# Elastic collision/ momentum question w/ conservation of energy

1. Feb 6, 2014

### mjmontgo

1. The problem statement, all variables and given/known data

In deep space a 7.0 kg rubber ball moving along the x-axis with a speed of 20 m/s collides ELASTICALLY with another ball of mass = 25 kg. After the collision the 7.0kg rubber ball's velocity is directed in the positive y axis. Find the final speed of the 7 kg ball, as well as the VELOCITY of the 25 kg ball (speed and direction)

2. Relevant equations
m1v1= m1v1f+m2v2f

1/2m1v12= 1/2m1v1f2 +1/2m2v2f2

3. The attempt at a solution

so i know that because the smaller mass is afterwards directed in the positive y direction, that all of its x momentum is transferred to the bigger mass. ive found a velocity for the x component of the bigger mass, however im stucking finding the y component, which in turn would give me the over all final velocity, which i can use to calculate the angle as well as the final speed of the smaller mass. Would be greatly appreciated if someone could point out the extra equation im missing. Basically what i have so far boils down to these equations:

m1v1x= m2v2finalx and i work out the x component of the larger mass to be 140/25 m/s

the other equation i have is for the y direction and that is :
-m2v2fy= m1v1fy

i know i somhow need to use the energy conservation formula but im just not seeing it.
Thanks a lot in advance for you help and time guys.

2. Feb 6, 2014

### BvU

You're doing fine. Write out the energy conservation using v2 = vx2+vy2

3. Feb 6, 2014

### mjmontgo

Ok, so i've rewritten the energy conservation formula and what it comes down to is:

m1v1xi2= m1v1yf2+m2v2xf2+m2v2yf2

with some substitution with my known quantities i.e mass and m2v2xf=140/25

i get 2016= 7kgv1yf2+25v2yf2

which i solve in terms of v1yf and sub into -m2v2fy=m1v1yf

but when i calculate the velocity i get a negative answer, which doesnt make sence for v1yf because we already know from the question that it's moving in the positive y- direction after the collision.

Maybe i'm just making a silly arithmetic error but what i get is:

-sqrt(2016-7kg(v1yf2))=25kgv1yf2 and you can't take sqrt of a negative obviously?

4. Feb 7, 2014

### Staff: Mentor

-m2v2fy=m1v1yf

From this momentum equation you have one velocity in terms of the other, substitute into your energy equation.

5. Feb 7, 2014

### BvU

2016= 7kgv1yf2+25v2yf2 is fine. How come I continue with
2016 - 7kgv1yf2 = 25v2yf2 and never find a minus sign ?

Ah, I see, you solve in terms of v1 means you get v2,y2 = (2016 - 7kgv1yf2)/25 which has 2 solutions, right ?

And you continue with which one ?
Whatever, don't forget to check your outcome, because I think I'm missing something still.

Last edited: Feb 7, 2014
6. Feb 7, 2014

### haruspex

You mean v2xf=140/25 m/s, yes?
I don't see how you get that last equation. It doesn't make sense dimensionally. Did you mean -(2016-7kg(v1yf2))=25kgv1yf2? That would be a sign error somewhere. I suspect you squared -m1v1yf/m2 and left the result as negative.