Tennis Ball Impact: Calculating Force & Speed

[physco827]

Homework Statement

A tennis ball has a mass of 0.057 kg. A professional tennis player hits the ball hard enough to give it a speed of 52 m/s (about 117 miles per hour.) The ball moves toward the left, hits a wall and bounces straight back to the right with almost the same speed (52 m/s). As indicated in the diagram below, high-speed photography shows that the ball is crushed about 2 cm at the instant when its speed is momentarily zero, before rebounding.

Assume that the large force the ball exerts on the wall is approximately constant during contact.
What is the average speed of the ball during the period from first contact with the wall to the moment the ball's speed is momentarily zero?
26 = m/s
How much time elapses between first contact with the wall, and coming to a stop?
7.69e-4 seconds

What is the magnitude of the average force exerted by the wall on the ball during contact?

Homework Equations

change in momentum = fnet*deltat.

The Attempt at a Solution

1927.18 N
-1927.18 N
963.59 N
-963.59 N

 

[physixguru]

use the concept of impulse and proceed...

 

[Moetasim]

I would first like to commend the student for providing all the necessary information and calculations for this problem. It is clear that they have a good understanding of the concepts involved in calculating force and speed in the context of a tennis ball impact.

To answer the question about the average speed of the ball during the period of contact with the wall, we can use the equation for average speed, which is given by distance divided by time. Since we know the distance the ball traveled (2 cm or 0.02 m) and the time it took to travel that distance (7.69e-4 seconds), we can calculate the average speed to be 26 m/s.

Next, to find the time it takes for the ball to come to a stop, we can use the equation for final velocity, which is given by initial velocity plus acceleration multiplied by time. Since we know the initial velocity (52 m/s) and the final velocity (0 m/s), we can rearrange the equation to solve for time, which gives us 7.69e-4 seconds.

Finally, to find the magnitude of the average force exerted by the wall on the ball during contact, we can use the equation for change in momentum, which is given by the net force multiplied by the change in time. Since we know the change in time (7.69e-4 seconds) and the change in momentum (0.057 kg x 52 m/s = 2.964 Ns), we can rearrange the equation to solve for the average force, which gives us 3.85e3 N.

It is important to note that while these calculations provide an estimate of the average force exerted by the wall on the ball, the actual force may vary depending on the exact nature of the impact and the materials involved. Further experiments and analysis would be needed to determine the precise force exerted in this scenario. Overall, the student has shown a good understanding of the concepts involved and has provided a thorough and accurate response to the given content.