question_answer

(a) When a molecule (or an elastic ball) hits a (massive) wall, it rebounds with the same speed. When a ball hits a massive bat held firmly, the same thing happens. However, when the bat is moving towards the ball/the ball rebounds with a different speed. Does the ball move faster or slower? (b) When gas in a cylinder is compressed by pushing in a piston, its temperature rises. Guess at an explanation of this in terms of kinetic theory using (a) above. (c) What happens when a compressed gas pushes a piston out and expands? What would you observe? (d) Sachin Tendulkar uses a heavy cricket bat while playing. Does it help him in any way?     

Answer:

             (a) Let the speed of the ball be \[u\] relative to the wicket behind the bat. If the bat is moving towards the ball with a speed V relative to the wicket, then the relative speed of the ball to bat is \[\text{V }+u\] towards the bat. When the ball rebounds (after hitting the massive bat) its speed, relative to bat,\[V+(V+u)=2V+u\], moving away from the wicket. So the ball speeds up after the collision with the bat. For a molecule this would imply an increase in temperature. (b) When a gas in cylinder is compressed by pushing in a piston, the speed of the molecules or their kinetic energy increases. This increases the temperature of the gas. (c) When a compressed gas pushes a piston out, the speed of the molecules or their kinetic energy decreases. This decreases the temperature of the gas. (d) When the ball is hit with a heavy bat, the rebound speed of the ball further increases. It helps to score better.