# Collision of twos spheres

1. Nov 19, 2008

### Welshy

1. The problem statement, all variables and given/known data
A sphere of mass m1 travelling at velocity u1 collides elastically with a stationary sphere of m2. The particles move away with v1 and v2 respectively.

I'm at part 4, of 5. It asks us to resolve the conservation of momentum equations normal and tangential to the post-collision velocity of m2. I obtained these equations using the diagram that's provided. The part I'm stuck on is where they ask us to obtain an expression for tanB involving only the masses and angle A.

A = angle of incidence
B = angle of reflection

The 5th part asks "Hence when does the angle of incidence equal angle of reflection?". So I know the resultant equation should be something along the lines of:

tanB = ((m1 + m2)/m2)*tanA

as m1 should be << m2

2. Relevant equations
m1u1cosA = -m1v1cosB + m2v2

m1u1sinA = -m1v1sinB

m1u12 = m1v12 + m2v22

3. The attempt at a solution

I found terms for v1 and equated them eventually getting:

tanB = ((m1u1cosA)/(m1u1cosA - m2v2))*tanA

But now I'm stuck. Any pointers?

Last edited: Nov 19, 2008
2. Nov 19, 2008

### tiny-tim

Welcome to PF!

Hi Welshy! Welcome to PF!

3. Nov 19, 2008

### Welshy

Re: Welcome to PF!

I used that in an earlier part of the question and when I tried to use it here it only complicated things by giving me more velocity terms which I couldn't cancel.

Any pointers on how it could be used - or even if my existing methods are on the right track?

4. Nov 19, 2008

### tiny-tim

Hint:

i] put A = B

ii] use (u1 + v1) and (u1 - v1), and the energy equation.

5. Nov 19, 2008

### Welshy

Sorry, I don't think I worded the question right. The bit I'm stuck on needs B = [mass terms]*A so I can't do that yet. But I'll try the other hint. Thanks.

6. Nov 19, 2008

### Welshy

I'm having no joy with this at all. Each of u1 and v1 can have 2 different equations. That gives a total of 8 combinations for (u1 - v1)(u1 + v1) and I'm sure I've tried them all.

I don't think I can make them cancel that way when A doesn't = B . :/

7. Nov 19, 2008

### Welshy

Any more hints that anyone can give? Is tiny-tim's method valid for A not equal to B? And, if so, where will I pull my speed equations from?

The sheer algebra of this just has me stumped. :/