In being served, a tennis ball is accelerated from rest to a speed of 31.6 m/s. The average power generated during the serve is 2920 W. Assuming that the acceleration of the ball is constant during the serve, find the force acting on the ball.

When a tennis ball is accelerated from rest to 31.6 m/s, a 92.4 N force generates a power of 2920 W.

In being served, a tennis ball is accelerated from rest (u = 0) to a speed of 31.6 m/s (v).

The average power (P) generated during the serve is 2920 W. We can relate the power to the work done (W) and the time elapsed through the following expression.

  [1]

Another way to express work is through its relation with the applied force (F) and the distance traveled (d).

  [2]

If we substitute [2] in [1], we get,

And d/t = v. Then,

When a tennis ball is accelerated from rest to 31.6 m/s, a 92.4 N force generates a power of 2920 W.

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The force acting on the ball is 92.4 N.

Explanation:

Given that,

Initial speed of the ball, u = 0

Final speed of the ball, v = 31.6 m/s

The average power generated during the serve is 2920 W. Power generated by an object is given by :

W is the work done, W = Fd

Since,

So,

F is the force acting on the ball

So, the force acting on the ball is 92.4 N. Hence, this is the required solution.

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