Momentum Question Involving Elastic Collision

[GarrettB]

Homework Statement

A 67.6g tennis ball with an initial speed of 28.8m/s hits a wall and rebounds with the same speed. The figure below shows the force of the wall on the ball during the collision. What is the value of Fmax, the maximum value of the contact force during the collision, if the force is applied for ti=19.1ms?

Homework Equations

I= p_f-p_i
I= area under the curvehttp://s1329.photobucket.com/user/GarrettSPB/media/momentum_zps3611f797.png.html

The Attempt at a Solution

I was able to find the impulse as the difference between the initial and final momentum. This ended up being 3.89 N*s. From that I know how to find Favg, but I'm stuck on how to find Fmax. Any suggestions would be appreciated.

 

[barryj]

IWhere is the figure?

 

[GarrettB]

http://s1329.photobucket.com/user/GarrettSPB/media/momentum_zps3611f797.png.html

Can you see that?

 

[barryj]

I cannot see a figure. Is it a graph of Force vs time or what? If you don't have some characteristics of the tennis ball other than it being elastic, I wouldn't know how to find the max force. You probably know the average force. Or does the ball hit a wall at an angle?

 

[GarrettB]

Yes, exactly its a force vs time graph.

http://i1329.photobucket.com/albums/w548/GarrettSPB/momentum_zps3611f797.png

 

[barryj]

You must integrate the curve which amounts to finding the area. The integral of the curve is the imnpulse that you have figured out. Is this enough help?

 

[GarrettB]

Unfortunately not. I don't know how knowing the area under there can help me find Fmax. If I could break up the the graph into geometric shapes then I would have a better idea how to find Fmax. Is there some equation I'm missing?

 

[barryj]

Look at the graph. You know what ti is, given to be 19.1 msec. Basically, the area under the curve is the impulse. You can break up the curve into three parts and find the area as a function of Fmax. Then equate this to what you have determined the impulse to be.

 

[GarrettB]

I've tried doing that and it doesn't work. I choose the rectangle in the middle of the graph (t=19.1/3) and then evaluate for 3.89 N*s= 6.37msec* Fmax; Fmax=611N. And that's not correct

 

[barryj]

The right side of the equation is incorrect. You have three geometric shapes, two triangles and 1 rectangle. The Area of the first triangle is (1/2)base X height = (1/2) * 0.00637 sec * Fmax. Now do the other triangel and the rectangle and add them.

 

[GarrettB]

Oh wow. Thank you so much

 

[barryj]

Your time is 19.1 not 19.1/3 if this makes a slight difference