A 52-kg person riding a bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 cm.
- What is the maximum torque she exerts?
- How could she exert more torque?
- pull up on handle bars or buy a longer crank...
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This is Giancoli Answers with Mr. Dychko. The maximum torque that the cyclist exerts occurs when their weight which is straight down is perpendicular to the crank or the lever arm; this crank is what connects the pedal to the bottom bracket or the gears here. So we have Θ equaling 90 degrees, in which case, Θ being the angle between the line of action of the force and the lever arm and being 90 degrees, sin of 90 is 1 so torque maximum is always gonna be lever arm multiplied by the force. So we have 0.17 meters—length of the crank— times 52 kilograms times 9.8 newtons per kilogram and that gives 87 newton meters of torque. And in order to increase their torque, the cyclist could pull up on the handle bars so that they could exert more force down than just their weight; they could push themselves upwards and accelerate their center of mass upwards for short period of time that would allow them to apply more force downwards or they could buy a longer crank. So increase this lever arm from 0.17 meters to something longer or wear a backpack so they increase their mass, something like that.
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