Answer:
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 :
[tex]P=\dfrac{W}{t}[/tex]
W is the work done, W = Fd
[tex]P=\dfrac{Fd}{t}[/tex]
Since, [tex]v=\dfrac{d}{t}[/tex]
So,
[tex]P=F\times v[/tex]
F is the force acting on the ball
[tex]F=\dfrac{P}{v}\\\\F=\dfrac{2920\ W}{31.6\ m/s}\\\\F = 92.4\ N[/tex]
So, the force acting on the ball is 92.4 N. Hence, this is the required solution.
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.
[tex]P = \frac{W}{t}[/tex] [1]
Another way to express work is through its relation with the applied force (F) and the distance traveled (d).
[tex]W = F.d[/tex] [2]
If we substitute [2] in [1], we get,
[tex]P = \frac{F.d}{t}[/tex]
And d/t = v. Then,
[tex]P = F.v\\\\F = \frac{P}{v} = \frac{2920W}{31.6m/s} = 92.4N[/tex]
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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