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Name: Bryan Meza
Lab #9: Conservation during Collisions
Objectives:
Collisions can be classified as elastic, inelastic, or completely inelastic. A collision is most frequently described as super-
elastic when kinetic energy is gained. In this experiment, we will observe most of these collisions and see if momentum and energy are preserved in each case. The energy changes that arise in different kinds of collisions with the carts will be
measured, and the outcomes will be classified as totally inelastic, somewhat inelastic, or elastic.
Equipment:
Station #: 8
Partner: Aiden
, rating: #5/5
Computer
Logger Pro Program
LabQuest Min iINterface
Two Vernier Motion Detectors
Track
Carts with Magnetic Bumpers
Digital Scale
Mass Set
Preliminary Questions:
#1:
#2: The collision is elastic, meaning that momentum and energy are both conserved, because the two balls did not adhere to one another. This is assuming that each ball has the same mass. Momentum and kinetic energy are both conserved in elastic collisions.
Procedure:
For this part of the lab, we setup the track that is level and put up motion detectors at each end of the track, so it can read the movement of the carts. This enabled them to read anything towards it as negative and moving away from it as positive. Once everything was setup, we practiced by creating gentle collisions. We then used magnetic bumper carts.
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This enabled us to get necessary data to determine our average velocity before and after collision for each cart to put in our data table.
Steps #1-14: Collision 1
Collision 2 Collision 3
Collision 4 Collision 5
Collision 6
Data Table A:
Velocity of
cart 1 before
collision
Velocity of
cart 2 before
collision
Velocity of
cart 1 after
collision
Velocity of
cart 2 after
collision
Cart 1
mass
Cart 2
mass
Trial
(m/s)
(m/s)
(m/s)
(m/s)
(kg)
(kg)
Part 1:
bounce
1
0.4386
0
-0.000836
0.4197
.499
.495
2
0.3324
0
-0.0007887
0.2992
.499
.495
Part 2:
stick
3
0.5853
0
0.2671
0.2653
.499
.495
4
0.5821
0
0.2683
0.2687
.499
.495
Part 3:
crash
5
0.6181
0
0.1339
0.5103
.499
.495
6
0.5080
0
0.1151
0.4395
.499
.495
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Analysis:
#1:
The Law of Conservation of Momentum asserts that "the total momentum of the system before collision is equal to the total momentum of the system after collision." Pi = Pf. The system's total momentum before and after collisions is expressed as Pf/Pi. Consequently, the total momentum before and after the contact have a ratio of 1.0.
#2:
In the elastic collision, the kinetic energy of the system is conserved. Kf = Ki as a result. Before and after the impact, the system's total kinetic energy ratio was as follows: As Kf/Ki, 1. As a result, the ratio of the system's total kinetic energy after impact to its total kinetic energy before impact is 1.0.
#3:
Mv = m(v1 + v2)
V = v1 + v2
Data Table B:
Momentum
of cart 1
before
collision
Momentum
of cart 2
before
collision
Momentum
of cart 1
after
collision
Momentum
of cart 2
after
collision
Total
momentum
before
collision
Total
momentum
after
collision Ratio of
total
momentum
after/before
Trial
(kg
•
m/s)
(kg
•
m/s)
(kg
•
m/s)
(kg
•
m/s)
(kg
•
m/s)
(kg
•
m/s)
1
0.2189
0
-0.000417
0.2078
0.2189
0.2073
0.95
2
0.1659
0
-0.000394
0.1481
0.1659
0.1477
0.89
3
0.2921
0
0.1333
0.1315
0.2921
0.2648
0.91
4
0.2905
0
0.1339
0.1223
0.2905
0.2562
0.88
5
0.3084
0
0.0668
0.2332
0.3004
0.2322
0.75
6
0.2535
0
0.0574
0.1999
0.2535
0.2574
1.02
#4:
Pf= Pi. Pf/Pi = is the ratio of the system's overall momentum before and after collisions
Data Table C:
KE of
cart 1
before
collision
(J)
KE of
cart 2
before
collision
(J)
KE of
cart 1 after
collision
(J)
KE of
cart 2 after
collision
(J)
Total KE
before
collision
(J)
Total KE
after
collision (J)
Ratio of
total KE after/before
Trial
1
0.04800
0
~0
0.04395
0.04800
0.04395
0.91
2
0.02757
0
~0
0.02234
0.02757
0.02234
0.81
3
0.08547
0
0.01780
0.01601
0.08457
0.03381
0.3956
4
0.08454
0
0.01796
0.01643
0.08454
0.03439
0.41
5
0.09532
0
0.00447
0.03924
0.09532
0.0637
0.67
6
0.06439
0
0.003305
0.04394
0.06439
0.04725
0.7338
#5:
Our momentum is conserved in our collisions, since the ratios are close to 1
#6:
(p1)^2/2m
They are conserved since the ratio of total KE. After and before are close to 1 in the first and second collision. The third is
a little off but not by much
#7:
Elastic collisions, such the way pool balls bounce off one another and continue to travel at their previous speeds, happen
when both momentum and kinetic energy are conserved. When kinetic energy is not preserved and just momentum is, an inelastic collision occurs. When two objects collide, no kinetic energy is transferred or gained—this is known as a totally elastic collision.
Extensions:
#1: Collision 1
#2: Our first trial was not conserved, but the rest were since the ratio was close to 1.
Collision 1
Collision 2a
Collision 2c
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Data Table A:
Velocity of cart
1 before
collision
Velocity of
cart 2 before
collision
Velocity of
cart 1 after
collision
Velocity of
cart 2 after
collision
Cart 1
mass
Cart 2
mass
Ext
(m/s)
(m/s)
(m/s)
(m/s)
(kg)
(kg)
1
0.04800
0
0.2769
0.2749
.499
.455
2a
0.3364
0
0.01967
0.2061
.499
.455
2b
0.4578
0
0.1369
0.1321
.499
.455
2c
0.2537
0
0.1302
0.1338
.499
.455
Data Table B:
Momentum
of cart 1
before
collision
Momentum
of cart 2
before
collision
Momentum
of cart 1
after
collision
Momentum
of cart 2
after
collision
Total
momentum
before
collision
Total
momentum
after
collision Ratio of
total
momentum
after/before
Ext.
(kg
•
m/s)
(kg
•
m/s)
(kg
•
m/s)
(kg
•
m/s)
(kg
•
m/s)
(kg
•
m/s)
1
0.0240
0
0.138
0.125
0.0240
0.263
10.96
2a
0.168
0
0.00982
0.125
0.168
0.135
0.80
2b
0.228
0
0.0683
0.0601
0.228
0.1284
0.56
2c
0.127
0
0.0650
0.0609
0.127
0.1259
0.99
Data Table C:
KE of
cart 1
before
collision
(J)
KE of
cart 2
before
collision
(J)
KE of
cart 1 after
collision
(J)
KE of
cart 2 after
collision
(J)
Total KE
before
collision
(J)
Total KE
after
collision (J)
Ratio of
total KE after/before
Ext.
1
0.000575
0
0.0191
0.0172
0.000575
0.0363
63.1
2a
0.0282
0
0.0000965
0.00966
0.0282
0.00976
0.34
2b
0.0282
0
0.0191
0.00966
0.0282
0.101
3.58
2c
0.0161
0
0.00423
0.00407
0.0161
0.0083
0.52
Conclusion:
In this lab, we tested the momentum and, in some situations, energy conservation that result from the collision of two carts on a track. It is possible to categorize collisions into three groups: totally elastic, inelastic, and elastic. We saw a collision between two carts in order to test the conservation of momentum in this experiment. The method by which we
would test it would be to compute the momentum and kinetic energy for every kind of collision. We could categorize as one of three collisions after we figured it out. I discovered that an elastic collision occurs when the ratio is almost one and the kinetic energy is conserved. The kinetic energy is wasted in an inelastic collision. And in the event of a collision, the objects remain together—completely inelastic. I become more proficient at reading collisions and energy as a result of doing this experiment. I expected the outcomes we predicted because my initial responses were quite accurate. Naturally, there were mistakes made during the entire experiment. Should I repeat this experiment, I would ensure that the track is leveled as it has the potential to distort our results. Additionally, I would ensure that the sensors are accurately reading the carts as there were instances in which our ratios were far off.
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