Coefficient of restitution

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A sphere of mass m moving with a constant velocity u hits another stationary sphere of same mass. If e is the coefficient of restitution, then ratio of velocities $\frac{v_{2}}{v_{1}}$ of the two spheres after collision will be

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Solution

$\begin{array}{l} Applying conservation of linear momentum \\ m u = m v_{1} + m v_{2} \\ u = v_{1} + v_{2} ...... (1) \\ T h e coefficient of restitution \\ e = \frac{v_{1} - v_{2}}{u} ....... (2) \\ Solving these two equations, we get \\ v_{1} = (\frac{1 + e}{2}) u \\ v_{2} = (\frac{1 - e}{2}) u \\ ∴ \frac{v_{2}}{v_{1}} = \frac{1 - e}{1 + e} \end{array}$

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Coefficient of restitution

Remember concepts with our Masterclasses.

A sphere of mass m moving with a constant velocity u hits another stationary sphere of same mass. If e is the coefficient of restitution, then ratio of velocitiesv2v1 of the two spheres after collision will be

Applying conservation of linear momentummu=mv1+mv2 u=v1+v2 ......1The coefficient of restitution e=v1−v2u .......2Solving these two equations, we get v1=1+e2u v2=1−e2u ∴v2v1=1−e1+e

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A sphere of mass m moving with a constant velocity u hits another stationary sphere of same mass. If e is the coefficient of restitution, then ratio of velocities $\frac{v_{2}}{v_{1}}$ of the two spheres after collision will be