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Chapter 7: Problem 7

A ball of mass \(5.0 \mathrm{kg}\) moving with a speed of $2.0 \mathrm{m} / \mathrm{s}\( in the \)+x$ -direction hits a wall and bounces back with the same speed in the \(-x\) -direction. What is the change of momentum of the ball?

Short Answer

Expert verified
Answer: The change in momentum of the ball is -20 kg·m/s.

Step by step solution

01

Determine the initial momentum of the ball

Calculate the initial momentum (before hitting the wall) using the formula p_i = m * v_i, where m = 5.0 kg and v_i = 2.0 m/s: p_i = (5.0 kg) * (2.0 m/s)
02

Calculate the initial momentum

Now, compute the initial momentum: p_i = (5.0 kg) * (2.0 m/s) = 10 kg·m/s
03

Determine the final momentum of the ball

After bouncing off the wall, the ball moves with the same speed but in the opposite direction. So, the final velocity will be v_f = -2.0 m/s. Calculate the final momentum (after bouncing off the wall) using the formula p_f = m * v_f, where m = 5.0 kg and v_f = -2.0 m/s: p_f = (5.0 kg) * (-2.0 m/s)
04

Calculate the final momentum

Now, compute the final momentum: p_f = (5.0 kg) * (-2.0 m/s) = -10 kg·m/s
05

Calculate the change in momentum

To find the change in momentum, use the formula Δp = p_f - p_i: Δp = (-10 kg·m/s) - (10 kg·m/s)
06

Find the change in momentum

Finally, calculate the change in momentum: Δp = (-10 kg·m/s) - (10 kg·m/s) = -20 kg·m/s The change in momentum of the ball is -20 kg·m/s.

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