Ball moving in a Train!

Classical Mechanics Level 5

A ball is bouncing elastically with a speed of 1 m s − 1 1ms^{-1} between walls of a railway compartment of size 10 m 10m in a direction perpendicular to walls. The train is moving at a constant velocity of 10 m s − 1 10ms^{-1} parallel to the direction of motion of the ball. As seen from the ground

( A ) (A) The direction of motion of the ball changes every 10 10 seconds.

( B ) (B) Speed of ball changes every 10 10 seconds.

( C ) (C) Average speed of ball over any 20 20 second interval is fixed.

( D ) (D) The acceleration of ball is the same when observed either from ground or train.

( A , C ) (A,C) None of These ( A , C , D ) (A,C,D) ( B , D ) (B,D) ( A , B , C ) (A,B,C) ( B , C , D ) (B,C,D) ( A , D ) (A,D) ( A , B ) (A,B)

Nishant Rai by Nishant Rai , 25, India

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1 solution

Mat Baluch
Aug 17, 2015

To answer properly, let us make the assumption that the ball is moving along one axis only (parallel to the speed of the train). This means that the ball is rather rolling (or sliding with no friction) on the ground than "boucing" through the compartment.

In this case, the speed pattern as seen from the ground is the following (please let us ignore relativity effects !)

  • speed 11 m / s 11 m/s on the way from back wall to front wall (wich takes 10 seconds)

  • speed 9 m / s 9 m/s on the way from front wall to back wall (10 seconds)

This gives a 20 seconds periodicity of the speed pattern.

In conclusion :

  • (A) the direction of the motion never changes from the ground (always in the direction of the train speed)

  • (B) speed of ball changes every 10 seconds

  • (C) Average speed of ball over any 20 seconds interval is fixed, as a directe consequence of the 20 seconds periodicity of speed

  • (D) The acceleration of the ball is the same in train / ground, since the train has a uniform motion in straight line.

Remark : the problem could be better stated, in particular precise the absence of vertical motion, otherwise:

  • (A) remains fasle, but for different reason: speed direction changes continuously

  • (B) becomes fasle (continuous change)

  • (C) is not possible to assess (vertical movment are periodic bounces, with a period depending on the maximum height of the trajectory)

  • (D) remains true

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