A train is moving along a track with constant speed v 1 relative to the ground.

Question

A train is moving along a track with constant speed v1 relative to the ground. A person on the train holds a ball of mass m and throws it toward the front of the train with a speed v2 relative to the train.

Part A

Calculate the change in kinetic energy of the ball in the Earth frame of reference.

Express your answer in terms of the variables m, v1, and v2.

Part B

Calculate the change in kinetic energy of the ball in the train frame of reference.

Express your answer in terms of the variables m, v1, and v2.

Part C

How much work was done on the ball in the Earth frame of reference?

Express your answer in terms of the variables m, v1, and v2.

Part D

How much work was done on the ball in the train frame of reference?

Express your answer in terms of the variables m, v1, and v2.

Explanation / Answer

velocity of ball in train reference = v2

velocity of ball in earth referece = v1+v2

PART A

ke1 = 1/2mv12

ke2 =1/2m (v1+v2)2

change in KE =ke2-ke1

=1/2m(v22+2v1v2)

Part B

train frame of reference

ke1=0

Ke2=1/2mv22

Diffence inKE = 1/2mv22

part C

work done = change in kinectic enrgy =1/2m(V22+2v1v2)

part D

work done = change in kinectic enrgy=1/2mv22

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