A sphere of mass 4 kg moving to the right with velocity v A = 8 m / s strikes at point B of the frictionless surface of half cylinder of mass 7 kg which is at rest. The half cylinder rests on a smoo

Question

A sphere of mass 4 kg moving to the right with velocity v A ​ = 8 m / s strikes at point B of the frictionless surface of half cylinder of mass 7 kg which is at rest. The half cylinder rests on a smooth horizontal floor and may move freely on the horizontal floor in the horizontal direction. If e = 1/4 be the coefficient of restitution. Take the angle BOC as θ = 3 0 ∘ .

TestHub · Accepted Answer

Along the common normal (60° to horizontal): approach speed $= 8 cos 6 0^{\circ} = 4$ m/s.

Impulse on the ball: $N Δ t = 4 (v_{2} + 4)$ ; on the cylinder: $N Δ t sin 3 0^{\circ} = 7 v_{1}$ .

Restitution along the normal: $v_{2} + \frac{v _{1}}{2} = \frac{1}{4} \times 4 = 1$ .

Solving: $v_{1} = 1.25$ m/s, $v_{2} = 0.375$ m/s; the ball keeps its tangential component $8 sin 6 0^{\circ} = 43$ , so its speed $= 48 + 0.37 5^{2} = 6.94$ m/s - (A), (B)

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