First slide

Coefficient of restitution

Question

A mass m moves with a velocity v and collides elastically with another identical mass. After collision the first mass moves with velocity v / $\sqrt{3}$ direction perpendicular to the initial direction of motion. Find the speed of the second mass after collision

Moderate

A

v
B

$\sqrt{3 v}$
C

$\frac{2}{\sqrt{3}} v$
D

$\frac{V}{\sqrt{3}}$

Solution

In x-direction
${mv}_{1} + 0 = 0 + m v_{x} o r v_{x} = v_{1} = v I n y - d i r e c t i o n 0 + 0 = m (\frac{v}{\sqrt{3}}) + m v_{y} o r v_{y} = \frac{v}{\sqrt{3}} ∴ V e l o c i t y of second mass afte r collision v^{'} = \sqrt{{(\frac{v}{\sqrt{3}})}^{2} + v^{2}]} = \sqrt{(\frac{4}{3} v^{2})} = \frac{2}{\sqrt{3}} v$

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