6. A bicyclist is riding a bicycle at a constant speed of 7 m/s. She has to peda

Question

6. A bicyclist is riding a bicycle at a constant speed of 7 m/s. She has to pedal to overcome a drag force of 40 N. The bicycle’s rear tire has a radius of 40 cm. There are two rear sprockets: one with a radius of 5 cm (“high gear”), and one with a radius of 10 cm (“low gear”). The front sprocket has a radius of 10 cm. Note that the chain connecting the sprockets moves at a constant speed and thus has a = 0, so the force it exerts on the front sprocket is the same as the force it exerts on the rear sprocket. Note: The rotational equivalent to the power-velocity relation P = F~ ·~v is exactly what you think it would be: P = . (a) When in high gear, how much torque must she deliver to the pedals to maintain her speed? What is her power output when doing so? (b) When in low gear, how much torque must she deliver to the pedals to maintain her speed? What is her power output when doing so? (c) Do your answers match your experience with riding a bicycle?

Explanation / Answer

V= rW

P=FV = 40x7m/s=280 Nm/s

a) P= T W where T= Torque, W= angular velocity

P = T x 7/5

T = 280 x 5/7 =200 N-m

b) P = T x 7/10

T = 400 N-m

c) Yes

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