A tennis ball bounces off a wall....

[eglaud]

Homework Statement

A 60 g tennis ball with an initial speed of 37m/s hits a wall and rebounds with the same speed. This collision lasts for two seconds. What is the maximum value of contact force during the collision?

Homework Equations

p=mv

The Attempt at a Solution

So I multiplied the mass by the velocity and divided by the time, which gives me 1140N, the correct answer. My issue is that this shouldn't be the right answer in my eyes, because I thought Newtons are measured in kg*m/s². Wouldn't I need to convert grams to kg, which would make my answer 1.14N?

 

[TSny]

Hello.

There are a few things about this problem that are odd.

2 seconds is an unreasonable time for a collision of a tennis ball with a wall. Perhaps it is 2 milliseconds?

The problem does not state the angle at which the ball strikes the wall. But maybe that is for you to decide in order to maximize the collision force.

The problem asks for the maximum value of the contact force during the collision. There is actually no way to find this based on the information given. The force builds up to a maximum during the collision and then dies out. The maximum force occurs at one instant of time and it is not possible to determine the value of the instantaneous maximum force based on the information given. But maybe they are asking for the maximum average force during the collision where you are to choose the direction of impact to maximize this average force of the collision.

Yes, you need to convert the grams to kilograms to get the force in Newtons.

Your method of solution is not correct since you did not account for the fact that the ball rebounds with the same speed that it hit the wall.

 

[eglaud]

Hello.

There are a few things about this problem that are odd.

2 seconds is an unreasonable time for a collision of a tennis ball with a wall. Perhaps it is 2 milliseconds?

The problem does not state the angle at which the ball strikes the wall. But maybe that is for you to decide in order to maximize the collision force.

The problem asks for the maximum value of the contact force during the collision. There is actually no way to find this based on the information given. The force builds up to a maximum during the collision and then dies out. The maximum force occurs at one instant of time and it is not possible to determine the value of the instantaneous maximum force based on the information given. But maybe they are asking for the maximum average force during the collision where you are to choose the direction of impact to maximize this average force of the collision.

Yes, you need to convert the grams to kilograms to get the force in Newtons.

Your method of solution is not correct since you did not account for the fact that the ball rebounds with the same speed that it hit the wall.

Yikes, I've been studying for too long. You're correct, it is two milliseconds, which would give me the correct answer. And perhaps for real physics it is impossible to solve with the information given, but this is just intro which I've been told simplifies a lot of things - if I replace the 2 seconds with 0.002 seconds then I arrive at the correct answer. Otherwise I copied the real question word for word, so they just ask for the maximum force - a graph is provided showing the force growing, then leveling out for those two milliseconds, then decreasing, but I think I included the only necessary part in my question (The time, which I got wrong...).Thanks, and sorry, I should've read closer.

 

[TSny]

I don't believe your approach to the problem is correct even though you ended up with the correct answer. It is important to take into account the fact that the ball rebounds with the same speed that it hit the wall. But it does not look like you considered this.

It will help if you state the physics principles that you are using to solve the problem. There should be more relevant equations than just p = mv.

a graph is provided showing the force growing, then leveling out for those two milliseconds, then decreasing

It appears that the graph of the force is essential to working the problem correctly. Is there any way you can post the graph? Does the entire collision last 2 milliseconds, or just the part of the graph where the force is constant?

 

[eglaud]

I don't believe your approach to the problem is correct even though you ended up with the correct answer. It is important to take into account the fact that the ball rebounds with the same speed that it hit the wall. But it does not look like you considered this.

It will help if you state the physics principles that you are using to solve the problem. There should be more relevant equations than just p = mv.

It appears that the graph of the force is essential to working the problem correctly. Is there any way you can post the graph?

The graph is below. That equation is honestly the only one I am using, honestly I have such a loose grasp on physics (env. sci. major here taking his basic physics requirement) that I really just know how to do these problems, so I can't really provide any supplemental physics principles that I am actively/aware of that I'm using. I just looked at chegg and saw it done the same way (someone else used integrals, but we were told not to use this method). I think the fact the ball rebounds with the same speed is just there so we don't go down any tangents - like I said my grasp is minimal so I didn't plan on doing so even if this fact wasn't included.

http://session.masteringphysics.com/problemAsset/1013809/5/jfk.Figure.P09.08.jpg

 

[TSny]

I suspect this problem is designed to test your understanding of the "Impulse-Momentum" theorem.

Note that the collision lasts for 6 milliseconds. Do you know how to obtain the total impulse from the graph?

 

[eglaud]

I suspect this problem is designed to test your understanding of the "Impulse-Momentum" theorem.

Note that the collision lasts for 6 milliseconds. Do you know how to obtain the total impulse from the graph?

In a way that avoids integrals, I don't think so. I am familiar with this theorem, I'd just take the final momentum and subtract it from the initial momentum, correct?

 

[TSny]

I am familiar with this theorem, I'd just take the final momentum and subtract it from the initial momentum, correct?

That will give you the change in momentum. How is the change in momentum related to the force graph?

 

[eglaud]

Here are we looking at only the moment of impact, or is the entire graph relevant? Or is this graph the entire moment of impact? We never look at graphs in class, the homeworks are all through Pearson.

 

[TSny]

There are three key things that you need for this problem.

(1) Know the definition of impulse of a force.

(2) Know the impulse-momentum theorem (that relates impulse to change in momentum).

(3) Use a graph of the force versus time to determine the impulse of the force..

This video might help. A relevant example starts in the video at about 4:20