A block of mass m moves horizontally against the vertical wall of a cylindrical room of radius R. The floor is smooth, wall-block friction coefficient is µ, and initial speed is v₀. As functions of speed v, find (a) wall normal force; (b) wall friction; (c) tangential acceleration; (d) speed after one full revolution.
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Question

A block of mass m moves horizontally against the vertical wall of a cylindrical room of radius R. The floor is smooth, wall-block friction coefficient is µ, and initial speed is v₀. As functions of speed v, find (a) wall normal force; (b) wall friction; (c) tangential acceleration; (d) speed after one full revolution.

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G1 Physics · Accepted Answer

The wall normal supplies centripetal force: N=mv²/R. Friction is f=µN=µmv²/R opposite motion, so aₜ=-µv²/R. Using dv/dt=v dv/ds gives dv/v=-µ ds/R. Over s=2πR, v=v₀ e ( − 2 π µ ) . e^(-2πµ). e ( − 2 π µ ) .