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Question: A particle of mass m moves along the internal smooth surface of a vertical cylinder of radius r. Fin...

A particle of mass m moves along the internal smooth surface of a vertical cylinder of radius r. Find the force with which the particle acts on the cylinder wall if at t = 0, its velocity is v0 and it makes an angle α with the horizontal.

A

mv02R\frac{mv_{0}^{2}}{R}

B

mv02Rcos⁡α\frac{mv_{0}^{2}}{R}\cos\alpha

C

mv02sin⁡αR\frac{mv_{0}^{2}\sin\alpha}{R}

D

mv02cos⁡2αR\frac{mv_{0}^{2}\cos^{2}\alpha}{R}

Answer

mv02cos⁡2αR\frac{mv_{0}^{2}\cos^{2}\alpha}{R}

Explanation

Solution

F = mvx2R\frac{mv_{x}^{2}}{R} = mv02cos⁡2αR\frac{mv_{0}^{2}\cos^{2}\alpha}{R}