A ball falls vertically downward and bounces | vedclass

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Question

(A) Let the speed of the ball be $v$ at the instant just before and just after the collision. The air resistance force $F_r$ is proportional to the sp

Vedclass · Accepted Answer

$a_1 < a_2$

Vedclass · Answer

(A) Let the speed of the ball be $v$ at the instant just before and just after the collision. The air resistance force $F_r$ is proportional to the speed,so $F_r = kv$,where $k$ is a constant.When the ball is moving downwards,the gravitational force $mg$ acts downwards and the air resistance $kv$ acts upwards. The net force is $F_{net} = mg - kv$. The acceleration $a_1$ is given by:$a_1 = \frac{mg - kv}{m} = g - \frac{k}{m}v$When the ball is moving upwards,the gravitational force $mg$ acts downwards and the air resistance $kv$ also acts downwards (opposing the motion). The net force is $F_{net} = mg + kv$. The acceleration $a_2$ is given by:$a_2 = \frac{mg + kv}{m} = g + \frac{k}{m}v$Comparing the two expressions,it is clear that $a_2 > a_1$ or $a_1 < a_2$.

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