In a tennis serve, a 7.9×10−2 ball can be accelerated from rest to 33 over a distance of 0.80. Find the magnitude of the average force exerted by the racket on the ball during the serve.
To find the magnitude of the average force exerted by the racket on the ball during the serve, we can use Newton's second law of motion:
F = ma
Where:
F is the force exerted on the ball
m is the mass of the ball
a is the acceleration of the ball
First, we need to calculate the mass of the ball. The mass is not given in the question, so let's assume a standard tennis ball mass of 0.057 kg.
Now, we can calculate the acceleration of the ball using the given information:
Initial velocity, u = 0 (as the ball starts from rest)
Final velocity, v = 33 m/s
Distance, s = 0.80 m
Using the formula:
v^2 = u^2 + 2as
We can rearrange the equation to solve for acceleration:
a = (v^2 - u^2) / (2s)
Substituting the given values:
a = (33^2 - 0^2) / (2 * 0.80) = 697.5 m/s^2
Now, we can calculate the force exerted by the racket using Newton's second law of motion:
F = ma
F = 0.057 kg * 697.5 m/s^2 = 39.86625 N
Therefore, the magnitude of the average force exerted by the racket on the ball during the serve is approximately 39.87 N.