A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sk

Question

A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy $K$ with time $t$ most appropriately? The figures are only illustrative and not to scale. [2014]

Smart Achievers · Accepted Answer

(2)

As tennis ball is dropped, so initial velocity $t$

$K.E. = \frac{1}{2} m v^{2} = \frac{1}{2} m {[u + a t]}^{2} = \frac{1}{2} m {[0 + g t]}^{2}$

$∴$ $K.E. = \frac{1}{2} m g^{2} t^{2}$ $∴$ $K.E. \propto t^{2} ...(i)$

i.e., The relation between $k$ and $t$ is parabolic.

First the kinetic energy will increase as per eq (i). As the ball touches the ground it starts deforming and loses its K.E., when the deformation is maximum, K.E. = 0. As the ball moves up it loses K.E. and gains gravitational potential energy in the same time interval. These characteristics are best illustrated by $k t$ graph shown in (2).

Solution

1

2

3

4

Want Us to Email you About Special Offers & Updates?