# Law of Restitution & Momentum

1. Apr 18, 2012

### ZxcvbnM2000

Hello everyone , here we go :

I understand that momentum is always conserved as long as no external forces act on a given system . I also understand that the law of restitution applies to the axis perpendicular to the line of impact between two objects .However i have a problem .

For example . A ball hits the ground at an angle of 45 degrees and bounces up at an angle of 30 degrees.

So from the law of restitution : e= - ( Vball*sin30 - Vground)/(Uball*sin45 - U ground) , the ground does not move therefore Uground = Vground=0 so

e = - Vball*sin30/(Uball*sin45).

My question is , why can't we apply momentum conservation on the y axis ? Is it because the reaction force when hitting the ground is considered an external force ?

I am very confused please explain :S

Thank you !

2. Apr 18, 2012

### Staff: Mentor

Exactly. If you look at the ball itself, its direction reverses when it bounces. So obviously, momentum of the ball is not conserved--it's being smacked by the ground!

If you expand your 'system' to be 'ball + ground/earth', then momentum will be conserved again. (The force between ground and ball would then be an internal force.)

3. Apr 18, 2012

### ZxcvbnM2000

So my restitution formula is wrong and the only thing i have in my "system " is the ball , no ground etc . So it should be e= - V*sin30/(u*sin45) but e can't be negative ....argh !!! :S

4. Apr 19, 2012

### ZxcvbnM2000

Let's assume that two balls(m1=m2=m ) collide with one another .

The first ball is traveling at a speed u while the second ball is stationary.The first ball strikes the second one at an angle θ to the line of impact.If the coefficient of restitution is e , find the angle at which the second ball travels after the impact.

What i don't understand in this case is why isn't momentum conserved both along the line of impact and on the axis perpendicular to it as well ? I mean , both balls are part of our system so there are no external forces ?!

Could you please solve this exercise and explain each step thoroughly so i can finally understand ? Thank you very much !!!

5. Apr 19, 2012

### Staff: Mentor

Why would you think that momentum isn't conserved in all directions?