Momentum, enegy and collisions

[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.

 

[LowlyPion]

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.

 

[hellothere123]

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.

 

[The Bob]

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

The Bob

 

[hellothere123]

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

 

[LowlyPion]

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.

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.

 

[hellothere123]

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

 

[LowlyPion]

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

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