Chapter 6, Problem 52A

A regular tennis ball and another one filled with sand are dropped at the same time from the top of a high building. Your friend says that even though air resistance is present, both balls should hit the ground at the same time because they are the same size and pass through the same amount of air. What do you say?

To determine

To Explain: Whether regular tennis ball or sand filled ball will reach the ground first.

Explanation of Solution

Introduction:

Terminal velocity is defined as the maximum velocity attained by an object when it falls through a fluid (air). It occurs when the total sum of buoyancy and drag force is equal to the downward force of gravity that acts on an object.

When both the balls are dropped from the building top at the same time then both will achieve terminal velocity. But the ball filled with sand will first hit the ground. So, a friend is incorrect.

When a ball falls, the weight of the ball ( mg ) will push it downwards while air resistance force ( R ) will push it upwards. So, the net force experienced by ball is,

  $F_{net}=mg-R$

Weight will remain same but there will be change in air resistance force. While falling down, air resistance will increase, so the net force will decrease and thus the acceleration will decrease. When net force will be zero (means air resistance force will be equal to weight of ball) then the net force on ball will be zero and the ball stop accelerating, means terminal velocity is attained by the ball.

A regular tennis ball is lighter in weight than the tennis ball having sand in it. Due to less weight of regular tennis ball, it will encounter lesser air resistance force for balancing the weight of ball. Thus, it will reach its terminal velocity sooner while sand filled tennis ball is still accelerating. Also, it will have lesser terminal velocity then sand filled ball. So, the sand filled ball will hit the ground first because it falls through air with greater acceleration.

Conclusion:

The sand ball will touch the ground prior than tennis ball.