Chapter 10, Problem 72P

In bicycling, each foot pushes on the pedal for half a rotation of the pedal shaft; that foot then rests and the other foot takes over. During each half-cycle, the torque resulting from the force of the active foot is given approximately by τ = τ₀ sin ωt, where τ₀ is the maximum torque and ω is the angular speed of the pedal shaft (in s⁻¹, as usual). A particular cyclist is turning the pedal shaft at 70.0 rpm, and at the same time τ₀ is measured at 38.5 N·m. Find (a) the energy supplied by the cyclist in one turn of the pedal shaft and (b) the cyclist’s average power output.