opposite directions through the
same medium.
If one end of a light, flexible string is attached to a vibrator and the other end passes
over a fixed pulley to a weight holder, the waves travel down the string to the pulley and
are then reflected, producing a reflected wave moving in the opposite direction. The
vibration of the string is then a composite motion resulting from the combined effect of
the two oppositely directed waves. If the proper relationship exists between the
frequency, the length and the tension, a standing wave is produced and when the
conditions are such as to make the amplitude of the standing wave a maximum, the
system is said to be in resonance. A standing wave has points of zero displacement
(due to destructive interference) and points of maximum displacement (due to
constructive interference). The positions of no vibration are called nodes (N) and the
positions of maximum vibration are called antinodes (A). The segment between two
nodes is called a loop. Standing waves with one, two, three and four loops are found
below.
12
The solid line represents the form of the string at an instant of maximum displacement
and the dotted line represents the configuration one half-period later when the
displacements are reversed. In each case _ = 2l, where _ is the wavelength and l is the
distance between two nearby nodes. For a string with both ends fixed the allowed
wavelengths for standing waves can only take fixed values related to the length L of the
string, as can be seen in the figure above.
If one changes the tension in a vibrating string, the number of loops between the ends of
the string change. As a result the distance between neighboring nodes changes, thus
producing a change in wavelength. The speed of the wave can be obtained if the
frequency f is known and the wave length has been measured:
v=λf
(Eq. 1)
The frequency is fixed by the string vibrator; the wavelength can only take on fixed
values related to the length of the string, as shown in the figure above. Thus, standing
waves can only exist for particular values of v that is controlled in this experiment by the
tension of the string.
The velocity of the wave is given by the Mercenne's law:
(Eq. 2)
where m is the mass per length of the string and T is the tension. The tension of the
string (in newtons) equals the total hanging mass M times the gravitational acceleration
g = 9.8 m/s 2, that is, T = Mg. The main objective of the work is to compare the
experimental value of the wave speed given by Eq. (1) and its theoretical value of Eq.
(2).
Method:
A string is attached to a vibrator made of steel and then passed over a small pulley as
shown in Fig.1. The coil producing the alternating magnetic field acting on the vibrator is
being fed by the standard ac current with a fixed frequency of 60 Hz. The attraction force
exerted on the vibrator is proportional to the square of the magnetic field and thus of the
electric current in the circuit. As the result, the vibrator is vibrating at the double
frequency, 120 Hz. The weight on the hanger has to be adjusted to achieve the tension
T and thus the wave speed v at which a standing wave is clearly visible. As the range of
13
the tension is limited, not all kinds of standing waves can be observed without changing
the string length L. For instance, to observe lower overtones, the
tension T can be increased or L can be decreased. The best way to measure the
wavelength is to measure the distance d between the end of the string at the pulley
(where there is a node) and the node closest to the vibrator and count the number n of
loops within this region. Then
Keep in mind that there is no node directly at the vibrator, thus using L to obtain as
shown in the figure above will result in errors.
Prodecure:
1. Measure the length of the loose string (not the one attached to the vibrator) and
then measure its mass using the analytical balance to the nearest milligram.
Calculate the mass per unit length (m) for the string.
2. Suspend a light weight holder from the string and adjust the load until the string
vibrates with maximum amplitude. Record the load in kilograms, including the
weight of the holder. Measure as explained above and record it in the table
together with the number of loops you observe.
3. Repeat the observations with load (and maybe the string length) adjusted to give
other numbers.
Data:
Your data table should include the following at the very least.
f=Frequency (Hz)
l=Length of loose string (m)
M=Mass of loose string (kg)
m=Mass/length of string (kg/m)
Number of Loops
=Wavelength
Analysis:
1. Calculate the mass per unit length and express it in kg/m.
2. Calculate the velocity of the wave on the string using equations (1) and (2) and
compare the results. Calculate the percent discrepancy. Fill all of this in the data
table.
3. In your conclusion discuss your results
4. If the frequency of the vibrator were 240 Hz, calculate theoretically how much
tension is necessary to produce a standing wave of two loops. Consider that the
string is fixed at its two ends, has a length of 1 meter and has the same mass per
length as determined before.
14
Wavelength of Sound
Purposes: To determine the wavelength of a sound wave and to determine the speed of
sound in air.
Theory: The speed of any wave is related to its wavelength and frequency by the
equation v = , where v is the speed of the wave,  is the wavelength, and  is the
frequency. The speed of sound in air varies according to the equation v = 331.45 m/s +
0.59 T m/soC where T is temperature in Celsius. The wavelength of a sound wave may
be determined by measuring the length of a column of air that produces resonance with
the wave. In a tube that is closed on one end and open on the other, the minimum length
that produces resonance is approximately ¼ the wavelength of the wave. Therefore, the
wavelength of the sound wave is roughly 4 times the length of the tube. (The precise
equation is  = 4(L + 0.4d) where L is the length of the tube and d is its diameter.)
Equipment: graduated cylinder, meter stick, 2 tuning forks with different frequencies
Method:
1. Obtain a graduated cylinder, a tuning fork, and some water.
2. Start the tuning fork vibrating gently by tapping it on your heel and hold it close to the
mouth of the graduated cylinder.
3. Carefully pour water into the cylinder until the sound from the tuning fork becomes
noticeably louder. At this point, measure and record the diameter of the cylinder and
the length of the air column within the graduated cylinder.
4. Repeat steps 1-3 with a second tuning fork.
Data: Record in a table the following for each trial: a) tuning fork frequency, b) air
column length, and c) air column diameter d) laboratory temperature.
Calculations: For each trial, calculate the following: a) the wavelength of sound based
on the air column length and diameter, b) the speed of sound in air based on the
wavelength of sound and the frequency of the tuning fork, c) the speed of sound in air
based on temperature, and d) the percent difference in the speed of sound as calculated
by the methods in part b and c.
Analysis: How does the speed of sound compare for the two methods of calculating it?
What are some possible problems with this experiment, and some possible ways the
experiment might be improved? Draw a tube that is open on one end and closed on the
other, and draw a representation of the first, second, and third harmonics that can exist
inside the tube. Now draw a tube that is open on both ends, and one that is closed on
both ends. Compare the first, second, and third harmonics that can exist inside these
tubes with the ones that can exist in a tube that is opened on one end and closed on the
other. Which type of tube can produce the lowest tone?
15
Electrostatics Lab
Part I : Determining Charge
Benjamin Franklin decided to name the charge that was deposited on a glass rod when
rubbed by a silk cloth ―positive.‖ (Current electrostatics holds that it is the negatively
charged electrons moving from the rod to the silk, but the net effect is the same.) All
other charges are determined in relationship to this definition of positive charge.
Use the materials available in the classroom to determine the sign of charges you are
able to transfer. List as many combinations of materials as you can, along with the
transferred charge. There is no numerical data to take here, but you will have to apply
some logical reasoning. Materials available in the front of the room include hard rubber,
glass, acrylic, PVC, polyethylene, and nylon. You may try others that you can find.
Hang a green plastic strip from a silk thread as shown in the front of the room. This is
your standard material. Always charge this standard with the same cloth! Then
experiment with other combinations of materials as test materials.
My standard material…
rubbed by this material…
(attracts /
repels)
glass
rubbed by
silk
and is
therefore
charged
(positive /
negative)
This material…
rubbed by this material…
(attracts /
repels) my
standard
and is
therefore
charged
(pos / neg)
Draw some general conclusions about charges on the other side of this page.
16
Part II : Coulomb’s Law
If you hung two conducting spheres from threads, then charged them, you could
measure the force between them for various distances. Then you could determine
exactly how the electric force varies with different distances. Unfortunately, that is very
difficult to do in practice; with the materials we have in this lab, it is practically
impossible.
If you could do it, however, you would get data very much like that in the table below.
Use that data to make a graph of force vs. distance. (Use a separate sheet of graph
paper.) Explain in your conclusion below what that graph looks like and why.
Using gravitation as an analogy (remember the inverse-square law), draw a graph of
force vs. 1/d2. Determine the slope of that line. Explain in your conclusion what physical
factors you think that slope depends on.
distance between electrostatic
the two spheres
force (N)
(cm)
0.5
3.88E-04
1.0
8.52E-05
1.3
5.53E-05
1.5
3.95E-05
1.9
2.40E-05
2.6
1.36E-05
3.1
9.09E-06
3.5
7.46E-06
3.8
5.87E-06
4.5
4.11E-06
17
Series and Parallel Circuits
Purpose: To measure current, voltage, and resistance in a simple, series, and parallel
circuit.
Part I Procedure – Simple Circuit
1. Connect one resistor (either 5  or 10  etc.) to one battery in
a simple circuit. Sketch the diagram of the circuit before you
wire it. Be sure to connect the ammeter in series with the
resistor, and the voltmeter in parallel with the resistor. Collect
data on the circuit, and record the highest voltage and current.
Using Ohm’s law, calculate a value for the resistance. This
calculated value for the resistance will be referred to as the
measured value since it is determined from two measured
quantities, and will be the value placed in the tables. Develop
a data table for collecting your information. Show all work and
calculations.
Analysis: Does the measured (calculated) value for the resistance match the value of
the resistance printed on the resistor? Note the Value of R in the table is the value
calculated using Ohm's Law. Calculate the percent difference between this measured
(calculated) resistance (R) and the known (printed) resistance, and show your work
below.
Obtain measurements for 2 batteries to increase the voltage a nd current.
Part II Procedure: Series Circuit
1. Connect three resistors in series on a breadboard.
Sketch the diagram of the circuit.
Q2. What should be the total resistance of
the three resistors in series?_______________
2. Repeat the voltage and current measurements
as in Part I, with the voltmeter across both resistors,
and calculate the total resistance using Ohm’s Law.
Q3. Does the answer to Q2 agree with your measured
Value (calculated) for the total resistance in series? Calculate
the percent difference between the two.
3. Repeat the measurements for 2 batteries to increase the
voltage and current, and complete a data table for this
information.
18
Part III: Parallel Circuit
1. Connect three resistors in parallel on a breadboard.
Sketch the diagram of the circuit at the right.
Q5. What should be the total resistance of the three resistors
in parallel?________________________
2. Repeat the voltage and current measurements
as in Part I, with the voltmeter across both resistors,
and calculate the total resistance using Ohm’s Law.
Q6. Does the answer to Q5 agree with your measured
value for the total resistance in parallel? Calculate the percent
difference between the two.
3. Repeat the measurements for 2 batteries to increase the volta ge and current with the
information collected in a data table you create.
Q7. What is the relationship between I1, I2, and Itot?
Circuit Lab Analysis
1. Why is the ammeter always connected in series with the resistor(s) whose current it
is trying to measure?
2. Why is the voltmeter always connected in parallel with the resistor(s) whose voltage
it is trying to measure?
3. In general, was Ohm’s law verified in this experiment? Explain.
4. Consider the resistors are light bulbs in the series and parallel circuits you wired.
(a) Which bulb draws the most current, and therefore burns the brightest? Explain.
(b) Explain what will happen to the remaining bulbs if one is removed from its socket.
Cycle through and make sure each bulb is removed while the other two remain.
(c) In what case is more power in the circuit generated? How do you know?
5. A 60  bulb and a 100  bulb are connected in series in a circuit.
(a) Which bulb will have the greater voltage across it? Explain.
(b) Which bulb will have the greater voltage across it if they are connected in
parallel? Explain.
Describe at least two sources of error in this lab
19
Capacitor Lab
Purpose: To determine the capacitance value of a capacitor by examining data for
discharging and discharging.
General Method:
 Construct graphs of current (I), voltage across resistor (Vr), and voltage on
capacitor (Vc) as functions of time for charging and discharging.
 Calculate charge on the capacitor by finding area under I vs t graphs or by
integrating the equations for the I vs t graphs.
 From charged capacitor voltage and charge, calculate capacitance:
Q = CV
 Compare experimental capacitance to marked value on capacitor.
Background:
Charging
[Note: The entire experiment needs to be done on a non-conducting surface, such as
cardboard, to make sure discharging doesn't take place on the surface.]







Schematic for charging circuit:
Find a resistor that has suitable size, based upon time constant (approximately
100 k charges a 2200 F capacitor in 7-8 minutes), to slow down the charging
and discharging processes:
 = RC (time for 62% of charge on exponential curve)
Make sure voltage supplied is within range marked on capacitor.
Connect capacitor in series with resistor, as marked on package. [Note:
Attempting to charge an electrolytic capacitor with poles reversed can damage
the capacitor or cause it to overheat and explode.]
Do a trial run on the circuit with a voltmeter to check power supply voltage.
Record this value and keep it constant.
Discharge the capacitor completely by holding a conductor (screwdriver, e.g.,
with an insulated handle) across the capacitor leads.
Connect a voltmeter across the resistor.
20



Immediately upon closing the charging circuit, start recording the voltage across
the resistor every 10 seconds until the voltage readings level off (e.g., the same
reading 3 times in a row).
Careful: You now have a charged capacitor!
Quickly disconnect the circuit.
Discharging:
 Without allowing any discharge of the capacitor, immediately remove the power
supply to connect only the charged capacitor and resistor in series.
 Leave the voltmeter connected across the resistor.
 Immediately upon closing this circuit, start recording the voltage across the
resistor every 10 seconds until the voltage readings level off.
Analysis: To determine current values to make the I vs t plots, use the voltage values
and the known resistance for the resistor. (Remember: The only current is through the
resistor; no current flows through the capacitor.) To find the voltage values for the
charging and discharging capacitor, remember Kirchoff's Loop Rule—that the total
voltage change throughout any circuit adds to zero. Thus, the sum of the voltages of the
resistor and capacitor equals the power supply voltage any given time.
After plotting I vs t for charging and discharging, determine the charge by finding the
area under each plot line—or by integrating the equation of each line.
Use the equation Q = CV to determine a value for capacitance.
Addendum 1:
Addendum 2:
Addendum 3:
Addendum 4:
Directions for graphing.
Sample Excel plots.
Sample Results.
Further Analysis Information.
21
ADDENDUM 1: Analysis Notes for Capacitor Lab
Purpose: To gather data from the charging and discharging cycles of a capacitor; to
construct graphs of circuit current, capacitor voltage, and resistor voltage for both
charging and discharging; to calculate the charge on the capacitor; and to determine an
experimental value for capacitance.
Background: Include all relevant equations, schematic diagrams for both charging and
discharging (including meters), and sketches of expected curves (with asymptotes)---basically class notes. Use RC to estimate a resistor value to use that would make the
charging time around 5 minutes.
Data: First, record the given (constant) values of , R, and C that were used. Then set
up a table in the journal on which you can record time (t) and voltage across the resistor
(VR) until the values reach a plateau, for both charging and discharging.
Set up (and print, with gridlines, to attach to your book) in Excel spreadsheet, the
following table. Use imbedded formulas to make calculations for the new columns.
Record the formulas used. [For example, the formula to calculate voltage on the
capacitor from voltage across the resistor would be: -VR, so you would put =-B3 in box
C3 (and EDIT, FILL, DOWN commands). Then, if you are using, for example, a 100,000
ohm resistor, the formula to calculate I would be I=VR/R, so you would type
=B3/1E5 in box D3.]
A
Charging
t
B
C
D
VR
Vc
I
E
Discharging
t
F
G
H
VR
Vc
I
Analysis: Attach the spreadsheet and all six graphs—each including a best fit curve and
equation. Then determine the charge (for both charging and discharging), using one or
both of the following methods: (a) Draw a "best fit" line onto the I vs t graph that
approximates the area by including about the same amount of extra area above the
curve as it omits below the curve. Then determine the area, which will be the charge.
(b) Integrate the equation for the Current vs Time graph, then substitute a value to time
when you stopped charging. Use your values for charge and voltage to calculate a value
for capacitance; compare this to the marked value on the capacitor.
22
ADDENDUM 3. Sample Results.
(Note: The charging data will yield much better results, as some charge is leaked before
discharging cycle. However, it's still worth performing the discharge cycle to see the
graphing patterns.)
Data from May, 2005, Group 1:
Marked value of capacitor: 2200 F
Resistance used: 50 k (actually, two 100 k resistors in parallel, as available)
Charging voltage: 5.49 V
Charging - Time for reduction of resistor voltage from 5.02 V to 0.18 V: 470 seconds
Discharging – Time for reduction of resistor voltage from 4.9 V to 0.13 V: 470 seconds
Equation for Vc vs t, Charging: V = 5.49(1 – e-/109)
Equation for VR vs t, Charging: V = 4.97 e-0.0077
(Note: -0.0077 = 1/RC)
Value obtained for capacitance: 2301 F
% error: 4.60 %
Some observations in student analyses:
 The largest source of error probably came in not taking values quickly enough
after the circuit was first connected for charging. Some voltage drop across the
resistor occurred before the first readings were taken. The quickest changes
occur in the first seconds, so would have a large effect.

Slightly better results were obtained by deriving the equations and integrating
than by using the Excel best fit equations.

Regression fits were over 0.99 for the plots.
23
ADDENDUM 2 – Sample Capacitor Lab Data (Charging)
time, t (s)
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
resistor voltage, Vr (V)
1.41
0.92
0.58
0.38
0.26
0.18
0.11
0.08
0.07
0.06
0.04
0.03
0.03
0.03
0.03
0.03
Capacitor Charging
1.6
Voltage, V (V.)
1.4
1.2
Charging Voltage
across Capacitor
1
0.8
0.6
Charging Voltage
across Resistor
0.4
0.2
0
0
20
40
60
80
Time, t (s)
24
100
120
140
160
Addendum 4: Capacitor Lab, Further Analysis Information
Charging Circuit:
I
+
+
During charging, the positive charge flow (conventional current flow) is from high
potential side of power supply to positive side of capacitor.
Charging Circuit:
I
I
+
During discharging of the capacitor, the positive charge now flows from the positive
side of the capacitor, thus reversing the direction of current flow in the resistor
To calculate capacitance from data (t, Vr, Vc, I):
1.Find the maximum charge accumulated on the capacitor by finding the area under the
Current vs Time curve, by: (a)integrating the equation for the I vs t graph; (b)
photocopying the graph onto quadrille paper, finding the value of each square, and
counting squares; or (c) drawing a "best fit" line over the I vs t curve that includes about
the same amount of extra space as it excludes, and finding the area of the triangle.
2. Use the maximum charging voltage (the asymptote of the V vs t charging graph) and
the charge obtained from area of the I vs t graph:
C = Q/V
25
Magnetic Forces Lab
You will be using a magnetic field sensor to measure the magnetic field generated by a
current flowing through a wire.
Set up your circuit as shown here and in the front of the room. Tape down the switch
and the wire so the wire runs straight along the table. Tape the meterstick perpendicular
to the wire, so you can measure the linear distance from the wire to the probe.
The resistor in your circuit is a 1 , 10 watt resistor. The maximum current the resistor
can withstand is therefore about 3 A. Set your power supply to 3 V for the entire
experiment.
Set up the PHYSICS program to recognize the magnetic field probe. For calibration, use
a stored value. Enter ―HIGH (MTESLA)‖ to measure the magnetic fields in millitesla.
Make sure the switch on the probe is set to ―HIGH‖.
Collect data from the probe by choosing ―MONITOR INPUT.‖ The calculator will then
display the value of the magnetic field read by the probe about once every second. (You
should really only record two decimal places; the third will be changing too fast.)
With the switch open, turn on your power supply. Place your magnetic field probe face
down on the table, perpendicular to the wire, and a small distance away from the wire
(as measured by the meterstick). Record the distance from the wire to your meterstick
and the magnetic field value with the current off. Now carefully close the switch to start
current flowing and record the magnetic field value with the current on. Open the switch
again; the current should not flow through this circuit for more than about a minute at a
time.
Move the probe farther away from the wire and repeat these measurements: first with
the current off and then with the current on. Be sure to record measurements at least
every centimeter up to 10 centimeters from the wire. (Hint for successful lab completion:
you will need to hold the probe very still while making measurements.)
Analyze your data by taking the difference between the field values without current and
with current. Make a graph of the field due to the current as a function of distance from
the wire. Analyze this graph.
26
Refraction Lab
Purpose:
(1) Determine the index of refraction and speed of light for glass by ray tracing. Four
pins, a glass block, and a sheet of graph paper are required for this experime nt.
(2) Determine the index of refraction and speed of light for water. Three pins, a plastic
dish containing water, and a sheet of graph paper are required for this experiment.
Report should include:
(1) A clear sketch of a single ray of light through a glass block that clearly illustrates the
normal at each surface, as well as the angle of incidence and the angle of refraction at
each surface. To get good measurements, you must have fairly large angles of
incidence! Figure out how to do this without getting ―internal reflection‖. Your calculations
of index of refraction and speed of light should be clearly indicated.
(2) A clear sketch of two rays of light through the plastic dish of water. You must put one
pin at the center of the flat side of the dish to eliminate bending of the light on the curved
surface; your measurements will involve the bending at the flat surface. To get good
measurements, you must have large angles of incidence but you must avoid ―internal
reflection‖. Your calculations of index of refraction and speed of light should be clearly
indicated.
Reflection Lab
Purpose: Determine the location of a virtual image in a mirror.
Place a mirror on edge along a line of rectangular graph paper. Place a thumbtack so
that you can see it in the mirror. Mark the location of the thumbtack and mirror on the
page.
With your eyes at the level of the table, look at the image of the thumbtack in the mirror
and mark two points along the line between your eye and the image of the thumbtack.
Repeat for multiple sight lines.
Remove the mirror and draw the sight lines until they intersect. What conclusions can
you draw about object formation in mirrors?
27
Lens Systems Lab
Purpose(s): To observe the positions and characteristics of images produced by convex
lenses.
Theory: Ray diagrams can be used to locate images produced by lenses. Also, the following
equations can be used to characterize images: hi/ho = - si/so = M, where hi and ho are image
and object height, respectively, si and so are image and object distances, respectively, and M
is magnification. The focal length of a lens is related to the image distances by the equation
1/f = 1/so + 1/si.
Equipment:
meter stick and supports
light holder with bulb
card with cutout object
card to act as screen
concave and convex lenses
lens holders for meter stick
card holders for meter stick
Basic experiment:
Using the equipment provided, create a real image on the screen.
Data:
Record the positions of object, image, and lens. You should create a data table that includes
the following:
Approximate
Distance of Object
from Lens
Measured
Position of Lens
Measured
Position of Object
Measured
Position of Image
Type of Image
(real/virtual)
Image Size
(enlarged/true/reduced)
Image Orientation
(upright/inverted)
Distance
of Object from Lens
Distance
of Image from Lens
Calculated Focal
Length of Lens
% Error in
Focal Length
Large
distance
Beyond
2F
2F
Between F
and 2F
Less than F
Analysis: Characterize the image produced by your setup using three words virtual/real,
true/enlarged/reduced and upright/inverted). Approximate the focal length of the lens from
your recorded data. Repeat the basic experiment for a total of three (3) trials. All three trials
must use different distances between the object, lens, and image. For each trial, record
the data and analyze the image. How does your average approximate focal length for the
three trials compare to the focal length printed on the box?
28
Diffraction Lab
Purpose: To use the methods of diffraction to find the wavelengths of the helium-neon,
red diode, and green diode lasers.
Background and Method:
m = d sin 
 = tan-1 (y/x)
m = order number
 = laser wavelength
d = slit width or slit spacing
 = angle of beam from central maximum for given order beam
y = distance from central maximum to given order beam projection
x = distance from diffraction grating to beam projection





Do not assume a small-angle approximation for , i.e., that sin   . Instead,
measure x and d and calculate the angle.
Make angle measurements and calculations for the first three orders (if
possible) for each laser and each diffraction grating.
Repeat angle measurements and calculations using three diffraction gratings of
different slit spacings.
Perform the above 9 trials for each of the three lasers, averaging the calculated
values of wavelength to report a wavelength for each laser.
Calculate a percent error for your reported value of laser wavelength for each
laser.
Analysis:
Some suggested ideas to incorporate into the analysis include:
 What is the effect on the projected pattern of changing distance between laser
and diffraction grating or changing distance between diffraction grating and
projection screen?
 How does the pattern change with changes in laser color?
 How does the pattern change with changes in slit spacing?
 How does the pattern change if the grating is rotated?
 Why are only 2 or 3 orders visible for some gratings? (Substantiate your
answer with a sample calculation.)
 How do the diffraction slit spacing widths compare to the wavelengths being
examined?
 Which laser color produced best results?
 Discuss the precision vs accuracy of your results.
29
Bohr Model of the Atom Lab
Introduction
The bright-line spectra of various gases had been studied and analyzed for at least a
decade before they could be explained. In 1914, Niels Bohr, a Danish physicist,
incorporated Planck's theory about energy and the Rutherford model of the atom into a
new model of the atom. The new model was able to successfully explain the spectrum
produced by glowing hydrogen. The main idea in this model was that the energy given
off by an atom is due to the jumping of the electrons between "orbits". An electron in a
"low energy state" (an orbit close the nucleus) could be excited to a higher energy state
(further from the nucleus). Once in a higher state, the electron could "fall" to a lower
state, releasing a quantum of energy. An atom could also have so much energy added
to it that an electron would jump completely off of the atom, thus causing
the atom to become a cation.
Purpose
The purpose of this lab is to gain a thorough understanding of the Bohr model of the
hydrogen atom. Also, you will practice determining frequencies and energies of
electromagnetic radiation, and use them to make some predictions about the spectrum
of hydrogen.
General Procedure
Observe the bright-line spectrum of hydrogen as carefully as you are able. Use the
spectroscope set up in the lab, and record the wavelengths of the light given off -- there
are four lines in hydrogen's spectrum. Determine the frequency and energy of the
photons of light associated with each of the wavelengths of light which you observed.
Record all the values in a table format in the data section. Show a sample calculation for
each type of calculation performed. In the results section for this lab, you are to use your
calculated data for the energies of light given off by hydrogen in constructing an "energy
level diagram" for the hydrogen atom.
You will need to start with this information:
• The "ground state" of an atom is the lowest energy state. This is the most stable
arrangement of electrons. The atom is in the ground state when its electrons are in the
orbits closest to the nucleus. This orbit can be called the first orbit, and is given a label n
= 1. (n is called the ―principal quantum number‖.)
• The second orbit, n = 2, is 1.64 X 10-18 J higher in energy than the 1st orbit for
hydrogen. I’m giving this information to you for free.
• The visible energy (light) produced by hydrogen occurs when an electron in an energy
level, or orbit, higher than n = 2 drops to the second energy level. Thus, the lowest
energy visible light occurs when an electron moves from n = 3 to n = 2.
• The ionization energy of hydrogen is 2.18 X 10 -18 J. This energy represents the
energy difference between the ground state and the highest possible excited state for
the electron in hydrogen, n = ∞.
• Planck’s constant (―h‖) is 6.62 x 10-34 J·s; The speed of light (―c‖) is 3.00 x 108 m/s.
30
Questions for Conclusion:
One thing to address in your discussion is the following: According to Bohr, electrons
jumping to the second energy level from higher levels produce the visible bright line
spectrum for hydrogen.
But electrons could jump to any orbit from a higher orbit. What wavelengths of
electromagnetic radiation are associated with electrons jumping to the ground state (n =
1) from higher orbits? What wavelengths of radiation are associated with electrons
jumping to the 3rd orbit from higher orbits? Do some research to find out if these
wavelengths of energy have ever been observed coming from hydrogen. Look up Bohr,
Planck, Lyman, Balmer, and Paschen. Find out how atomic spectra were used by
astronomers studying stars at the beginning of this century.
The radius of an orbit in the Bohr model of the hydrogen atom is given by:
where h is Planck’s constant, m is the mass of an electron, e is the charge of an
electron, Z is the atomic number, and n is the principal quantum number (or energy
level). Calculate the radii of the first few Bohr orbits in nm and in Å, and show your work
in your discussion.
31
Half-Life Lab
Purpose:
Using the hole punchouts a paper hole puncher, shake the punchouts out onto a flat
surface. Compare the rate of retention of the coins that land dark side up to the rate at
which a radioactive substance decays to a new substance.
Materials:
2 containers, 200 punchouts (one side white and one side black, 2 containers to hold
punchouts
Procedure:
1. Count out exactly 200 punchouts and put them into a container.
2. Hold the container about one meter from a flat, horizontal surface and gently pour the
punchouts onto the surface.
3. Count the number of punchouts that land dark side up. Record this number in the
blanks below. Assume dark side up punchouts to be unchanged and white side up
puNchouts to be changed.
4. Put the dark side up punchouts back into the container so they may be poured out
again and put the white side up punchouts into the other container.
5. Continue the series 2 – 4 until all the punchouts have landed white side up or until you
have completed 9 shakes.
Analysis:
You will need to graph the data you collect in order to answer the questions below:
1. If you were dealing with the decay of radioactive Carbon-14 to the stable Nitrogen-14
a) Which element would the punchouts that landed white side up represent?
b) Which element would the punchouts that landed dark side up represent?
2. After 2 shakes, about what fraction of your paper disk sample had decayed?
3a. Was the rate of decay change of light side punch-out to dark side putout uniform
from shake to shade always the same?
3b. What is it about your graph that caused you to answer question 3a. as you did?
IF EACH POURING OUT OF YOUR PAPER DISK ELEMENT TOOK 87 DAYS
4. How many days would it take for ½ of your paper disk element sample to decay?
5. What, in this case, is the half-life or your paper disk element?
6. Define the term half-life
7. An old piece of cotton cloth is found to contain .0000156 grams of C-14 in it. A sample
of new cotton cloth of equal mass, is determined to contain .00200 grams of C-14. How
old is the old cotton cloth? (The half life of C-14 is 5730 years.)
32
Binding Energy Lab
Purpose: To understand how the total nuclear binding energy and the binding energy
per nucleon vary from nuclide to nuclide.
In this activity, you are going to use an internet database of properties of the elements in
the periodic table in order to plot three graphs of nuclear properties and then use these
to see some trends. You will do this by copying the information from the internet
database into a spreadsheet program (Excel) and then using the spreadsheet’s Chart
Wizard to make your graphs.
1. First, open the spreadsheet program Excel. You should see a blank grid of many
empty boxes (cells) into which you are going to paste data. Notice that each cell
is identified by a vertical column letter (A,B,C…) and a horizontal row number
(1,2,3…). Thus, the first cell in the upper left hand corner is named A1 and to the
right of it is A2 while below it is B1, etc.
2. The data in the internet database will come in the following form:
Notice that there are 10 columns of information to import into the spreadsheet
although we will only use three of them: proton (atomic) number Z, nucleon
number (mass number = A) and Binding Energy (BE). Unfortunately, there is no
way to copy just these three columns so we will have to copy them all and delete
what we don’t want later.
3. In Excel, label column 2 ―Nucleon Number‖ (in cell B1) and label column 5
―Binding Energy‖ (in cell E1) and column 11 Neutron number. Now you’re ready
to import the data.
4. Go to http://hyperphysics.phy-astr.gsu.edu/hbase/pertab/pertab.html#c1 to see
the Periodic Table of Elements. Each element is clickable and will give you both
atomic and nuclear data. Start off by choosing Hydrogen and scrolling down to
the Nuclear Data chart. Highlight all three rows (and ten columns) of nuclear
data and right-click to copy this data.
33
5. Now go back to Excel to paste in this data. Do this by right clicking in cell A2 and
clicking Paste. You should now have all the nuclear data about hydrogen in your
spreadsheet.
6. One good thing about spreadsheets is that it’s easy to put lots of data in them
and that’s what we need to do. Repeat what you did for hydrogen for each of the
first ten elements of the periodic table, then for every fifth element thereafter.
Also, include each of the elements 24-28 as well as Uranium and Plutonium. Try
to do this in numerical order so that it’s easier to format the graph later on.
That’s a lot of data! (Good thing you didn’t have to enter it by hand!)
7. We’re almost ready to start processing the data and graphing it. First though, it’s
a good idea to save this data file in case you make a mistake. Save the file on
the desktop or your flash drive.
8. Now, you should get rid of the data columns you don’t need.
9. Have Excel calculate the number of neutrons in each isotope in column K.
Graph #1: Neutron Number vs. Atomic Number
10. Graph the neutron number vs. the atomic number. For reference, plot the line N =
Z on the same graph. Using Paint, draw the line N=Z on the graph.
11. Copy your graph to a word document. Save it as ―yournamebindinglab.doc‖
Graph #2: Binding energy vs. nucleon number
12. Graph Binding energy vs. nucleon number. Copy to your document.
Graph #3: Binding energy per nucleon vs. nucleon number
13. Have Excel calculate the binding energy per nucleon in column C.
14. Graph the binding energy per nucleon vs. nucleon number; copy it to your
document.
Conclusion Questions: Inspect your graphs and your data table to answer the
following questions in your document.
1. As the nucleon number increases, what happens to the total binding energy of a
nucleus?
2. As the nucleon number increases, what happens to the binding energy per
nucleon of a nucleus?
3. Which nuclide has the highest binding energy per nucleon?
4. The majority of the binding energy per nucleon values is between what two
values? (Give your answers to the nearest whole numbers of MeV.)
34
5. What is the trend shown in the neutron vs. atomic number graph? What does this
imply?
6. As you move from hydrogen to iron on the periodic table, what happens to the
binding energy per nucleon?
7. As you move from iron to uranium on the periodic table, what happens to the
binding energy per nucleon?
35
Photoelectric Effect Virtual Lab
This virtual lab exercise consists of analyzing a simulation of a photoelectric effect
experiment. The objective of the lab is to collect data for three metals in order to create a
graph that will allow the students to find the value of Planck's constant.
The Web page contains a downloadable student worksheet and a link to the simulation:
http://physicsquest.homestead.com/quest8ac3.html.
Other photoelectric effect simulations can be found at the following Web sites:
MSU Applet: The Photoelectric Effect
This applet shows the photoelectric effect with three different materials: sodium, cesium,
and silver. The user can vary the light intensity, light wavelength, and the voltage and
then observe whether or not an electric current was produced.
Photoelectric Effect by Phillip Warner(The applet can be found on other Web sites as
well.)
This applet shows 14 different metals. The user can set the intensity to either low or high
and vary the wavelength. This applet offers a visualization of the electrons being ejected
from the metal and gives a reading of the energy of the electron in electron volts.
After the AP Physics Exam
One of the most popular topics to teach after the AP Exam is special relativity.
I like to introduce the topic by having a discussion on the concept of time. I divide my
students into teams of two and have them read a vignette from Alan Lightman's book,
Einstein's Dreams (ISBN 0-679-41646-3). Students receive a few discussion questions,
and their task is to present their conclusions in front of the class. A detailed lesson plan
can be found on my Web page: http://physicsquest.homestead.com/quest8ac2.html.
After that activity, I present a unit on special relativity divided into five sections as
follows:
1. What is relativity?


Introduce the concept of relativity before Einstein, including a discussion of
Galilean transformations
Define event and frame of reference
2. Einstein's relativity



Present an overview of the difficulties with frames of reference in Maxwell's
equation for the speed of light
Explain the significance of the Michelson-Morley experiment
Discuss Einstein's postulates of relativity:
a. All laws of physics are the same in all inertial frames of reference.
b. The speed of light in a vacuum is the same in all inertial frames of
reference.
36
3. Relativity of time and relativity of length



Understand how the principle of relativity leads to the relativity of simultaneity
and thus to time dilation and length contraction
Use the Lorentz transformations of position and velocity
Discuss the twin paradox
4. Relativistic energy


Recognize the significance of Einstein's famous equation E = mc2
Explore relativistic energy and momentum
5. Relativity of velocity

Apply the relativistic velocity transformations
Recommended textbook
Einstein's Special Relativity: Discover It for Yourself by Ernie McFarland
ISBN 1-895579-23-6
Trifolium Books Inc.
This inexpensive book ($8.95) contains a straightforward approach to special relativity.
My students found Dr. McFarland's book readable and engaging. He presents exercises
with clear, detailed solutions, and each chapter contains a set of exercises and
challenging problems. A separate Solutions Manual is available to instructors.
Online Resources
Special Relativity
Einstein Light
I strongly recommend this Web site from the University of New South Wales in Australia.
The different modules are presented in attractive Flash simulations and are
accompanied with great explanations with or without math. If you prefer, you can view
this page in HTML format.
Galileo and Einstein Lectures
This site features excellent lectures by Michael Fowler from the University of Virginia.
How Stuff Works: How Special Relativity Works
Easy-to-understand explanations on special relativity can be found on this Web site.
HyperPhysics Concepts
This is section from Georgia State University's HyperPhysics online textbook covers
relativity.
Introduction to Special Relativity
The Dummies' Guide to Special Relativity by "Arfur Dogfrey" is a humorous Web site
that contains 12 chapters explaining in simple terms what special relativity is about.
Lecture 21: Special Relativity
An illustrated summary of the main concepts in special relativity is presented by Terry
Herter from Cornell University.
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Notes on Special Relativity
These excellent lecture notes are by Tatsu Takeuchi from Virginia Tech.
SR1: The Theory Special Relativity
This is an excellent Web site by Jim Doyle, with thorough and detailed explanations on
special relativity.
NOVA: Einstein's Big Idea
This Web site is related to the original NOVA program on Einstein. It also includes a
Teacher's Guide.
Classroom Activity: A Classical and Relativistic Trip to a Black Hole
This activity by PBS effectively connects concepts from Newtonian mechanics to special
relativity with astrophysics.
Simulations
Michelson-Morley Experiment
http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/mmexpt6.htm
In this excellent simulation of the famous experiment, the user can change the rotation of
the mirrors and the velocities of light and ether.
Untitled Light Clock Experiment
Einstein's famous clock bouncing light between two mirrors is shown in this excellent
simulation of two observers moving at different speeds. (This site requires Flash.)
Light Clock
This simulation of the light clock is a useful visualization when explaining the concept of
time dilation.(Be aware that the English text on this site is difficult to understand.)
Space-Time Lab
This Java simulation from Cal Tech includes six experiments. Each experiment includes
a visualization and a space-time graph.
Concept of Space and Time in Special Relativity
This simulation by Fu-Kwun Hwang shows a light clock simulation. It includes a good
explanation.
Exhibits
A Walk Through Time
This Web site by the NIST (National Institute of Standards and Technology) Physics
Laboratory present an evolution of time and how it has been measured throughout the
ages.
Einstein -- Image and Impact
Presented by the American Institute of Physics' Center for History, this is the most
comprehensive online exhibit on Einstein.
American Museum of Natural History: Einstein
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This Web site offers an overview of the exhibit of Einstein's life and work at the American
Museum of National History.
Recommended Reading
Einstein: A Life by Denis Brian
ISBN 0-471-19362-3
John Wiley and Sons
I greatly enjoyed reading this biography of Einstein. Brian presents an outstanding
portrait of Einstein's life with explanations of his scientific accomplishments.
E = mc2: A Biography of the World's Most Famous Equation by David Bodanis
ISBN 0-8027-1352-1
Walker and Company
This interesting book introduces the reader to the concepts behind Einstein's famous
equation.
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