Solving Snooker Ball Physics Problem: u^2(m-M)=v^2(M+m)

[alias25]

snooker ball moving with mass m and vel u collides with stationary ball M, after collision m rebounds and moves with v vel. and M moves velocity V, if collision is elastic show that
v = ((M-m)/(M+m))multipliedby u rearrange this u get..v(M+m) = u(M-m)

using conservation laws i got (and I've taken the final vel of m as a negitive value (-v))

mu^2 = MV^2 - mv^2 (got that from E = 1/2mv^2)

and

mu = MV - mv (conservation of momentum

then I've rearranged the first equation for V and subbed it into the second
i ended up with a similar equation to the one they asked, i got

u^2(m - M) = v^2 (M + m)

i don't kno how to get rid of the squares or change (m -M) to (M-m)
did i approach the question right or is there something in the statement "if collision is elastic" that i havnt picked up on?

anyone here think i shouldn't be considering taking physics at uni if i can't do a question like this?

 

[Diane_]

It's a very general question. That makes it a hard one for a beginner. Don't let it get you down.

You are wrong to assume that v is negative. Throwing that minus sign in there will skew your final answers and get you nothing. The negative is a directional indicator - all you're saying with it is that the speed you end up with is in the opposite direction from what actually happens. To put it another way, it is physically possible for v to be in either the same direction as V or in the opposite direction. Putting the minus sign in just clouds the issue.

Getting rid of that extraneous minus sign will actually solve your problem. Just remember that (u^2 - v^2) factors. To get the actual form you need, you'll have to multiply some things out and group similar terms.

 

[alias25]

so i have (u^2-v^2) factorises to (u+v)(u-v)

but i end up with M(u+v)(u-v) = m(u+v)(u-v)

they cancel and i end up with m = M
thats wrong

i can rearrange the equation that I am looking for again to
Mv +mv = Mu - mu
- > mv + mu = Mu - Mv
--> m(v+u) = M (u -v)

which is similar to the equation i ended up with but mine cancelsss.

 

[Mulder]

anyone here think i shouldn't be considering taking physics at uni if i can't do a question like this?

I'm in my fourth year and can't do most of the school questions. Even the "simple" ones seem hard if you don't practise occasionally.

i can rearrange the equation that I am looking for again to
Mv +mv = Mu - mu
- > mv + mu = Mu - Mv
--> m(v+u) = M (u -v)

rearrange that and that's what you're trying to get isn't it?

btw I'd agree with Diane about not usually assuming the direction of the moving ball after impact, but if it says rebound in the question that does make it sound like it's going to reverse.

 

[Diane_]

Alias - Recheck your algebra. I ended up with

M(u^2 - v^2) = m(u-v)^2

There's only one factor of (u-v) that cancels on each side. Multiply out what you're left with and group u on one side and v on the other.

 

[alias25]

i see where u go that from so once u-v cancels
u get
M(u+v) = m(u-v)
which isn't equal to
m(v+u) = M (u -v)
the equation that I am looking for is it? hang onnn. if i sub in negitive v now ill get..
M(u-v) = m(u+v)
ive got it!
thank you