What is the Average Force Exerted by a Wall on a Bouncing Ball?

[student 1]

Homework Statement

A 3.00 Kg steel ball strikes a wall with a speed 10 m/s at an angle of 60 degrees with the surface. It bounces off with the same speed and angle. If the ball is in contact with the wall for 0.20 s, what is the average force exerted by the wall on the ball?

Homework Equations

The Attempt at a Solution

Find Pf and Pi and use I=Pi-Pf then solve for F. I do not know what do use this to solve for F.

 

[alphysicist]

Hi student_1,

What is the equation relating the change in momentum and the (external) force?

 

[student 1]

I=[$$\int Fdt$$

 

[alphysicist]

I=[$$\int Fdt$$

That's the idea (since you have I in your original post). However, you do have to take into account the vector nature of this problem, so you should probably think of it as:

$$\int \vec F_{\rm ext}\, dt = \vec p_f - \vec p_i$$

You can simplify this formula a bit for this problem, because they are asking for the average force. What does that mean, and how will that affect the integral?

Once you have that, you will need the x and y components for the initial and final momentum. What do you get?

 

[student 1]

I got 30$$\sqrt{3}$$ for my I. I subtracted the Pi-Pf

 

[student 1]

What do I do with that?

 

[alphysicist]

I got 30$$\sqrt{3}$$ for my I. I subtracted the Pi-Pf

Good, that's the magnitude of I. (Although you should have done final-initial.) Using your other equation for I, you can then write:

$$\int F_{\rm ext} \, dt = 30\sqrt{3}$$
along the direction of I, and this will let you solve for the force. To simplify this, just answer the question in my last post: Since they are asking for the average force, what does that mean for the force you are solving for? In other words, what can you do with the left hand side when they ask for the average force?

(After you get the magnitude, you'll probably need the direction of the force, which is in the same direction as I. What is the direction of I?)