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Please finish all the questions, there is three parts.
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Graphical Analysis 18
Momentum, Energy, and Collisions
(Motion Detector)
The collision of two carts on a track can be described in terms of momentum conservation and, in
some cases, energy conservation. If there is no net external force experienced by the system of two
carts, then we expect the total momentum of the system to be conserved. This is true regardless of
the force acting between the carts. In contrast, energy is only conserved when certain types of
forces are exerted between the carts.
Collisions are classified as elastic (kinetic energy is conserved), inelastic (kinetic energy is lost) or
completely inelastic (the objects stick together after collision). Sometimes collisions are described
as super-elastic, if kinetic energy is gained. In this experiment, you can observe elastic and
inelastic collisions and test for the conservation of momentum and energy.
Figure 1
OBJECTIVES
• Observe collisions between two carts, testing for the conservation of momentum.
• Measure energy changes during different types of collisions.
• Classify collisions as elastic, inelastic, or completely inelastic.
MATERIALS
Chromebook, computer, or mobile device
Graphical Analysis 4 app
Vernier data-collection interface
two Motion Detectors
Vernier Dynamics Track
two Vernier Dynamics Carts with magnetic and hook-and-pile bumpers
PRELIMINARY QUESTIONS
1. Consider a head-on collision between two identical billiard balls. Ball 1 is initially in motion
toward ball 2, which is initially at rest. After the collision, ball 2 departs with the same
velocity that ball 1 originally had. Disregard any friction between the balls and the surface.
What happens to ball 1? What happens to ball 2?
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©Vernier Software & Technology
1
Momentum, Energy, and Collisions (Motion Detector)
Ball 1 will transfer all of the momentum to the balI 2.
2. Sketch a position vs. time graph for each ball in Preliminary Question 1, starting with the time
before the collision starts and ending a short time after the collision.
3. Based on your graph from Preliminary Question 2, is momentum conserved in this collision?
Is kinetic energy conserved?
PROCEDURE
1. Set up the carts with the hook-and-pile pads facing each other. Measure the masses of the carts
and record the values in Table 1. Label the carts as cart 1 and cart 2.
2. Set up the Dynamics Track so that it is horizontal. Test this by releasing a cart on the track
from rest. The cart should not move.
3. Set up the motion detectors and Graphical Analysis.
a. Set the motion detector sensitivity switches to Cart.
b. Connect the motion detectors to the data-collection interface, and then connect the
interface to your Chromebook, computer, or mobile device.
c. Launch Graphical Analysis.
d. To reverse the coordinate system in Graphical Analysis for one motion detector, click or
tap the Position meter for the second motion detector and select Reverse.
e. In this experiment, you need graphs of position vs. time and velocity vs. time. If only one
graph is displayed, click or tap View, , and choose 2 Graphs.
Figure 2
4. Practice creating a gentle collision. Position cart 2 at rest in the middle of the track. Release
cart 1 so it rolls toward cart 2 with the hook-and-pile pads toward one another. The carts
should collide, stick together, and roll together.
5. Click or tap Collect to start data collection. Repeat the collision you practiced and use the
position graphs to verify that the motion detectors can track each cart properly throughout the
entire range of motion. You may need to adjust the position of one or both of the motion
detectors.
6. Place the two carts at rest in the middle of the track, with their hook-and-pile bumpers toward
one another and in contact. Zero both sensors by clicking or tapping each Position meter and
choosing zero. This procedure will establish the same coordinate system for both sensors.
Verify that the zeroing was successful by starting data collection and allowing the still-linked
carts to roll slowly along the track. The graphs for each motion detector should be nearly the
same. If not, repeat the zeroing process.
2
Physics with Vernier
Momentum, Energy, and Collisions (Motion Detector)
Part I Hook-and-pile bumpers
7. Reposition the carts as in Step 4. Click or tap Collect to begin taking data and repeat the
collision. Keep your hands out of the way of the motion detectors after you push the cart.
8. From the velocity graphs, you can determine a mean velocity before and after the collision for
each cart. To measure the mean velocity during a time interval, select the data in the interval.
Click or tap Graph Tools, , and choose View Statistics. Record the mean value, and then
dismiss the Statistics box. Measure the mean velocity for each cart, before and after collision,
and enter the four values in Table 2.
9. Repeat Steps 7–8 to collect a second run with the hook-and-pile bumpers. Note: The previous
data set is automatically stored.
Part II Hook-and-pile to empty bumpers
10. Remove the hook-and-pile inserts from one cart. Measure the mass of this cart and record it in
Table 1. The other cart’s mass should stay the same.
11. Face the hook-and-pile bumper on one cart to the empty bumper on the other. Practice this
collision, again starting with cart 2 at rest. The carts will not stick, but they will not smoothly
bounce apart either.
12. Click or tap Collect to start data collection and repeat the new collision. Use the procedure in
Step 8 to measure and record the cart velocities in Table 2.
13. Repeat the previous step to collect a second run with the hook-and-pile to empty bumpers.
Part III Magnetic bumpers
14. Insert magnets into both carts, set so the carts will repel. Measure the masses of the carts and
record in Table 1.
15. Place the carts on the track with the magnetic bumpers facing each other. Practice making this
new gentle collision, again starting with cart 2 at rest. The carts should smoothly repel each
other without physically touching.
16. Click or tap Collect to start data collection and repeat the collision you practiced in Step 15.
Use the procedure in Step 8 to measure and record the cart velocities in Table 2.
17. Repeat the previous step as a second run with the magnetic bumpers.
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3
Momentum, Energy, and Collisions (Motion Detector)
DATA TABLE
Table 1
Part
Mass of cart 1 Blue
(kg)
Mass of cart 2 Yellow
(kg)
I
0.2615
0.2664
II
0.2615
0.2664
III
0.2615
0.2664
Table 2
Run
number
Velocity of
cart 1 before
collision
(m/s)
Velocity of
cart 2 before
collision
(m/s)
Velocity of
cart 1 after
collision
(m/s)
Velocity of
cart 2 after
collision
(m/s)
Hook-and-pile
1
0.518
0
0.175
0.175
Hook-and-pile
2
0.277
0
0.102
0.102
Mixed
3
0.375
0
0.004
0.217
Mixed
4
0.163
0
0.006
0.077
Magnetic
5
0.379
0
0
0.316
Magnetic
6
0.280
0
0
0.255
Bumper type
Part I:
Part II:
Part III:
Table 3
Run
number
Momentum
of cart 1
before
collision
(kg•m/s)
Momentum
of cart 2
before
collision
(kg•m/s)
Momentum
of cart 1
after
collision
(kg•m/s)
Momentum
of cart 2
after
collision
(kg•m/s)
Total
momentum
before
collision
(kg•m/s)
Total
momentum
after
collision
(kg•m/s)
Ratio of
total
momentum
after/before
1
0.135
0
0.0457
0.0466
0.135
0.923
1.462
2
0.0724
0
0.0266
0.0217
0.0724
0.0537
1.348
4
3
0
4
0
5
0
6
0
Physics with Vernier
Momentum, Energy, and Collisions (Motion Detector)
Table 4
Run
number
KE of cart 1 KE of cart 2 KE of cart 1 KE of cart 2
before
before
after
after
collision
collision
collision
collision
(J)
(J)
(J)
(J)
1
0
2
0
3
0
4
0
5
0
6
0
Total KE
before
collision
(J)
Total KE
after
collision
(J)
Ratio of
total KE
after/before
ANALYSIS
1. For each run, determine the momentum (mv) of each cart before the collision, after the
collision, and the total momentum before and after the collision. Calculate the ratio of the total
momentum after the collision to the total momentum before the collision. Enter the values in
Table 3.
2. For each run, determine the kinetic energy (KE = ½mv2) for each cart before and after the
collision. Calculate the ratio of the total kinetic energy after the collision to the total kinetic
energy before the collision. Enter the values in Table 4.
3. If the total momentum for a system is the same before and after the collision, we say that
momentum is conserved. If momentum were conserved, what would be the ratio of the total
momentum after the collision to the total momentum before the collision?
4. If the total kinetic energy for a system is the same before and after the collision, we say that
kinetic energy is conserved. If kinetic energy were conserved, what would be the ratio of the
total kinetic energy after the collision to the total kinetic energy before the collision?
5. Inspect the momentum ratios in Table 3. Even if momentum is conserved for a given collision,
the measured values may not be exactly the same before and after due to measurement
uncertainty. The ratio should be close to one, however. Is momentum conserved in your
collisions?
6. Repeat the preceding question for the case of kinetic energy, using the kinetic energy ratios in
Table 4. Is kinetic energy conserved in the magnetic bumper collisions? How about the hookand-pile collisions? Is kinetic energy conserved in the third type of collision? Classify the
three collision types as elastic, inelastic, or completely inelastic.
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5
Momentum, Energy, and Collisions (Motion Detector)
EXTENSIONS
1. Using the magnetic bumpers, consider other combinations of cart mass by adding weight to
one cart. Is momentum or energy conserved in these collisions?
2. Using the magnetic bumpers, consider other combinations of initial velocities. Begin with
having both carts moving toward one another initially. Are momentum and energy conserved
in these collisions?
6
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