A woman of mass m sits on a train that coasts along the tracks at a constant spe

Question

A woman of mass m sits on a train that coasts along the tracks at a constant
speed u. She gets up and begins to walk forward along the car at the speed v relative
to the car.

(d) How much additional work was done on the woman by the car while she was
putting herself into motion? Hint: To make sure that your answer is correct,
take into account the action-reaction law and the impulse-momentum theorem.
As the woman pushes with her feet against the floor of the car, the floor acts
with a reaction force onto the feet. That force increases the momentum of the
woman relative to the car. During the time when the force acts, the woman is
displaced relative to an outside observer, because of the motion of the car.

Explanation / Answer

when we take relative to the earth initial mechanical energy of the women = (1/2)*m*((u)^2) final mechanical energy of the women = (1/2)*m*((u+v)^2) work done by the car is = change in mechanical energy of the women = (1/2)*m*(((u+v)^2) - (u^2)) =(0.5)*m*((v^2) + 2*u*v) is the work done by the car

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