M2 Collisions help

From Edexcel M2 Jan 2001...

A particle A of mass 2m is moving with speed 2u on a smooth horizontal table. The particle collides directly with a particle B of mass 4m moving with speed u in the same direction A The coefficient of restitution between A and B is 1/2

a) Show that the speed of B after the collision is 3u/2

b) Find the speed of A after the collision

Both these parts were OK and I got them right. Got the right answer for a) and got u for the speed of A after the collision

This is the bit im struggling on

Subseqently B collides directly with a particle C of mass m which is at rest on the table. The coefficient of restitution between B and C is e. Given that there are no further collisions,

c) Find the range of possible values of e. (8 marks)

I've got the answers but no actual solutions for the questions and the answer is given as e is less than or equal to 2/3, so yeah any help with this would be great :smile:

Reply 1

yazan_l

u have the velocity of B before collision with C, you can find the velocity of B after collision interms of e.
as there are no further collisions, then velocity of A MUST be more than (or equal to) the velocity of B (after collision with C). because if velocity of B was towards A and more than the velocity of A, they will collide.