Momentum, Energy and Collisions
Temidayo Akinbi and Jacqueline Newland
12/14/18
Dr. Psaker
Abstract
For this experiment, we observed collisions between two carts, testing for the
conservation of momentum. To set up this experiment we used a Vernier Dynamics track, a
motion detector, two Vernier dynamic carts, Logger Pro and LabQuest. Next, we measured the
masses of the dynamic carts and recorded them in the data table. Then, we set up the motion
detector placing it 0.15 m away from the end of the dynamic track. For the bumper collisions in
part I we repositioned the carts to that they were facing one another and then we started the
collisions, collecting the data for the velocity vs time graph and position vs time graph. In trial
one we found that the total momentum before the collision was 0.1527 kg*m/s for trial two it
was 0.2201 kg*m/s for trial three it was 0.1698 kg*m/s and for trial four it was 0.2179 kg*m/s.
We also found that in trial one the total momentum after collision was 0.1400 kg*m/s for trial
two it was 0.2107 kg*m/s, for trial three it was 0.1554 kg*m/s and for trial four it was 0.2010
kg*m/s. Bringing the ratios for the total momentum before and after collision for trial one, two,
three and four to 0.9168 kg*m/s, 0.9573kg*m/s, 0.9152 kg*m/s and 0.9224 kg*m/s. Since these
ratios of the total momentum are close to 1 it tells us that the momentum was conserved in this
experiment. We also found that the ratios for total kinetic energy for trials 1, 2, 3, and 4 were
0.8162 J, 1.002 J, 0.4187 J and 0.4244 J. Some potential sources of error include human error
when resetting our collisions on the dynamic track we weren’t consistently putting them the
exact same distance apart which could have caused some variation in data.
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?
Ball one stops, the second ball moves with the same velocity as the first one.
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?
The momentum and kinetic energy are conserved in this collision. Since there are no
external forces momentum and kinetic energy are conserved.
Data
Mass of cart 1(kg) 0.4987
Table 1
Mass of cart 2(kg) 0.5019
Table 2
Bumper type Run number Velocity of
Velocity of
Velocity of
cart 1 before cart 2 before cart 1 after
collision
collisions
collision
(m/s)
(m/s)
(m/s)
Part I
1
0.3062
0
0.0033
Bumper
Bumper
2
0.4414
0
0.0170
Part II
3
0.3404
0
0.1538
Hook-andpile
Hook-and4
0.4370
0
0.1999
pile
Run
number
1
2
3
4
Moment
um of
cart 1
before
collision
(kg*m/s)
0.1527
0.2201
0.1698
0.2179
Moment
um of
cart 2
before
collision
(kg*m/s)
0
0
0
0
Table 3
Moment Moment
um of
um of
cart 1
cart 2
after
after
collision collision
(kg*m/s) (kg*m/s)
0.0016
0.1384
0.0085
0.2022
0.0767
0.0787
0.0997
0.1013
Total
moment
um
before
collision
(kg*m/s)
0.1527
0.2201
0.1698
0.2179
Velocity of
cart 2 after
collision
(m/s)
0.2757
0.4028
0.1569
0.2019
Total
moment
um after
collision
(kg*m/s)
0.1400
0.2107
0.1554
0.2010
Ratio of
total
momentu
m
(after/bef
ore)
0.9168
0.9573
0.9152
0.9224
Run
number
1
2
3
4
KE of
cart 1
before
collision
(J)
0.0234
0.0486
0.0289
0.0476
KE od
cart 2
before
collision
(J)
0
0
0
0
Table 4
KE of
KE of
cart 1
cart 2
after
after
collision collision
(J)
(J)
2.715*10-6 0.0191
7.206*10-5 0.0407
0.0059
0.0062
0.0100
0.0102
Total KE
before
collision
0.0234
0.0486
0.0289
0.0476
Total
KE
after
collision
(J)
0.0191
0.0487
0.0121
0.0202
Ratio of
total KE
after/before
0.8162
1.002
0.4187
0.4244
Data
Velocity vs time graph
Figure 2. Velocity vs. Time graph of the two carts as they collide.
Analysis
1. See Data Table 1 and 3.
2.
See Data Table 4.
3. If momentum were conserved, the ratio of the total momentum after the collision to the
total momentum before collision would be 1:1.
4. If kinetic energy were conserved, the ratio of the total kinetic energy after the collision to
the total kinetic energy before the collision would be 1:1.
5. Yes, momentum is conserved in our collision. We can come to this conclusion based on
the fact all four of the trials had ratios very close to 1. The average percent difference
between 1 and the average total momentum ratio is 7.48%.
6. Yes, kinetic energy is conserved in our completely inelastic collisions. Our four collisions
were completely inelastic and since their ratios were very close to one, we can infer that
kinetic energy was conserved. Recognizing that only two collisions were exactly
inelastic one can make inferences about the other collisions. From the data, an inference
can be made that the second two trials (Velcro to Velcro) can be classified as inelastic
because they were both recorded in the 0.4 range. The first two trials (bumper to bumper)
can be classified as completely inelastic because 1.0 and 0.8 are not close in the same
range.
References:
GMU Reference By:
https://mymasonportal.gmu.edu/webapps/blackboard/execute/content/file?cmd=view&content_i
d=_4531146_1&course_id=_34409_1