A) What is the velocity of the center of mass of the system? B) What is the init

Question

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

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

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

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

Bumper Cars 1 2 3 45 67 8 m2 A bumper car with mass m1-117 kg is moving to the right with a velocity of v1-4.2m/s. A second bumper car with mass m2 81 kg is moving to the left with a velocity of v2- 3.3 m/s. The two cars have an elastic collision. Assume the surface is frictionless.

Explanation / Answer

A) v(cm) =m1v1 + m2v2 / m1 + m2

= 117*4.2 + 81*-3.3 / 117 + 81

= 1.13 m/s

B) initial velocity of car 1 in com reference frame = (4.2-1.13) = 3.07 m/s

C) for finding the final velocity

by the conservation of momentum

m1u1 + m2u2 = m1v1 + m2v2

117*4.2 - 81*3.3 = 117v1 + 81 v2 ------(1)

v2 - v1 = u1- u2

v2 - v1 = 4.2 + 3.3

v2 - v1 = 7.5 ----------(2)

multiply (2) by 117 and adding to the (1) we have

198v2 = 1101.6

v2 = 5.56 m/s

v1 = v2 - 7.5 = -1.93 m/s

final velocity in COM Frame of reference = -1.93 - 1.13 = -3.06 m/s

D) final velocity of car 1 in the ground reference = -1.93 m/s

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