Solving Torque & Forces: Bicyclist w/ 71 kg Weight

[ibrahim1996]

Hey, I've tried working on this and I just cannot figure it out. I went to someone for help and they got confused. Can someone please SHOW ME how it is done. I prefer to see step by step so I know where I went wrong.

Thanks,

A bicyclist weighing 71 kg starts his ride by putting all his weight on one pedal. The pedal arm is
15 cm long and is initially positioned up at an angle of 31° from the perpendicular.

a. Sketch the pedal and draw the forces acting on it. Calculate the torque initially generated by
the rider.
b. Under the same conditions, how much torque is generated if the pedal arm is horizontal?
c. The material of the pedal arms is only rated for a maximum torque of 250 Nm. What is the
maximum weight of a rider that this bicycle can withstand?

 

[HallsofIvy]

Hey, I've tried working on this and I just cannot figure it out. I went to someone for help and they got confused. Can someone please SHOW ME how it is done. I prefer to see step by step so I know where I went wrong.

Thanks,

A bicyclist weighing 71 kg starts his ride by putting all his weight on one pedal. The pedal arm is
15 cm long and is initially positioned up at an angle of 31° from the perpendicular.

a. Sketch the pedal and draw the forces acting on it. Calculate the torque initially generated by
the rider.

Have you drawn the picture? Do you know that torque is "force perpendicular to the length of the lever". Here, the rider is putting all his weight vertically so you need to mulltiply that by the horizontal component of the length of the pedal arm.

b. Under the same conditions, how much torque is generated if the pedal arm is horizontal?

This is easier than (a). Do you see why?

c. The material of the pedal arms is only rated for a maximum torque of 250 Nm. What is the maximum weight of a rider that this bicycle can withstand?

The maximum torque for a given weight occurs when the pedal arm is horizontal (part b). Do you see why? Set the length of the pedal arm, times the unknown weight, equal to 250 and solve for the weight.