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## #1 2017-04-21 02:19:05

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

### collision

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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## #2 2017-04-21 19:46:01

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

### Re: collision

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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## #3 Yesterday 02:46:20

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

### Re: collision

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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## #4 Yesterday 03:11:19

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

### Re: collision

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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## #5 Yesterday 11:03:13

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

### Re: collision

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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