A cyclist exerts a vertical force on a bike pedal. This pedal is at the end of a crank that is \(0.20 \mathrm{~m}\) long and pivoted to rotate about the axle of the chain wheel. If the cyclist pushes downward with a force of \(150 \mathrm{~N}\), determine the magnitude of the torque caused by this force when the crank is

(a) horizontal,

(b) \(30^{\circ}\) from the horizontal,

(c) \(45^{\circ}\) from the horizontal,

(d) \(60^{\circ}\) from the horizontal, and

(e) vertical. 

( \(f\) ) Calculate the average magnitude of this torque exerted by one of the cyclist's feet during one cycle of the pedals, assuming there is no clip holding the cyclist's feet to the pedals.