First slide

Types of collision

Question

A ball A, moving with kinetic energy E, makes a head on collision with a stationary ball with mass n times that of A. The maximum potential energy stored in the system during the collision is

Moderate

A

nE/(n + 1)
B

(n + 1)E/n
C

(n - 1)E/n
D

E/n

Solution

When elastic P.E is maximum, the balls momentarily move together with common velocity v
$\large mu + nm(0) = (n + 1)mV$
$\large V = \left( {\frac{1}{{n + 1}}} \right)u;\;E = \frac{1}{2}m{u^2}$
$\large {E}{}' = \frac{1}{2}(n + 1)m{V^2}$
$\large = \frac{1}{2}(n + 1)m{\left( {\frac{u}{{n + 1}}} \right)^2} = \frac{E}{{n + 1}}$
$\large P.E = E - E{}' = E - \frac{E}{{n + 1}} = \frac{{nE}}{{n + 1}}$

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