Question

When serving a tennis ball, a player hits the ball when its velocity is zero (at the highest point of a vertical toss). The racquet exerts a force of 509 N on the ball for 5.26 ms, giving it a final velocity of 45.3 m/s. Using these data, find the mass (in g) of the ball.

a. Calculate the acceleration of the ball.
b. Determine the work done by the racquet on the ball.
c. Find the initial velocity of the ball before the racquet hit.
d. Calculate the mass of the ball.

Answer 1

To find the mass of the tennis ball, the acceleration is calculated based on the force applied and the time duration, which is then used to find the mass. The mass of the tennis ball is found to be 60 grams.

Step-by-step explanation:

When serving a tennis ball, a player hits the ball when its velocity is zero. The racquet exerts a force of 540 N on the ball for 5.00 ms, giving it a final velocity of 45.0 m/s. To find the mass of the ball, we use Newton's second law of motion (F = ma) and the relationship between impulse and momentum (Impulse = Change in Momentum).

First, we convert the time from milliseconds to seconds by dividing by 1000: 5.00 ms = 0.005 s.

Then we calculate the acceleration (a) using the formula:
= Δv / Δt = 45.0 m/s / 0.005 s = 9000 m/s2.

Given F = ma, we can solve for the mass (m) of the ball:
m = F / a = 540 N / 9000 m/s2 = 0.06 kg.

To find the mass in grams, we convert kilograms to grams by multiplying by 1000: 0.06 kg * 1000 = 60 g.