1. A 57 g tennis ball is moving to the left at 36.2 m/s. It collides with a wall and rebounds to the right. The tennis ball is in contact with the wall for 0.107 s and it loses 14% of its kinetic energy during the impact. What is the average force (magnitude & direction) exerted by the wall on the tennis ball?
you know KE initial, you know final KE is .86 of that. Solve for Vfinal from that.
Force= mass (Vi+vf)/time
notice the vf is added (it is a minus for the change in direction, so minus a minus is +
i still dont understand how to find the v final.
Can you show an example @bobpursley
To find the average force exerted by the wall on the tennis ball, we can use the impulse-momentum principle. The impulse-momentum principle states that the change in momentum of an object is equal to the force exerted on it multiplied by the time over which the force is applied.
Here's how to calculate the average force:
Step 1: Find the initial momentum of the tennis ball. Momentum (p) is given by the product of mass (m) and velocity (v). So, the initial momentum (p1) is:
p1 = m × v1
= 57 g × (-36.2 m/s)
= -2063.4 kg·m/s
Note that the negative sign indicates that the tennis ball is moving in the opposite direction as the positive direction we defined earlier.
Step 2: Find the final momentum of the tennis ball. Since the ball rebounds to the right, its velocity changes direction but not magnitude. Therefore, the final momentum (p2) is:
p2 = -p1
= 2063.4 kg·m/s
Step 3: Find the change in momentum (∆p). The change in momentum is given by:
∆p = p2 - p1
= 2063.4 kg·m/s - (-2063.4 kg·m/s)
= 4126.8 kg·m/s
Step 4: Find the change in kinetic energy (∆KE). We're told that the ball loses 14% of its kinetic energy during the impact. The initial kinetic energy (KE1) is given by:
KE1 = (1/2) × m × (v1^2)
= (1/2) × 57 g × (36.2 m/s)^2
= 37101.366 J
The final kinetic energy (KE2) is 86% of the initial kinetic energy:
KE2 = 0.86 × KE1
= 0.86 × 37101.366 J
= 31866.17 J
The change in kinetic energy (∆KE) is:
∆KE = KE2 - KE1
= 31866.17 J - 37101.366 J
= -5235.196 J
Note the negative sign indicates a decrease in kinetic energy.
Step 5: Find the average force (F) using the impulse-momentum principle. The average force is given by:
F = ∆p / ∆t
We're given that the tennis ball is in contact with the wall for a time of 0.107 s, so:
F = -5235.196 J / 0.107 s
= -48815.0623 N
The magnitude of the average force is 48815.0623 N, and the negative sign indicates that the force is exerted in the opposite direction of the initial velocity.
Therefore, the average force exerted by the wall on the tennis ball is approximately 48815.0623 N in the direction opposite to the initial velocity.