A bicycle travels at v4fts The rear wheel diameter is 26in T

A bicycle travels at v=4ft/s. The rear wheel diameter is 26in. The rear gear diameter is 4in. The pedal gear diameter is 10in. The distance from the center of the pedal to axis of the pedal gear is 12in.

Find of the rear wheel and of the pedal gear.

If the bicyclist exerts a force of 200lbf on the pedal, what is the torque about the axis of the pedal?

What is the torque about the axis of the wheelgear?

What force is exerted through the wheel on to the road to accelerate the bicycle?

How much power is produced in units of hp?

Solution

given,

velocity of bicycle = 4ft/s

rear wheel dia = 26in

rear gear dia = 4in

pedal gear dia = 10in

centre of pedal to axis of pedal gear = 12in

force on pedal = 200lbf

1. angular velocity of rear wheel = V/r = 4/1.08 = 3.7 rad/s

2. angular velocity of pedal gear = V/r = 4/5 = 0.8 rad/s

3. torque about axis of pedal = Fxr = 200 x 5 = 1000 ft lb

4. T1/T2=R2/R1

1000/T2=2/5 , T2=2500 ft-lb

5. power = TxW = 1000x0.8 = 800 hp