A bumper car with mass m1 = 103 kg is moving to the right with a velocity of v1

Question

A bumper car with mass m1 = 103 kg is moving to the right with a velocity of v1 = 4 m/s. A second bumper car with mass m2 = 91 kg is moving to the left with a velocity of v2 = -3.4 m/s. The two cars have an elastic collision. Assume the surface is frictionless.

1) What is the velocity of the center of mass of the system?

2) What is the initial velocity of car 1 in the center-of-mass reference frame?

3) What is the final velocity of car 1 in the center-of-mass reference frame?

4) What is the final velocity of car 1 in the ground (original) reference frame?

5) What is the final velocity of car 2 in the ground (original) reference frame?

6) In a new (inelastic) collision, the same two bumper cars with the same initial velocities now latch together as they collide. What is the final speed of the two bumper cars after the collision?

Explanation / Answer

a) Velocity of COM = (103*4 - 91*3.4)/(103+91) = 0.528865 m/s
b) initial Velo = 3.47113 m/s
c) From conservation of momentum
103*4 - 91*3.4 = 103u + 91v
v = 1.12747 - 1.13186u
from conservation of energy
103*4^2 + 91*3.4^2 = 103*u^2 + 91v^2 = 219.582u^2 -2.55228u + 1.27118
u = 3.4999 m/s
v = 5.0888 m/s

final velo = 2.9710 m/s
d) final velo = 3.4999 m/s
e) final velo = v = 5.0888 m/s
f) From conservation of momentum
103*4 - 91*3.4 = 194v
v = 0.52886 m/s

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