Question
1. A student strikes a tennis ball that is initially at rest so that it leaves the racquet at a speed of 64ms^-1 The ball has a mass of 0.058 kg and the contact between the ball and the racquet lasts for 25 ms. a. Calculate: i. the average force exerted by the racquet on the ball ii. the average power delivered to the ball during the impact.
Solution
4.1
(219 Votes)
Laila
Master · Tutor for 5 years
Answer
**1.a.i. Calculating the average force:*** **Identify the knowns:** * Initial velocity (vi) = 0 m/s (ball at rest) * Final velocity (vf) = 64 m/s * Mass (m) = 0.058 kg * Time (t) = 25 ms = 0.025 s* **Determine the relevant equation:** We can use the impulse-momentum theorem, which states that the impulse (change in momentum) is equal to the average force multiplied by the time interval: Impulse = Favg * t = m * Δv* **Solve for average force (Favg):** * Δv = vf - vi = 64 m/s - 0 m/s = 64 m/s * Favg = (m * Δv) / t * Favg = (0.058 kg * 64 m/s) / 0.025 s * Favg = 148.48 N* **Answer:** The average force exerted by the racquet on the ball is approximately 148.5 N.**1.a.ii. Calculating the average power:*** **Identify the knowns:** We already know the average force (Favg) and the final velocity (vf). We also know the time (t).* **Determine the relevant equation:** Average power is the work done divided by the time taken. We can also express it in terms of force and velocity: Pavg = W/t. Since work is related to the change in kinetic energy, and we're given information allowing us to calculate the average force, we can use the following: Pavg = (1/2 * m * vf2) / t. Alternatively, since the force is constant, we can use Pavg = Favg * vavg, where vavg is the average velocity.* **Solve for average power (Pavg):** * vavg = (vi + vf)/2 = (0 m/s + 64 m/s)/2 = 32 m/s * Pavg = Favg * vavg = 148.48 N * 32 m/s * Pavg = 4751.36 W* **Answer:** The average power delivered to the ball during the impact is approximately 4751.4 W or 4.75 kW.