# Momentum, enegy and collisions

1. Mar 1, 2009

### hellothere123

A proton (mass 1 u) moving at 7.80 x10^6m/s collides elastically and head-on with a second particle moving in the opposite direction at 2.40x10^6 m/s. After the collision, the proton is moving opposite to its initial direction at 6.60x10^6m/s. Find the mass and final velocity of the second particle. [Take the proton's initial velocity to be in the positive direction.]

I tried using the conservation of momentum and kinetic energy to do this. I get this big mess that i cannot solve for.. Please show me how i would do this. i would like to learn to do these problems. thanks.

2. Mar 1, 2009

### LowlyPion

Re: momentum

You should have 2 equations with 2 unknowns from each of the conservations.

Make it simpler by dropping the powers of 10 and add it back as a factor at the end.

Try writing out your equations here.

3. Mar 2, 2009

### hellothere123

Re: momentum

so if we let m1 be the proton. we have..
(7.8)-(m2)(2.4)=(-6.6)+m2v2
(7.8^2)+m2(2.4^2)=(6.6^2)+m2(v2)^2

m2 = [(7.8^2)-(6.6^2)]/[(v2)^2-(2.4^2)]

and then when i plug it back in, i get a quadratic. that gives me a mass considerably larger than the other one.

4. Mar 2, 2009

### The Bob

Re: momentum

What do you mean considerably? If your maths is right then what stops the second particle being very large?

The Bob

5. Mar 2, 2009

### hellothere123

Re: momentum

my math is probably bad, that is why i was hoping someone could show me the math so i can see where i went wrong

6. Mar 2, 2009

### LowlyPion

Re: momentum

OK. So you can say that

m*(v + 2.4) = 14.4 from the first equation. And ...

m*(V2 - 2.42) = 7.82 - 6.62

Note that this factors easily into

m*(V + 2.4)(V - 2.4) = 7.82 - 6.62

But from the first equation you know m*(v + 2.4) = 14.4 So ...

14.4*(V - 2.4) = 7.82 - 6.62

Much easier than a quadratic to solve.

EDIT: Sorry the 7.82 and 6.62 terms got translated incorrectly. I fixed them now.

Last edited: Mar 2, 2009
7. Mar 2, 2009

### hellothere123

Re: momentum

that is much easier and such.. and after working it out.. i did not get the right answer. the answer was 3.6 doing that gave me 1.2

8. Mar 2, 2009

### LowlyPion

Re: momentum

Sorry. I apparently switched two terms inadvertently in typing it out. I just fixed it.