A bumper car with mass m1 = 119.0 kg is moving to the right with a velocity of v

Question

A bumper car with mass m1 = 119.0 kg is moving to the right with a velocity of v1 = 4.4 m/s. A second bumper car with mass m2 = 83.0 kg is moving to the left with a velocity of v2 = -3.5 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? m/s 2) What is the initial velocity of car 1 in the center-of-mass reference frame? m/s 3) What is the final velocity of car 1 in the center-of-mass reference frame? m/s 4) What is the final velocity of car 1 in the ground (original) reference frame? m/s

Explanation / Answer

1)Vcm= (m1v1+m2v2)m1+m2

= (119x4.4-83x3.5)/119+83

=1.154 m/s towards right

2)intial veloctiy of car 1 in COM frame= V1-Vcm

=4.4-1.154=3.246 m/s towards right

3)Vcm doesn't change due to elastic collision,

intial momentum=final momentum

m1v1+m2v2=m1v1'+m2v2'

119x4.4-83x3.5=119v1'+83v2'

also, e =1

v2'-v1'/v1-v2=1

v2'-v1'=4.4+3.5=7.9

v2'=7.9+v1'

233.108=119v1'+83(7.9+v1')

233.108=202v1'+655.7

v1'= -422.6/202 = -2.092m/s

v2' = 7.9-2.092 = 5.807m/s

v1' in COM reference frame = -(2.092+1.154) = 3.246m/s towards left

4) v1' = 2.092 m/s towards left

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