You throw a ball with a mass of 0.50kg against a brick wall. It hits the wall moving horizontallyto the left at 31 𝑚𝑠 and rebounds horizontally to the right at 25 𝑚𝑠 . Find the impulse of the netforce on the ball during its collision with the wall. If the ball is in contact with the wall for 0.02s,find the average horizontal force that the wall exerts on the ball during the impact. (1-2 sig. figs.)
Question
You throw a ball with a mass of 0.50kg against a brick wall. It hits the wall moving horizontallyto the left at 31 𝑚𝑠 and rebounds horizontally to the right at 25 𝑚𝑠 . Find the impulse of the netforce on the ball during its collision with the wall. If the ball is in contact with the wall for 0.02s,find the average horizontal force that the wall exerts on the ball during the impact. (1-2 sig. figs.)
Solution
Sure, let's break this down step by step.
Step 1: Calculate the initial and final momentum of the ball.
The initial momentum (p_initial) of the ball can be calculated using the formula:
p_initial = mass * velocity_initial
where: mass = 0.50 kg velocity_initial = -31 m/s (negative because the ball is moving to the left)
So, p_initial = 0.50 kg * -31 m/s = -15.5 kg*m/s
The final momentum (p_final) of the ball can be calculated using the formula:
p_final = mass * velocity_final
where: velocity_final = 25 m/s (positive because the ball is moving to the right)
So, p_final = 0.50 kg * 25 m/s = 12.5 kg*m/s
Step 2: Calculate the impulse of the net force on the ball.
The impulse (J) of the net force on the ball can be calculated using the formula:
J = p_final - p_initial
So, J = 12.5 kgm/s - (-15.5 kgm/s) = 28 kg*m/s
Step 3: Calculate the average horizontal force that the wall exerts on the ball during the impact.
The average force (F_avg) can be calculated using the formula:
F_avg = J / Δt
where: Δt = 0.02 s
So, F_avg = 28 kg*m/s / 0.02 s = 1400 N
Therefore, the impulse of the net force on the ball during its collision with the wall is 28 kg*m/s, and the average horizontal force that the wall exerts on the ball during the impact is 1400 N.
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