Math Is Fun Forum

markosheehan

Member

Registered: 2016-06-15

Posts: 51

Collision

A smooth sphere P, of mass m kg, moving with speed 5u m/s collides directly with a smooth sphere Q, of mass 2m kg, moving towards each other with speed 2u m/s.
The coefficient of restitution between the spheres is e.
find the condition satisfied by e if the 2 spheres move in the same direction after the collision.

using the 2 normal equations i got their final speeds to be 3u-2ue and 3u-ue
because they move in the same direction i let 3u-2ue >0 and 3u-ue>0
solving these i get e<3 and e>3/2
the answer at the back of the book is e<1/14
i can go though my answer in more detail if you need it
thanks

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Collision

hi markosheehan

Q, of mass 2m kg, moving towards each other with speed 2u m/s.

Strange wording.  Does this mean a relative velocity of -2u, or an absolute velocity of -2u ?

I've tried both and cannot get your final velocities with either.  Here's a start with the interpretation that leads to the book answer:

momentum along line of centres:

restitution law:

It's easy to show that Vq is greater than zero so the condition on Vp leads to the required condition on e.

Incidentally, you should have realised there's something wrong with your solution as you have

solving these i get e<3 and e>3/2

e can never be greater than 1.

Hope that helps,

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

markosheehan

Member

Registered: 2016-06-15

Posts: 51

Re: Collision

thanks i worked it out from what you told me

the problem was i thought the velocity of q was 2u and not -2u. i thought they were travelling in the same directions not the opposite.