Momentum and Collisions (with Motion Detectors)

Momentum and Collisions (with Motion Detectors)
Experiment
Momentum and Collisions
11A
INTRODUCTION
You may have learned that a moving object possesses kinetic energy. Momentum is another
property of an object, related to its mass and velocity, that is useful to describe its behavior.
Momentum, p, is the product of the mass and velocity of an object, p = m v .
co
py
You may have learned an external force produces a change in the momentum of an object. If we
consider as our system two carts that undergo a collision, then any forces they exert on one
another are internal to the system. In this experiment you will examine the momentum of both
carts before and after collisions to see what effect, if any, these forces have on the momentum of
a system.
OBJECTIVES
In this experiment, you will
n
Collect velocity-time data for two carts experiencing different types of collisions.
Compare the system momentum before and after collisions.
Compare the kinetic energy of the system before and after collisions.
MATERIALS
tio
•
•
•
ua
Vernier data-collection interface
Logger Pro or LabQuest App
two Vernier Motion Detectors
two Motion Detector brackets
neodymium magnets and Velcro®
patches for carts
Vernier Dynamics Track
standard cart
plunger cart
500 g standard lab mass
al
PRE-LAB QUESTION
Ev
Consider a head-on collision between a cue ball and a billiard ball initially at rest. Sketch a
velocity-time graph for each ball for the interval shortly before until shortly after the collision.
Justify your predictions for the final velocity of each billiard ball.
Advanced Physics with Vernier – Mechanics
©Vernier Software & Technology
11A - 1
Experiment 11A
PROCEDURE
1. Attach the Motion Detectors to the brackets and position them at opposite ends of the
Dynamics Track.
2. If your motion detectors have a switch, set each of them to
Track.
3. Adjust the leveling screws on the feet as needed to level the track. To make sure the track is
level, place a cart on the track and give it a gentle push. It should not slow more in one
direction than in the other.
4. Connect both motion detectors to the interface and start the data-collection program. Make
the necessary adjustments so that a velocity vs. time graph for each detector is shown in the
graph window.
5. Make sure that each of your carts has the neodymium magnets at one end and the Velcro
patches at the other. Place both carts, linked with their Velcro patches, in the center of the
track. Zero both motion detectors and reverse the direction of one of them.
6. Begin collecting data, then gently push the linked carts towards one of the motion detectors
(see Figure 1). Be sure to keep your hands out of the way of the motion detectors. Catch the
carts before they run off the track. The velocity-time graphs from each detector should be
nearly mirror images of one another; they will also show a slight decrease in velocity due to
friction. Adjust the level of the track until this decrease appears to be nearly the same in both
directions.
Figure 1
Part 1 Elastic collisions
7. Reverse the carts so that their magnet ends face one another. Separate them by about 40 cm.
Practice launching one cart toward the other so that at closest approach they exert forces on
each other without touching. A jarring collision will not yield satisfactory data.
8. Place the target cart in the middle of the track. Position the other cart at least 20 cm in front
of one of the motion detectors.
9. Start data collection. Then, when you hear the motion detectors clicking, launch one of the
carts toward the other. Because momentum, like velocity, is a vector quantity, check to see if
the signs of the velocities match your experimental setup. If necessary, reverse the direction
of one or both sensors.
10. In this experiment you are concerned with changes in momentum due to the collisions of the
carts. Some slowing due to friction is inevitable. To minimize the effect of frictional losses in
11A - 2
Advanced Physics with Vernier - Mechanics
Momentum and Collisions
your analysis, you should select short intervals of the velocity-time graphs just before and
just after a collision. Then, choose Statistics from the Analyze menu and record the mean
velocity of each cart for these intervals.
A data table has been provided for you. You may wish to use Logger Pro to help you record
and analyze your data.
11. Collect data for up to six elastic collisions, varying the initial velocity and the mass of either
cart. Try a collision in which both carts have an initial velocity, but different masses.
Part 2 Inelastic collisions
1. Reverse the carts so that the ends with the Velcro patches face one another. Practice
launching one cart toward the other so that when they collide, the carts link smoothly and
continue moving without a noticeable bounce. A jarring collision will not yield satisfactory
data.
2. Collect data as before for at least three inelastic collisions, varying the initial velocity and the
mass of either cart. Determine the velocity of the carts before and after the collision as you
did in Part 1. Since both motion detectors provide velocity data after the collision, you will
have to decide how to record the velocity of the linked carts.
Part 3 Explosions
1. Place the carts in the center of the track with the plunger end of one cart facing the other.
Depress and lock the mechanism on the plunger cart. Position the carts so that they are
touching.
2. Begin data collection, then give a quick tap to the release pin with something hard, such as
the support rod for a force sensor, as shown in Figure 2. Catch the carts before they run off
the track.
Figure 2
3. Repeat, varying the mass of either cart. Determine the velocity of the carts after the
explosion as you did in Part 1.
Advanced Physics with Vernier - Mechanics
11A - 3
Experiment 11A
EVALUATION OF DATA
Part 1 Elastic collisions
1. You can use the tables below to help with your evaluation of the momentum before and after
the collisions of the carts.
Cart 1
Ru
n
1
2
3
4
5
6
Mass
(kg)
Initial velocity
(m/s)
Cart 2
Final velocity
(m/s)
Mass
(kg)
Before
Run
p of cart 1
(kg-m/s)
p of cart 2
(kg-m/s)
Initial velocity
(m/s)
Final velocity
(m/s)
After
p of system
(kg-m/s)
p of cart 1
(kg-m/s)
p of cart 2
(kg-m/s)
Ratio
p of system
(kg-m/s)
p after
p before
1
2
3
4
5
6
Another approach is to use Logger Pro to help you organize your calculations.
2. How does the total momentum of the system after the collision compare with that before the
collision? Do your results agree with your expectations? Explain.
3. Calculate the total kinetic energy, E k = 1 2 m v 2 , of the system both before and after each of
the collisions. How do these quantities compare?
Part 2 Inelastic collisions
1. You can use the tables below to help with your analysis of the momentum before and after
the collision.
Cart 1
Run
Mass
(kg)
Initial velocity
(m/s)
Cart 2
Final velocity
(m/s)
Mass
(kg)
Initial velocity
(m/s)
Final velocity
(m/s)
1
2
3
11A - 4
Advanced Physics with Vernier - Mechanics
Momentum and Collisions
Before
Run
p of cart 1
(kg-m/s)
p of cart 2
(kg-m/s)
After
p of system
(kg-m/s)
p of cart 1
(kg-m/s)
p of cart 2
(kg-m/s)
Ratio
p of system
(kg-m/s)
p after
p before
1
2
3
How does the total momentum of the system after the collision compare to that before the
collision? Is the agreement in these inelastic collisions as good as that in the elastic
collisions? Try to account for any differences.
2. Calculate the total kinetic energy of the system both before and after each of the collisions.
How do these quantities compare? Compare your findings with those of others in your class.
3. We have used “elastic” to describe collisions in which the objects bounce, and “inelastic” to
describe collisions in which the objects stick. Based on your comparison of the kinetic
energy before and after collisions, provide a more conceptual definition of these descriptors.
Part 3 Explosions
1. You can use the tables below to help with your analysis of the momentum before and after
the collision.
Cart 1
Ru
n
1
2
3
Mass
(kg)
Initial velocity
(m/s)
Cart 2
Final velocity
(m/s)
Mass
(kg)
Before
Ru
n
1
2
3
p of cart 1
(kg-m/s)
p of cart 2
(kg-m/s)
Initial velocity
(m/s)
Final velocity
(m/s)
After
p of system
(kg-m/s)
p of cart 1
(kg-m/s)
p of cart 2
(kg-m/s)
Ratio
p of system
(kg-m/s)
% diff
How does the total momentum of the system after the explosion compare to that when the
carts were stationary? Report any discrepancy as a percentage of the momentum of one of the
carts.
2. Calculate the total kinetic energy of the system both before and after each of the explosions.
How do you account for the increase in kinetic energy?
Advanced Physics with Vernier - Mechanics
11A - 5
Vernier Lab Safety Instructions Disclaimer
THIS IS AN EVALUATION COPY OF THE VERNIER STUDENT LAB.
This copy does not include:
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The complete Advanced Physics with Vernier – Mechanics lab manual includes 4 Introductory
Activities and 19 experiments, as well as essential teacher information. The full lab book is
available for purchase at: http://www.vernier.com/cmat/phys-am.html
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