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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.

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.

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.

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LailaMaster · Tutor for 5 years

Answer

**1.a.i. Calculating the average force:**<br /><br />* **Identify the knowns:**<br /> * Initial velocity (v<sub>i</sub>) = 0 m/s (ball at rest)<br /> * Final velocity (v<sub>f</sub>) = 64 m/s<br /> * Mass (m) = 0.058 kg<br /> * Time (t) = 25 ms = 0.025 s<br /><br />* **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 = F<sub>avg</sub> * t = m * Δv<br /><br />* **Solve for average force (F<sub>avg</sub>):**<br /> * Δv = v<sub>f</sub> - v<sub>i</sub> = 64 m/s - 0 m/s = 64 m/s<br /> * F<sub>avg</sub> = (m * Δv) / t<br /> * F<sub>avg</sub> = (0.058 kg * 64 m/s) / 0.025 s<br /> * F<sub>avg</sub> = 148.48 N<br /><br />* **Answer:** The average force exerted by the racquet on the ball is approximately 148.5 N.<br /><br /><br />**1.a.ii. Calculating the average power:**<br /><br />* **Identify the knowns:** We already know the average force (F<sub>avg</sub>) and the final velocity (v<sub>f</sub>). We also know the time (t).<br /><br />* **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: P<sub>avg</sub> = 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: P<sub>avg</sub> = (1/2 * m * v<sub>f</sub><sup>2</sup>) / t. Alternatively, since the force is constant, we can use P<sub>avg</sub> = F<sub>avg</sub> * v<sub>avg</sub>, where v<sub>avg</sub> is the average velocity.<br /><br />* **Solve for average power (P<sub>avg</sub>):**<br /> * v<sub>avg</sub> = (v<sub>i</sub> + v<sub>f</sub>)/2 = (0 m/s + 64 m/s)/2 = 32 m/s<br /> * P<sub>avg</sub> = F<sub>avg</sub> * v<sub>avg</sub> = 148.48 N * 32 m/s <br /> * P<sub>avg</sub> = 4751.36 W<br /><br />* **Answer:** The average power delivered to the ball during the impact is approximately 4751.4 W or 4.75 kW.<br />
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