# 2-body collision: Min and Max speed

1. Dec 31, 2012

### unscientific

1. The problem statement, all variables and given/known data

A ball of mass M travelling at non-relativistic speed v elastically collides with a stationary ball of mass m.

(a)Show that the maximum speed which the second ball can have is:

2Mv/(M+m)

(b)What is the minimum speed?

3. The attempt at a solution

(a)
Method 1

Go into ZMF frame:

step 1: find VCM
step 2: u2' = u2 - VCM
step 2: pi = pf = 0
step 3: v2' = -u2
step 4: go back into lab frame by adding VCM

Method 2

1)Speed of approach = speed of separation
2)conservation of momentum
3)done.

But the puzzling thing is that why is this the maximum speed? Isn't this the actual acquired speed?

(b)
Do we assume a head-on collision? If it is a head-on collision won't the speed be the same as part (a)?

assuming a non head-on collision by including angles and stuff doesn't help..

2. Dec 31, 2012

### Staff: Mentor

If you assume a head-on collision where the second ball travels in the initial direction of ball 1, this is the maximal speed.
Every other collision will give a lower speed.

3. Jan 1, 2013

### unscientific

so for part (b) it isn't a head-on collision?

4. Jan 1, 2013

Right ;)