# M2 coefficient of restitution ranges

How do you do ranges for coefficient of restitution? i know you have to work it out by doing inequalities but how? here is an example for june 2001 paper.

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 diresction as A. the coefficient of restitution between A and B is 1/2.

(a)show that the speed of B after the collision is 3/2u.(i have done this part)

(b)Find the speed of A after the collision.(i have done this as well,answer=u)

Subsequently 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 is no further collisions,

(c)Find the range of possible values for e.(the answer is e is less than or the same as 2/3)

0 <= e <= 1

So, use e=1 to get the maximum, and e=0 to get the minimum. This method doesn't always work, btw.
foreverblue

Subsequently 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 is no further collisions,

(c)Find the range of possible values for e.(the answer is e is less than or the same as 2/3)

well, for no other collisions, C > B > A

(think about it for a sec)

so do something do with that.

i always think i know what im doing but htne they do something else though, so it may not be right.
foreverblue
How do you do ranges for coefficient of restitution? i know you have to work it out by doing inequalities but how? here is an example for june 2001 paper.

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 diresction as A. the coefficient of restitution between A and B is 1/2.

(a)show that the speed of B after the collision is 3/2u.(i have done this part)

(b)Find the speed of A after the collision.(i have done this as well,answer=u)

Subsequently 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 is no further collisions,

(c)Find the range of possible values for e.(the answer is e is less than or the same as 2/3)

how any marks are there for c?
SasunD
how any marks are there for c?

8
foreverblue
8
i see, so you will have to do another restitution and momentum equating equations for B and C to work out the values of e.

im working on it at the moment, so ill post the answer in a couple of mins.
its not working, ill get a fresh pad of paper to do some more wokring out.
This question was up last week here http://www.uk-learning.net/t48510.html
thanks Bezza, i was trying to use B and C, but it wasn't working.