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**markosheehan****Member**- Registered: 2016-06-15
- Posts: 46

Two smooth spheres of masses km and m collide obliquely. the sphere of mass m is brought to rest by the impact. the coefficient of restitution for the collision is 1/k (k greater or equal to 1) Prove before the impact the spheres were moving perpendicular to each other.

i have worked out k=-1. I know the sphere of mass m was xi+0j before and 0i+0j after.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,918

hi markosheehan

You can use a similar approach to the previous one. Take x as along the line of centres. I used Wx and Wy for km before ; Ux and Uy for m before ; Vx and Vy for km after.

You can make 4 equations: conservation of momentum in each direction; experimental law in the x direction; no change of relative velocity in the y direction*.

This last will allow you to show that Uy is zero. Looks like you already have Wx is zero.

Bob

* These problems are the first time I've had to use this 'no change' law, but I think it makes sense in terms of Newton's laws. In the y direction the spheres just scrape past each other without any 'bounce' so why should their relative velocities change.

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**markosheehan****Member**- Registered: 2016-06-15
- Posts: 46

i have used conservation of momentum in only the i direction as its pointless using it in the j direction.

a(km)+x(m)=y(km)+0(m)

then using the coefficient or restitution formula y-o/a-x =-1/k

solving these k=-1

actually wait i think i have it.

so when we compare these equations -a+x=yk and ak+x=yk they are inconsistent unless a=0 that means initially there speeds are bj for the sphere of mass km and xi for the sphere of mass m

Is this right??

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**markosheehan****Member**- Registered: 2016-06-15
- Posts: 46

the second part of the question is show that as a result of the collision the kinetic energy lost by the sphere of mass m is k times the kinetic energy gained by the sphere of mass km.

the kinetic energy lost by mass m sphere is .5mx^2

kinetic energy gained by mass km sphere is .5(km)(y)^2-.5(km)(a)^2

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,918

hi markosheehan

I agree that a=0. But you'll have to consider y direction too if you want to complete this question,

I don't see where you got that value of k from. It must be wrong as k cannot be negative.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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