Calculating Impulse and Final Velocity in a Ball Collision Problem

[pinky2468]

I have this homework problem that I keep going in circles with! Any hints?

A .500kg ball is dropped from rest at a point 1.20 m above the floor. The ball rebounds straight upward to a height of .700 m. What are the magnitude and direction of the impulse of the net force applied to the ball during the collision with the floor.

Ok so I know that Vo= 0m/s and I need to find the final velocity and time right? Do I need to break apart into x and y components?

 

[Galileo]

The impuls is the total change in the momentum of the ball.
First calculate the momentum of the ball just before it hits the ground.
Then calculate the momentum just after the ball looses contact with the floor (use the fact that it reaches a height of 0.7 m)
Then calculate the difference (watch the signs). That gives the magnitude of the impulse.

There's only a vertical component, so this is a 1-dimensional problem. No need to fuss with components.

 

[arildno]

1) All motion occurs in the vertical, so it is a one-dimensional problem.
(no need of vectorial description)
2) By conservation of energy, find the IMPACT velocity v(imp) of the ball at the moment of impact, just PRIOR to the collision.
3) By conservation of energy in the system AFTER collision, find the SEPARATION velocity v(sep) of ball.
4) Find the change of momentum DURING collision, that is M(v(sep)-v(imp))
Here, M is the mass of the ball. Mind your signs on velocities.

Hmm..Galileo beat me on this..

 

[pinky2468]

I get what both you are saying, but do I need to find the time? I am a little confused on which formula to use

 

[arildno]

Since the impulse of the applied force equals the net change of momentum, there is no need to "find" the time. In addition, there's no way you can find it..

 

[pinky2468]

I think I know which equations to use, but I still don't get how to find the final velocity?

 

[arildno]

What do you mean exactly with "final" velocity?
Separation velocity, or impact velocity?
These are given by energy conservation.

 

[pinky2468]

I got it! I used Vf=square root 2gh
Thanks for your help!

 

[arildno]

That is the equation you have to use twice:
1) To find the impact velocity (h=1.2)
2) To find the separation velocity (h=0.7)