A classical mechanics problem by Kundan Patil

Classical Mechanics Level 1

If a ball strikes a wall with velocity 3 m/s 3 \text{ m/s} at an angle 3 0 ∘ 30^\circ and rebounds back at angle 4 5 ∘ 45^\circ with velocity 2 m/s \sqrt{2} \text{ m/s} , then find the coefficient of restitution to three decimals places.


The answer is 0.666.

Kundan Patil by Kundan Patil , 23, India

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2 solutions

Caleb Townsend
Feb 18, 2015

The coefficient of restitution is C R = v 2 sin ⁡ θ 2 v 1 sin ⁡ θ 1 C_R = \frac{v_2\sin \theta _2}{v_1\sin \theta _1} This is a simple substitution, and simple arithmetic since we have convenient angles. 2 / 2 3 / 2 = 0.667 \frac{\sqrt{2}/\sqrt{2}}{3/2} = 0.667

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Prince Loomba
Apr 21, 2016

Coefficient of restitution = e = v s e p a r a t i o n v a p p r o a c h = 2 × s i n 4 5 ∘ 3 × s i n 3 0 ∘ = 2 3 = 0.666 =e=\frac{v_{separation}}{v_{approach}}=\frac{\sqrt{2}\times sin 45^{\circ}}{3\times sin 30^{\circ}}=\frac{2}{3}=0.666 . Note: v s e p a r a t i o n , v a p p r o a c h v_{separation},v_{approach} are in line of impact which in this case is normal to the wall.

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