# Oblique collision with two spheres one of which is at rest

1. Jul 17, 2013

### Woolyabyss

1. The problem statement, all variables and given/known data
A smooth sphere of mass m collides obliquely with a smooth sphere of mass 2m which is at rest.The velocity of the mass m was 8i + 4j before impact, where i is along the lines of centres at impact.the m mass is then deflected through 90 degreese by the impact. find
(i) its velocity immediately after impact.
(ii)the velocity of the 2m mass after impact.
(iii) the coefficient of restitution between the two spheres

2. Relevant equations
conservation of momentum

and

(v1 - v2)/(u1 - u2) = -e coefficient of restitution

3. The attempt at a solution
i is the horizontal axis along the line of centres at impact.
j is the vertical axis.

j is unaffected by the impact

(i)
conservation of momentum along the i axis
m(8) + 2m(0) = m(v1) + 2m(v2).............. 8 = v1 + v2

I'm not exactly sure what to do, i'd guess it involves the fact its deflected through an angle of 90 degrees?

since its original angle was j/i = 4/8 = 1/2 ............... tan-inverse(1/2)

would that not mean that the spheres angle relative to the i axis after impact is tan-inverse(2)

since tan-inverse(1/2) + tan-inverse(2) = 90 degrees?

2. Jul 17, 2013

### Woolyabyss

I think I got the answer to part (i)

since the original angle is tan-inverse(1/2) the new angle is tan-inverse(2)

we can use j/i again j/i = 2 we know j is unchange since i is along the line of centres at impact

so............ 4/i = 2

i = 2

but since its deflected "i" is actually negative so the velocity after impact is -2i + 4j

3. Jul 17, 2013

### Woolyabyss

I just finished the question there, sorry about that.