Better not stop pedaling

Between doing physics problems on Brilliant, some people like to unicycle. A unicyclist is cycling up a hill angled 1515^\circ with respect to the horizontal. The center of mass of the cyclist is directly over the axle of the wheel and the cyclist/unicycle system have a combined mass of 100 kg.\SI{100}{\kilo\gram}. The radius of the wheel is 0.5 m\SI{0.5}{\meter} and the coefficient of static friction between the wheel and the asphalt is 1.1.

What is the magnitude of the torque (in Nm\si{\newton\meter}) that the cyclist needs to exert on the pedals in order to cycle up the hill at a constant speed?

Details and assumptions

  • The unicycle does not slip against the hill.
  • You may take the acceleration of gravity to be 9.8 m/s2.-\SI[per-mode=symbol]{9.8}{\meter\per\second\squared}.
  • You may neglect air resistance.

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