Maximum potential energy after collision

[randomgamernerd]

Homework Statement

: A ball a, moving with kinetic energy E, makes a head on elastic collision with a stationary ball with mass n times that of A. The maximum potential energy stored in the system during the collision is
a)nE/(n+1)
b)(n+1)E/n
c)(n-1)E/n
d)E/n[/B]

Homework Equations

:Principle of Conservation of mechanical energy(PCME) and principle of conservation of linear momentum(PCLM)[/B]

The Attempt at a Solution

: I have done the sum and my answer matches correctly...I just want to confirm if my concept is correct.
Just at the instant when potential energy of the system is maximum, the two balls are moving with equal velocities(just at that instant).
So from PCLM[/B]
mu=m(n+1)V
where u=initial velocity
V=the common velocity

Now since the collision is elastic, we can conserve ME.
so
1/2mu²=1/2m(n+1)V²+ U
where U= P.E
Also
E=1/2mu²
so from the two equations above...I got
U = En/(n+1)
I just want to assure if my concept is correct
Sorry if the thread is a duplicate one...or if I've made any grammatical error...
Thanks for the help

 

[PeroK]

Looks good to me.

You could also consider using the centre of momentum reference frame, which might offer a neat alternative approach.

 

[randomgamernerd]

Looks good to me.

You could also consider using the centre of momentum reference frame, which might offer a neat alternative approach.

Thanks for your help