What Is the Average Force Exerted on a Rebounding Steel Ball?

[williams31]

A 56g steel ball is released from rest and falls vertically onto a steel plate. The ball strikes the plate and is in contact with it for .5ms. The ball rebounds elastically, and returns to its original height. The time interval for a round trip is 8.00s. In this situation, the average force exerted on the ball during contact with the plate is closest to:
A) 4390 N
B) 10,260 N
C) 5870 N
D) 7300 N
E) 8780 N

I was wondering what formula I should use to solve the problem.

 

[DaMastaofFisix]

This is an impulse question right here. The formulas for impulse are your best friend in this case. Remember that it's not exactly straitfoward, but requires a little though outside of the definition of Impulse. Hope that gets you started.

 

[williams31]

Im not sure if I am following you.

 

[nrqed]

A 56g steel ball is released from rest and falls vertically onto a steel plate. The ball strikes the plate and is in contact with it for .5ms. The ball rebounds elastically, and returns to its original height. The time interval for a round trip is 8.00s. In this situation, the average force exerted on the ball during contact with the plate is closest to:
A) 4390 N
B) 10,260 N
C) 5870 N
D) 7300 N
E) 8780 N

I was wondering what formula I should use to solve the problem.

the average force during a collision is the change of momentum divided by the time interval during which the force acts. Here, by change of momentum, I mean the final momentum (after the collision) minu sthe initial momentum (before the collision). You have to be careful, this is a vector difference!

 

[williams31]

Im lost...but thanks for your guys help anyway.

 

[nrqed]

Im lost...but thanks for your guys help anyway.

First step: find the momentum of the ball *just* before it hits the surface (you may essentially treat its height as being zero). You know it takes 4 seconds to fall and it started from rest so you may find the velocity it has once it reaches the surface. The magnitude of the momentum will be the mass times the speed. (here, I am treating the time that the collision last negligible compared to the time of fall)

Second step: If the collision is elastic, what is the momentum just after the collision? If you take the momentum vector just after minus the momentum vector just before the collision, you get a difference which is not zero. What is its magnitude?

Third step: take this last result and divide by the time interval of the collision.

 

[Andrew Mason]

Im lost...but thanks for your guys help anyway.

What is the height that the ball is dropped from? (You can work this out from the time of the round trip).
What is its velocity just before it strikes the plate?
What is it after?
What is the change in velocity?
What is the change in momentum?
What is the relationship between (average) Force, time, and change in momentum?

Answer those questions and you will have your answer.

AM