Elastic and Inelastic Collisions
Conservation of momentum that exists within elastic and inelastic collisions
Victor Jeung, Terry Tong, Cathy Liu, Jason Feng
November 25th, 2011
Elastic and Inelastic Collisions
1
Abstract
The type of collisions between two objects is differentiated by the conservation of kinetic energy after
the collision. When an elastic collision occurs between two objects regardless if one is stationary or
moving, the result is that the kinetic energy is transferred between the objects and conserved in a
perfect environment. During an inelastic collision the objects involved within the collision are stuck
together, while the total momentum of the object is conserved. Kinetic energy is lost through either
internal forces or heat. The lab that we have conducted is to verify the conservation of momentum by
changing the independent variables and recording the dependent variables in both elastic and inelastic
collisions.
Introduction
Hypothesis
The total momentum before and after the collision will be conserved, as stated by the conservation of
momentum law, while kinetic energy will or will not be conserved depending on the type of collision
that occurs.
Variables
Within this lab, we experience a number of variables that we can and cannot control. The controlled
variables are the initial velocity of one car, the mass of each car, the coefficient of kinetic friction
between the car and the track. The independent variable is the time the cars travel. The dependent
variable is the velocities of the cars during the collisions of both cars.
Equation
𝑝⃗ = mv
�⃗
𝐽⃗ = 𝐹⃗ ∆t = ����⃗
∆p
Momentum formula
Impulse formula
𝑝1 = ����⃗
����⃗
𝑝2
In conservative system this holds true
v𝑎 − 𝑣𝑏 = −(𝑣𝑎′ − 𝑣𝑏′ )
(In elastic collision)
1
2
K = 𝑚𝑣 2
Kinetic Energy formula
���⃗′
m𝑎 ����⃗
𝑣𝑎 + m𝑏 ����⃗
𝑣𝑏 = (𝑚𝑎 + 𝑚𝑏 )𝑣
(In inelastic collision)
p is the momentum of the object
J is the impulse of the object in a certain period
m is the mass of the object
F is the force acting on the object
v is the velocity of the object
t is the period for the force acting on the object
Elastic and Inelastic Collisions
2
K is the kinetic energy of the object
Experiment
Apparatus
•
•
•
•
2 dynamic cars (near frictionless cars)
An smooth aluminum dynamic track
Additional masses
2 Motion sensors
Conducting the experiment
Basic execution of the experiment is that we have two cars; one will be stationary placed at the 0.39 m
on the track, while the other will start off from 0 m on the track. The car that will be moving will be
propelled either by of a spring mechanism or a magnetic repulsion. When both cars are at their ready
position, the person at the computer will be instructed to start the motion sensor and we let the car go.
Elastic Collision
Elastic and Inelastic Collisions
3
During the elastic collision of the experiment we used the spring mechanism to propel the moving car.
During the collision the magnets situated at the front of the car will be responsible for repelling the
stationary car’s magnets. This ensures that the car does not fly in to each other and cause a bloody
mess, and makes the collision as efficient as possible (efficient meaning as much energy transferred as
possible).
Inelastic Collision
During an inelastic collision the car will be propelled using the repulsion of the magnets of the car to a
stationary magnetic plate. During the collision the front of the car is now placed with Velcro which will
attach to the stationary car during the collision. The Velcro will make sure that both of the cars will
defiantly be attached after the collision.
Data
Elastic
collision
1
2
3
4
5
6
7
8
9
Inelastic
initial
energy
Car1
5.99512
5
8.8445
6.78612
5
10.404
8.01025
19.6
4.802
11.7811
25
6.10512
5
final
energy
Car1
0.000781
25
0.4805
0.010125
final
energy
Car2
4.272576
8
5.1005
5.565125
Total
0.00025
0.21025
0.1
1.152
0.820125
6.105125
8.712
7.3205
10.30225
9.604
0.6845
9.216
6.105375
8.92225
7.4205
11.45425
10.42412
5
9.9005
2
initial
energy
Car1
3.2334067
36
6.216125
3
4
3.872
5.184
1.051111
25
1.1045
1.05625
5
4.8233025
1.40625
1
4.273358
05
5.581
5.57525
Initial
Momentu
m
54.75
Final
Momentu
m
-0.625
Final
Momentu
m
46.22
66.5
58.25
-15.5
-2.25
50.5
52.75
45.59
5
35
50.5
102
89.5
140
49
76.75
0.5
14.5
10
-24
-20.25
55.25
66
60.5
101.5
98
55.75
80.5
70.5
77.5
77.75
55.25
-18.5
54.5
36
final
energy
Car1
0.338
final
energy
Car2
0.338
Total
1.0511112
5
1.1045
0.528125
0.703125
2.10222
25
2.209
1.58437
5
2.10937
5
Elastic and Inelastic Collisions
0.676
Total
Initial
Momen
tum
40.2082
5
55.75
Final
Momen
tum
13
Final
Momentu
m
13
Total
22.925
22.925
45.85
44
72
23.5
32.5
23.5
16.25
47
48.75
69.45
37.5
18.75
56.25
26
4
6
7
14.4
4.851125
1.444
0.528125
0.722
1.05625
8
9
5
5.253125
0.4805
0.595125
0.961
1.19025
2.166
1.58437
5
1.4415
1.78537
5
120
49.25
38
16.25
19
32.5
57
48.75
50
51.25
15.5
17.25
31
34.5
46.5
51.75
Data Analysis
From the above we can see clearly that the kinetic energy within the elastic collision is well conserved
but with a high loss of energy from factors such as friction. Meanwhile the kinetic energy during an
inelastic collision is almost lost completely. The momentum is conserved very well but there is factors
which limits how well the momentum is conserved which is discussed within the conclusion in errors.
Conclusion
There were some random, systematic and human errors in our lab. These were:
•
•
•
•
•
The systematic error of the existence of friction between the cars and dynamics track. This
caused the cars to gradually slow down while in motion.
The systematic error of the dynamics track being not leveled and slightly at an angle. Our group
tried to minimize this error by adding additional pieces of cardboard underneath the track in
order to level and balance the track.
The human error of reaction time. The motion trackers started tracking the motion of the cars
sometimes before or after the car was released.
The random error of adding additional initial velocity when the cars were released. This caused
slight differences in initial velocities for each trial.
The random error of not always placing the cars at the exact starting position. Sometimes cars
would slide slightly forward or backward after being placed causing them to have a smaller or
larger displacement during the trials.
If we were to complete the momentum lab again, we would:
•
•
•
•
•
Try to use a surface that was not slanted so we would not need to use pieces of cardboard to
level out and balance the track.
Complete more trials to ensure that data collected is more accurate and that outlying data is
better averaged out.
Try to be more careful and ensure that no additional initial velocity is added when releasing the
cars and that the cars are placed at the exact same starting position every time.
Obtain data using video tracking software as it is more accurate than using motion sensors since
they are very sensitive.
Use adjustable friction pads to see how an external force of friction affects the momentum and
kinetic energy of the cars.
Elastic and Inelastic Collisions
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