14
Conservation of Momentum
Conservation of Momentum
Using PASCOTM Carts and Track to Study
Collisions in One Dimension
OBJECTIVE
Students will collide two PASCOTM carts on a track to determine the momentum before and after a
collision. They will use this information to verify the law of conservation of momentum.
T E A C H E R
P A G E S
LEVEL
Physics
NATIONAL STANDARDS
UCP.2, UCP.3, A.1, B.4, B.5
TEKS
2(A), 2(B), 2(C), 2(D), 2(E), 2(F), 4(B), 4(C), 5(A), 5(C), 5(D)
CONNECTIONS TO AP
I. Newtonian mechanics, D. Systems of particles, linear momentum, 2. Impulse and momentum,
3. Conservation of linear momentum, collisions
TIME FRAME
90 minutes
MATERIALS
(For a class of 30 working in groups of 5)
6 PASCOTM tracks
12 PASCO collision carts and bar masses
(4 magnetic, 2 plunger carts, 4 non-magnetic
carts with Velcro®)
12 photogates or 12 motion detectors
masking tape
6 Vernier LabPro® or PASCO interface devices
6 computers with Vernier Logger Pro® data
collection software or graphing calculators
12 ring stands and/or clamps to mount
photogates
12 3" × 5" index cards
TEACHER NOTES
In this activity the students will investigate the loss in momentum during the interaction of two PASCO
carts in three situations: an inelastic collision, an elastic collision, and the recoil of two carts away from
each other. The loss in momentum is found by subtracting the total momentum after the interaction from
the total momentum before the interaction. This calculation assumes that the total momentum will be
conserved if there are no dissipative forces such as friction.
430
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Conservation of Momentum
14
This activity is written in such a way that the students in each group will spend the entire time taking
data at only one station, and then share the data acquired with the other groups. If you can set up six lab
stations, you should set up two inelastic stations, two elastic stations, and two recoil stations. Encourage
the students in each group to run as many different runs as they can by varying the masses of each cart
in each run. The data tables are designed to display 5 runs, but students can always run more runs and
attach another page to the lab report.
Running the groups in this way serves several purposes. First, it allows the students to remain at one
station and run many runs on one type of interaction, saving equipment and rotation time. Since the data
at all of the lab stations are obtained in similar ways, the students are not missing out on any procedural
learning. Second, it encourages the students to obtain, record, and communicate their data in such a way
that other students can easily read and analyze it.
PASCO carts, tracks, photogates, and motion detectors can be obtained from www.pasco.com.
Vernier probes and software cane be obtained from www.vernier.com.
POSSIBLE ANSWERS TO THE CONCLUSION QUESTIONS AND SAMPLE DATA
P A G E S
DATA AND OBSERVATIONS
Mass of one empty cart: 0.500 kg
Mass of one “black bar” mass: 0.500 kg
Length of card: 0.126 m
Data Table 1: Inelastic Collision
Run
T E A C H E R
Although the instructions included here are written using photogates, the speeds of the carts before and
after the interactions can also be measured by placing a motion detector at each end of the track and
obtaining the speed from the position vs. time and/or velocity vs. time graphs.
Mass of
Mass of
Velocity v1
Incident Cart, Target Cart, of m1 Before
m1
m2
Collision
(kg)
(kg)
(m/s)
Velocity v2
of m2 Before
Collision
(m/s)
Velocity v1´
of m1 After
Collision
(m/s)
Velocity v2´
of m2 After
Collision
(m/s)
1
0.500
0.500
0.185
0.000
0.088
0.088
2
1.000
0.500
0.214
0.000
0.129
0.129
3
1.500
0.500
0.159
0.000
0.110
0.110
4
0.500
1.000
0.241
0.000
0.073
0.073
5
0.500
1.500
0.232
0.000
0.045
0.045
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
431
14
Conservation of Momentum
Data Table 2: Elastic Collision
Run
Velocity v2
of m2 Before
Collision
(m/s)
Velocity v1´
of m1 After
Collision
(m/s)
Velocity v2´
of m2 After
Collision
(m/s)
1
0.500
0.500
0.223
0.000
0.000
0.213
2
1.000
0.500
0.244
0.000
0.075
0.278
3
1.500
0.500
0.175
0.000
0.054
0.237
4
0.500
1.000
0.245
0.000
–0.039
0.137
5
0.500
1.500
0.266
0.000
–0.089
0.103
Velocity v1´
of m1 After
Collision
(m/s)
Velocity v2´
of m2 After
Collision
(m/s)
P A G E S
T E A C H E R
Mass of
Mass of
Velocity v1 of
Incident Cart, Target Cart,
m1 Before
m1
m2
Collision
(kg)
(kg)
(m/s)
Data Table 3: Recoil
Run
432
Mass of
Velocity v1
Velocity v2
Mass of Plunger
Second Cart, of m1 Before of m2 Before
Cart, m1
m2
Collision
Collision
(kg)
(kg)
(m/s)
(m/s)
1
0.500
0.500
0.000
0.000
0.202
–0.197
2
1.000
0.500
0.000
0.000
0.113
–0.207
3
1.500
0.500
0.000
0.000
0.062
–0.175
4
1.500
1.000
0.000
0.000
0.106
–0.158
5
1.000
1.500
0.000
0.000
–0.158
0.106
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Conservation of Momentum
14
ANALYSIS
In the tables below, calculate the momentum for each cart before and after the collision or recoil.
Indicate the velocity of any cart which reverses its direction by using a negative sign.
Momentum for Inelastic Collision
Run
Momentum
p1 of m1
Before
Collision
(kg⋅m/s)
Momentum
p2 of m2
Before
Collision
(kg⋅m/s)
Total
Momentum
pT of the
System
Before
Collision
(kg⋅m/s)
Momentum
p1´ of m1
After
Collision
(kg⋅m/s)
1
0.093
0.000
0.093
0.044
0.044
0.088
2
0.214
0.000
0.214
0.129
0.065
0.194
3
0.239
0.000
0.239
0.165
0.055
0.220
4
0.121
0.000
0.121
0.037
0.073
0.110
5
0.116
0.000
0.116
0.023
0.068
0.091
Total
Momentum
Momentum
p2´ of m2
pT´of the
After
System After
Collision
Collision
(kg⋅m/s)
(kg⋅m/s)
T E A C H E R
Run
Momentum
p1 of m1
Before
Collision
(kg⋅m/s)
Momentum
p2 of m2
Before
Collision
(kg⋅m/s)
Total
Momentum
pT of the
System
Before
Collision
(kg⋅m/s)
1
0.112
0.000
0.112
0.000
0.107
0.107
2
0.244
0.000
0.244
0.075
0.139
0.214
3
0.263
0.000
0.263
0.081
0.119
0.200
4
0.123
0.000
0.123
–0.020
0.137
0.117
5
0.133
0.000
0.133
–0.045
0.155
0.110
Momentum
p1´ of m1
After
Collision
(kg⋅m/s)
Total
Momentum
Momentum
p2´ of m2
pT´of the
After
System After
Collision
Collision
(kg⋅m/s)
(kg⋅m/s)
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
433
P A G E S
Momentum for Elastic Collision
14
Conservation of Momentum
Momentum for Recoil
T E A C H E R
P A G E S
Run
Total
Momentum Momentum Momentum Momentum
p1 of m1
p2 of m2
pT of the
p1´ of m1
Before Recoil Before Recoil
System
After Recoil
Before Recoil
(kg⋅m/s)
(kg⋅m/s)
(kg⋅m/s)
(kg⋅m/s)
Total
Momentum Momentum
p2´ of m2
pT´of the
After Recoil System After
Recoil
(kg⋅m/s)
(kg⋅m/s)
1
0.000
0.000
0.000
0.101
–0.099
0.002
2
0.000
0.000
0.000
0.113
–0.104
0.009
3
0.000
0.000
0.000
0.093
–0.088
0.005
4
0.000
0.000
0.000
0.159
–0.158
0.001
5
0.000
0.000
0.000
–0.158
0.159
0.001
CONCLUSION QUESTIONS
Using the data obtained in all three groups, answer the following questions.
1. In general, does the data collected for the inelastic collision seem to verify the law of conservation of
momentum? Explain your answer and indicate which run of the inelastic collision best conserves
momentum.
•
In general, momentum is reasonably conserved, that is, the total momentum before the collision
is nearly equal to the total momentum after the collision. The least amount of momentum loss
occurs in Run 1, where only 0.005 kg·m/s is lost.
2. In general, does the data collected for the elastic collision seem to verify the law of conservation of
momentum? Explain your answer and indicate which run of the elastic collision best conserves
momentum.
•
In general, momentum is reasonably conserved, that is, the total momentum before the collision
is nearly equal to the total momentum after the collision. The least amount of momentum loss
occurs in Run 1, where only 0.005 kg·m/s is lost.
3. In general, does the data collected for the recoil of the two carts seem to verify the law of
conservation of momentum? Explain your answer and indicate which run of the recoil of the two
carts best conserves momentum.
•
434
In general, momentum is reasonably conserved, that is, the total momentum before the recoil is
nearly equal to the total momentum after the recoil. The least amount of momentum loss occurs
in Run 4, where only 0.001 kg·m/s is lost.
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Conservation of Momentum
14
4. List two sources of error, and explain how each affected the results of your experiments.
•
One source of error would be friction between the cart and the track. Friction reduces the speed
of the carts and contributes to the loss of momentum.
•
Another source of error might be the slight variations in the timing of the photogates as the cards
pass through them. We cannot guarantee they are perfectly consistent with each other in their
timing.
5. The screenshot below represents the interaction of two carts in either an inelastic collision, elastic
collision, or the recoil of the two carts. The target cart is initially at rest. Answer the questions that
follow.
T E A C H E R
P A G E S
a. Which type of interaction does the data table represent? Check the appropriate answer below,
and justify your answer.
√ inelastic collision
_____
•
_____ elastic collision
_____ recoil
There is only one velocity after the collision, and it is less than the initial velocity of the
incident cart, so we know that it is not two equal carts colliding elastically.
b. If the carts each have a mass of 0.500 kg, and the only available bar masses are 0.500 kg each,
how is the mass most likely distributed in this interaction? Explain your answer.
•
The velocity of the pair of carts after the collision is about half the initial velocity of the
incident cart. This indicates that the mass has doubled after the collision. So, this is a
collision between two carts of equal mass, perhaps each having a mass of 0.500 kg.
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
435
14
Conservation of Momentum
•
m⎞
kg m
⎛
pbefore = m1v1 = ( 0.500 kg ) ⎜ 0.1846 ⎟ = 0.0923
s⎠
s
⎝
•
m⎞
kg m
⎛
pafter = ( m1 + m2 ) v′ = ( 0.500 kg + 0.500 kg ) ⎜ 0.0841 ⎟ = 0.0841
s⎠
s
⎝
•
pbefore − pafter = 0.0923
kg m
kg m
kg m
= 0.0082
− 0.0841
s
s
s
6. The screenshot below represents the interaction of two carts in either an inelastic collision, elastic
collision, or the recoil of the two carts. The target cart is initially at rest. Answer the questions that
follow.
T E A C H E R
P A G E S
c. Assuming that your answer to part b is correct, how much momentum is lost in the interaction?
Show your calculation in the space below.
a. Which type of interaction does the data table represent? Check the appropriate answer below,
and justify your answer.
_____ inelastic collision
•
_____ elastic collision
_____
√ recoil
There is only one velocity through each photogate, and the second velocity recorded by the
photogate (Velocity 1 in the table) is smaller that the first velocity recorded (Velocity 2).
Thus, it is not an inelastic collision, and must be a recoil interaction.
b. If the carts each have a mass of 0.500 kg, and the only available bar masses are 0.500 kg each,
how is the mass most likely distributed in this interaction? Explain your answer.
•
436
Since Velocity 1 (0.1128 m/s) is about half the value of Velocity 2 (0.2068), the mass
moving at Velocity 1 must be about twice the mass moving at Velocity 2 for momentum to
be reasonably conserved. Perhaps the mass moving at Velocity 1 is 1.000 kg, and the mass
moving at Velocity 2 is 0.500 kg.
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Conservation of Momentum
14
c. Assuming that your answer to part b is correct, how much momentum is lost in the interaction?
Show your calculation in the space below.
•
pbefore = 0
•
m⎞
m⎞
kg m
⎛
⎛
pafter = m1v1′ + m2 v2′ = (1.000 kg ) ⎜ 0.1128 ⎟ − ( 0.500 kg ) ⎜ 0.2068 ⎟ = 0.0094
s⎠
s⎠
s
⎝
⎝
•
The difference between the total momentum before and after the recoil interaction is
0.0094 kg·m/s.
7. Consider the two screenshots A and B below, which represent two different elastic collisions.
In each case, the target cart is initially at rest, and one cart is twice as massive as the other cart.
T E A C H E R
Screenshot A
P A G E S
Screenshot B
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
437
14
Conservation of Momentum
Which screenshot represents an elastic collision in which the incident cart is more massive than the
target cart? Explain your answer.
• The incident cart is more massive in Screenshot B, since both carts continue forward through
photogate 2 after the collision.
P A G E S
8. The screenshot below represents the elastic collision between two carts of equal mass. Each cart has
a mass of 0.500 kg.
T E A C H E R
a. On the axes below, sketch a graph of momentum p vs. time t for the incident and target carts.
Be sure to indicate important values on both the horizontal and vertical axes.
•
•
438
m⎞
kg m
⎛
p1 = m1v1 = ( 0.500 kg ) ⎜ 0.2228 ⎟ = 0.1114
s⎠
s
⎝
p1′ = m1v1′ = 0
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Conservation of Momentum
14
Incident Cart:
Momentum vs. Time
p(kg·m/s)
0.1114
kg·m/s
t(s)
0.300
T E A C H E R
Target Cart:
p2 = m2 v2 = 0
•
m⎞
kg m
⎛
p2′ = m2 v2′ = ( 0.500 kg ) ⎜ 0.2133 ⎟ = 0.1067
s⎠
s
⎝
P A G E S
•
Momentum vs. Time
p(kg·m/s)
0.1067
kg·m/s
t(s)
0.300
b. Calculate the amount of momentum lost in this collision. Show your work in the space below.
•
p1 − p2′ = 0.1114
kg m
kg m
kg m
− 0.1067
= 0.0047
s
s
s
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
439
14
Conservation of Momentum
Conservation of Momentum
Using PASCOTM Carts and Track to Study
Collisions in One Dimension
When two objects collide momentum is transferred between them. Momentum p is defined as the
product of mass and velocity of an object (p = mv), and like velocity, momentum is a vector. The law of
conservation of momentum states that in the absence of any external forces, the total momentum before
a collision is equal to the total momentum after the collision. In this activity you will observe and
determine the momentum transferred for an inelastic collision (in which the carts stick together), an
elastic collision (in which the carts bounce off each other), and a recoil interaction (in which the carts
“explode” apart).
PURPOSE
In this activity you will determine the total momentum before and after three interactions of carts:
an inelastic collision, an elastic collision, and a recoil interaction. You may be placed in a group to
investigate just one of the interactions, and then asked to share your data with the other groups.
MATERIALS
PASCOTM track
2 PASCO collision carts and bar masses
2 photogates or 2 motion detectors
masking tape
Vernier LabPro® or PASCO interface devices
computer with Vernier Logger Pro® data
collection software or graphing calculator
2 ring stands and/or clamps to mount photogates
2 3" × 5" index cards
PROCEDURE
GROUP I – INELASTIC COLLISION
1. Place the two carts on the track. The ends with the Velcro® should be facing each other so that when
the carts collide they will stick together. The carts will be referred to as the incident cart (first) and
the target cart (hit by the incident cart).
2. Attach an index card of known length to each cart so that the card will pass through a photogate
before and after the collision.
3. Mount the photogates above or beside the carts so that the attached index cards will pass through the
photogates before and after the collision, as shown in Figure 1.
440
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Conservation of Momentum
14
Mounted
Photogates
Index cards
PASCO track and carts
Figure 1
4. Connect the two photogates into the DIG/SONIC 1 and DIG/SONIC 2 ports on the LabPro interface.
Open the Logger Pro data collection software, go to File, Open, Probes and Sensors, Photogate,
Two Gate Timing. You should see a graph like the one in Figure 2 below.
Figure 2
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
441
14
Conservation of Momentum
5. Measure the length of the card attached to each cart. A typical 3" × 5" index card has a length
of 0.126 m.
6. Follow the instructions on the screen to calibrate the photogate to the length of the card mounted on
the cart. If the computer knows the length of the card and the time it takes the card to pass through
the photogate, it can calculate the average velocity of the cart as it passes through the photogate.
Figures 3 and 4 show the pictures you will see as you calibrate the photogates.
Figure 3
442
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Conservation of Momentum
14
Figure 4
7. Place one cart on the track between the two photogates, and the other cart on the track outside the
photogates. Arrange the carts so that the incident cart will pass through the first photogate, collide
with the target cart, and then the target cart will pass completely through the second photogate.
When you are ready to collect data, click on the Collect button on the toolbar and roll the incident
cart toward the first photogate. The cart should pass completely through the photogate and collide
with the target cart. You may want to stop the carts as soon as the target cart passes through the
photogate so that the second photogate will not record the velocity of the incident cart. However, if
both carts pass through the photogate after the collision, we are only interested in the velocity
recorded for the target cart passing through the photogate. Record the before and after velocities of
the carts in the data table for inelastic collision on your student answer page.
8. Repeat the experiment for several more runs, adding various amounts of mass to each cart to see
how the amount of mass affects the velocity and momentum of the carts before and after the
collision. Remember to record the data in such a way that another lab group can understand how
you have organized your data and use it to answer questions about your data.
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
443
14
Conservation of Momentum
GROUP II – ELASTIC COLLISION
1. Place the two magnetic carts on the track so that they repel each other when they collide.
2. Follow steps 2–6 listed in the procedure for Group I.
3. Place one cart on the track between the two photogates and the other cart on the track outside the
photogates. Arrange the carts so that the incident (first) cart will pass through the first photogate,
collide with the target cart (the cart which is hit by the incident cart), and then the target cart will
pass completely through the second photogate. Depending on the masses and speeds of the carts, the
second cart may pass through the second photogate, or reverse its direction and pass back through
the first photogate again.
4. When you are ready to collect data, click on the Collect button on the toolbar and roll the incident
cart toward the first photogate so that it passes completely through it and collides with the target cart.
Record the before and after velocities of the carts in the data table for elastic collision on your
student answer page.
5. Repeat the experiment for several more runs, adding various amount of mass to each cart to see how
the amount of mass affects the velocity and momentum of the carts before and after the collision.
Remember to record the data in such a way that another lab group can understand how you have
organized your data and use it to answer questions about your data.
GROUP III – RECOIL
1. Using one cart with a retractable “plunger” and another cart without a plunger, place the two carts on
the track between the two photogates. Push the retractable plunger into the plunger cart so that it
locks and does not pop out. Place the plunger end of the plunger cart up against the other cart so that
when you tap the peg on the top of the plunger cart, the spring-loaded plunger pops out and pushes
the two carts apart, each passing through a photogate.
2. Follow steps 2–6 listed in the procedure for Group I.
3. When you are ready to collect data, click on the Collect button on the toolbar and lightly tap the peg
on the top of the plunger cart so that the spring-loaded plunger pops out and pushes the two carts
apart causing each cart to pass through a photogate.
4. Record the velocity of the carts in the data table for recoil on your student answer page for the time
just after they recoil away from each other.
5. Repeat the experiment for several more runs, adding various amount of mass to each cart to see how
the amount of mass affects the velocity and momentum of the carts before and after the collision.
Remember to record the data in such a way that another lab group can understand how you have
organized your data and use it to answer questions about your data.
444
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Conservation of Momentum
14
Name _____________________________________
Period ____________________________________
Conservation of Momentum
Using PASCOTM Carts and Track to Study
Collisions in One Dimension
DATA AND OBSERVATIONS
After you have taken all of the data for your group, obtain the data taken by the other two groups and
enter the results in the tables below.
Mass of one empty cart: _______________________ kg
Mass of one “black bar” mass: __________________ kg
Length of card: _______________ m
Data Table 1: Inelastic Collision
Run
Mass of
Mass of
Velocity v1
Velocity v2
Incident Cart, Target Cart, of m1 Before of m2 Before
m1
m2
Collision
Collision
(kg)
(kg)
(m/s)
(m/s)
Velocity v1´
of m1 After
Collision
(m/s)
Velocity v2´
of m2 After
Collision
(m/s)
1
2
3
4
5
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
445
14
Conservation of Momentum
Data Table 2: Elastic Collision
Run
Mass of
Mass of
Velocity v1
Velocity v2
Incident Cart, Target Cart, of m1 Before of m2 Before
m1
m2
Collision
Collision
(kg)
(kg)
(m/s)
(m/s)
Velocity v1´
of m1 After
Collision
(m/s)
Velocity v2´
of m2 After
Collision
(m/s)
Velocity v1´
of m1 After
Collision
(m/s)
Velocity v2´
of m2 After
Collision
(m/s)
1
2
3
4
5
Data Table 3: Recoil
Run
Mass of
Mass of
Velocity v1
Velocity v2
Plunger Cart, Second Cart, of m1 Before of m2 Before
m1
m2
Collision
Collision
(kg)
(kg)
(m/s)
(m/s)
1
2
3
4
5
446
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Conservation of Momentum
14
ANALYSIS
In the tables below, calculate the momentum for each cart before and after the collision or recoil.
Be sure to indicate and the velocity of any cart which reverses its direction with a negative sign.
Momentum for Inelastic Collision
Run
Momentum
p1 of m1
Before
Collision
(kg⋅m/s)
Momentum
p2 of m2
Before
Collision
(kg⋅m/s)
Total
Momentum
pT of the
System
Before
Collision
(kg⋅m/s)
Momentum
p1´ of m1
After
Collision
(kg⋅m/s)
Total
Momentum
Momentum
p2´ of m2
pT´of the
After
System After
Collision
Collision
(kg⋅m/s)
(kg⋅m/s)
1
2
3
4
5
Momentum for Elastic Collision
Run
Momentum
p1 of m1
Before
Collision
(kg⋅m/s)
Momentum
p2 of m2
Before
Collision
(kg⋅m/s)
Total
Momentum
pT of the
System
Before
Collision
(kg⋅m/s)
Momentum
p1´ of m1
After
Collision
(kg⋅m/s)
Total
Momentum
Momentum
p2´ of m2
pT´of the
After
System After
Collision
Collision
(kg⋅m/s)
(kg⋅m/s)
1
2
3
4
5
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
447
14
Conservation of Momentum
Momentum for Recoil
Run
Total
Momentum Momentum Momentum Momentum
p1 of m1
p2 of m2
pT of the
p1´ of m1
Before Recoil Before Recoil
System
After Recoil
Before Recoil
(kg⋅m/s)
(kg⋅m/s)
(kg⋅m/s)
(kg⋅m/s)
Total
Momentum Momentum
p2´ of m2
pT´of the
After Recoil System After
Recoil
(kg⋅m/s)
(kg⋅m/s)
1
2
3
4
5
CONCLUSION QUESTIONS
Using the data obtained in all three groups, answer the following questions.
1. In general, does the data collected for the inelastic collision seem to verify the law of conservation of
momentum? Explain your answer and indicate which run of the inelastic collision best conserves
momentum.
2. In general, does the data collected for the elastic collision seem to verify the law of conservation of
momentum? Explain your answer and indicate which run of the elastic collision best conserves
momentum.
448
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Conservation of Momentum
14
3. In general, does the data collected for the recoil of the two carts seem to verify the law of
conservation of momentum? Explain your answer and indicate which run of the recoil of the two
carts best conserves momentum.
4. List two sources of error and explain how each affected the results of your experiments.
5. The screenshot below represents the interaction of two carts in either an inelastic collision, elastic
collision, or the recoil of the two carts. The target cart is initially at rest. Answer the questions that
follow.
a. Which type of interaction does the data table represent? Check the appropriate answer below,
and justify your answer.
_____ inelastic collision
_____ elastic collision
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
_____ recoil
449
14
Conservation of Momentum
b. If the carts each have a mass of 0.500 kg, and the only bar masses available are 0.500 kg each,
how is the mass most likely distributed in this interaction? Explain your answer.
c. Assuming that your answer to part b is correct, how much momentum is lost in the interaction?
Show your calculation in the space below.
6. The screenshot below represents the interaction of two carts in either an inelastic collision, elastic
collision, or the recoil of the two carts. The target cart is initially at rest. Answer the questions that
follow.
a. Which type of interaction does the data table represent? Check the appropriate answer below,
and justify your answer.
_____ inelastic collision
450
_____ elastic collision
_____ recoil
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Conservation of Momentum
14
b. If the carts each have a mass of 0.500 kg, and the only bar masses available are 0.500 kg each,
how is the mass most likely distributed in this interaction? Explain your answer.
c. Assuming that your answer to part b is correct, how much momentum is lost in the interaction?
Show your calculation in the space below.
7. Consider the two screenshots A and B below, which represent two different elastic collisions.
In each case, the target cart is initially at rest, and one cart is twice as massive as the other cart.
Screenshot A
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
451
14
Conservation of Momentum
Screenshot B
Which screenshot represents an elastic collision in which the incident cart is more massive than the
target cart? Explain your answer.
8. The screenshot below represents the elastic collision between two carts of equal mass. Each cart has
a mass of 0.500 kg.
452
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
Conservation of Momentum
14
a. On the axes below, sketch a graph of momentum p vs. time t for the incident and target carts.
Be sure to indicate important values on both the horizontal and vertical axes.
Incident Cart:
Momentum vs. Time
p(kg·m/s)
t(s)
Target Cart:
Momentum vs. Time
p(kg·m/s)
t(s)
b. Calculate the amount of momentum lost in this collision. Show your work in the space below.
Laying the Foundation in Physics
©2007 Laying the Foundation, Inc. All rights reserved. Visit: www.layingthefoundation.org
453