Question

# A bicycle rider has a drag area of 0.22 m2. She is riding at a velocity...

A bicycle rider has a drag area of 0.22 m2. She is riding at a velocity of 8.3 m/s along the road and the air density is 1.2 kg/m3. Total mass of the rider and bike is 93 kg. The coefficient of rolling resistance is 0.004. She is riding into a headwind with velocity 1.8 m/s. The road is horizontal. What power (watts) must the cyclist produce to maintain the speed of 8.3 m/s?

drag force is given by the drag equation=0.5*pho*v^2*Cd*A

where pho=density of air=1.2 kg/m^3

v=speed of the rider w.r.t. air=8.3+1.8 (as headwind means the air is moving in the opposite direction of the vehichle)

==>v=10.1 m/s

drag coefficient for bicylce=0.9

A=0.22 m^2

then drag force=0.5*1.2*10.1^2*0.9*0.22=12.119 N

rolling friction force=coefficient of rolling resistance*normal force

=0.004*mass*g

=0.004*93*9.8=3.6456 N

total force to be applied by the cyclist=3.6456+12.119=15.765 N

then power to be developed=force*speed

=15.765*8.3=130.85 W

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