GateWay CC
PHY101 Physics Lab:
ELASTIC COLLISION
A collision between two objects in which the total kinetic energy of the two objects before the
collision is equal to total kinetic energy of the two objects after the collision – conservation of
energy is called ELASTIC COLLISION. In one dimensional elastic collision between two objects,
total momentum of the two objects before the collision is equal to total momentum of the two
objects after the collision – conservation of momentum. The purpose of this lab is to calculate
the velocities of the two objects before and after the collision, using the principle of
conservation of momentum and conservation of energy during the
collision.
Theory
Measurement of velocity in this lab is based on the principle of conservation of momentum
and conservation of energy. If m1 is the mass of the first object and m2 is the mass of the
second object in elastic collision, then based on the principle of conservation of momentum
and energy:
Momentum before the collision = Momentum after the collision:
m1  v1i  m2  v 2i  m1  v1 f  m2  v 2 f
(1)
Energy before the collision = Energy after the collision:
1
1
1
1
2
2
2
2
 m1  v1i   m 2  v 2i   m1  v1 f   m 2  v 2 f
2
2
2
2
(2)
where:
v1i - is the initial velocity of the of the first object.
V2i - is the initial velocity of the of the second.
V1f - is the final velocity of the of the first.
V2f - is the final velocity of the of the second.
Simplifying last equation we obtain the relation between the velocities before and after the
collision:
v1i  v1 f  v 2i  v 2 f
(3)
Figure 1. Object before and after the in one dimensional elastic collision
Solution of the system of equations (1) and (3) will provide the information on final
velocities.
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INITIAL SETUP
a) Go to the following website and follow instructions bellow.
http://www.gwc.maricopa.edu/class/phy101/simulation/collision/index.htm
Description of the one dimensional elastic collision simulation: To run the simulation, set the
masses of two objects and their initial velocities (velocities before the collision) by clicking on + or
– arrows next to masses or velocities. Press "Go" to initiate the simulation. Record the velocities of
the two objects after the collision. Press "reset" at the end of simulation to initialize the
experiment. m1 is the mass of red box, m2 is the mass of blue box, v1 is the velocity of red box,
and v2 is the velocity of blue box.
In this lab you are going to analyze the following 5 cases of elastic collision.
Case 1: Elastic collision between two Boxes of Equal Mass
Two objects (red and blue) are with identical masses (m1 = m2 = 1 kg). Red object travels at
velocity of v1i = 1 m/s toward the blue object at rest v2i = 0 m/s.
Case 2: Elastic collision between two Boxes of Different Mass
Two objects are with different masses (m1 = 1 kg and m2 = 3 kg). Red object travels at velocity of
v1i = 1 m/s toward the blue object at rest v2i = 0 m/s.
Case 3: Elastic collision between two Boxes with Equal Mass traveling toward each other
Two objects (red and blue) are with identical masses (m1 = m2 = 1 kg). Red object travels at
velocity of v1i = 1 m/s toward the blue ball that travels in opposite direction with velocity of v 2i = –
1 m/s.
Case 4: Elastic collision between two Boxes with Different Masses traveling toward each
other
Two objects are with different masses (m1 = 1 kg and m2 = 3 kg). Red object travels at velocity of
v1i = 1 m/s toward the blue ball that travels in opposite direction with velocity of v 2i = – 1 m/s.
Case 5: Elastic collision between two Boxes in motion and Different Mass and Different
Velocities
Two objects are with different masses (m1 = 3 kg and m2 = 1 kg). Red object travels at velocity of
v1i = 1 m/s toward the blue ball that travels in opposite direction with velocity of v2i = – 3 m/s.
Pre collision data for all five cases are summarized in table 1.
Table 1:
Case
1
2
3
4
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m1
kg
1.0
1.0
1.0
1.0
V1i
m/s
+ 1.0
+ 1.0
+ 1.0
+ 1.0
Page 2
m2
kg
1.0
3.0
1.0
3.0
V2i
m/s
0.0
0.0
- 1.0
- 1.0
Last Updated: 2/17/2016
GateWay CC
5
3.0
+ 1.0
1.0
-3.0
Use the data from Table 1 to calculate initial momentum and initial kinetic energy for each object
and for the system, before the collision:
P1i – initial momentum of object 1 before the collision = m1∙v1i
P2i – initial momentum of object 2 before the collision = m2∙v2i
Pi – total momentum of objects 1 and 2 before the collision = p1i + p2i
KE1i – kinetic energy of object 1 before the collision = ½ ∙m1∙v1i2
KE2i – kinetic energy of object 2 before the collision = ½ ∙m2∙v2i2
KEi – total kinetic energy of objects 1 and 2 before the collision = KE1i + KE2i
Complete table 2 using given formulas above.
Table 2:
Case
p1i
kg∙m/s
p2i
kg∙m/s
pi
kg∙m/s
KE1i
J
KE2i
J
KEi
J
1
2
3
4
5
Next we find the velocity of each object just after the collision for each case.
Case 1: We are going to use equations 1 and 3 and apply data from case 1:
Substitute data from case 1 in table 1:
1kg  1
m
m
 1kg  0  1  v1 f  1  v 2 f
s
s
1
m
m
 v1 f  0  v 2 f
s
s
Ignoring the units:
1  v1 f  v 2 f
1  v1 f  v 2 f
Last two equations represent a system of linear equation that can be solved using substitution
method. Substitute v2f into first equation:
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1  v1 f  1  v1 f
Solving for v1f:
v1 f  0
m
s
After the collision object 1 is going to be at rest. Substituting v1f = 0 m/s into one of the equations
of the system we find the velocity of object 2 after the collision is:
v2 f  1
m
s
After the collision second object will travel at 1 m/s.
Repeat these calculations for case 2, 3, 4, and 5 and complete the table with calculated values
Table 3:
Case
Calculated Values for
velocity after the
collision
V1f
V2f
m/s
m/s
Animation values for
velocity after the
collision
V1f
V2f
m/s
m/s
1
2
3
4
5
To verify your calculations, setup the case 1 parameters in the simulation by using + and – arrows.
Press "GO" and watch the simulated collision. Computer will display final velocities of two objects
after the collision. Record these velocities on your table 3 under animation values. Indicate the
direction of the motion with a + or - sign. Plus sign indicate motion to the RIGHT; minus sign
indicate motion to the LEFT. Calculated and simulated values should match.
Reset the Experiment.
Repeat this procedure for case 2, 3, 4, and 5 to complete table 3.
Use the next set of formulas to complete Table 4 with the data for momentum and enery after the
collision
P1f – final momentum of object 1 after the collision = m1∙v1f
P2f – final momentum of object 2 after the collision = m2∙v2f
Pf – total momentum of objects 1 and 2 after the collision = p1f + p2f
KE1f – kinetic energy of object 1 after the collision = ½ ∙m1∙v1f2
KE2f – kinetic energy of object 2 after the collision = ½ ∙m2∙v2f2
KEf – total kinetic energy of objects 1 and 2 after the collision = KE1f + KE2f
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Table 4:
Case
p1f
kg∙m/s
p2f
kg∙m/s
Pf
kg∙m/s
KE1f
J
KE2f
J
KEf
J
1
2
3
4
5
Use the next set of formulas to determine the change in velocity, momentum, and energy, before
and after the collision, to complete Table 5.
Change in velocity for object 1: v1f – v1i
Change in velocity for object 2: v2f – v2i
Change in momentum for object 1: p1f – p1i
Change in momentum for object 2: p2f – p2i
Change in energy for object 1: KE1f – KE1i
Change in energy for object 2: KE2f – KE2i
Table 5:
Case
v1f – v1i
m/s
v2f – v2i
m/s
p1f – p1i
kg∙m/s
p2f – p2i
kg∙m/s
KE1f – KE1i
J
KE2f – KE2i
J
1
2
3
4
5
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