The mass of a bicyclist and bike is 80 kg. The drag coefficient is 0.79. Frontal

Question

The mass of a bicyclist and bike is 80 kg. The drag coefficient is 0.79. Frontal area is 0.42 m^2. The density of air is 1.1 kg/m^3 at this elevation. The terminal velocity is reached when the drag force of a free falling object is equal to the weight.

a)Estimate the magnitude of the terminal velocity of the cyclist after he has ridden his bike off of a cliff. Assume that the frontal area remains constant during the fall.

b)Estimate the terminal velocity of the cyclist coasting down an incline of 15 degrees. Note that it is not the entire weight of the cyclist that is pulling him down the hill. Assume no friction in the wheels.

c) What happens to the terminal velocity of the cyclist as his mass is increased?

d) What is the magnitude of the drag force when the cycling velocity is equal to the terminal velocity in part b?

e) How much negative work would the drag force in part d do during a 40 km ride?

Explanation / Answer

given

masss of the bicyclist = m = 80 kg

drag coefficient, Cd = 0.79

Frontal Area, A = 0.42 m^2

rho = 1.1 kg/m^3

a. terminal velocity = v

drag = weight

mg = 0.5Cd*rho*v^2*A

hence

v = sqrt(2mg/Cd*rho*A) = 65.5782709 m/s

b. for theta = 15 deg

drag = weight*sin(theta)

mg = 0.5Cd*rho*v^2*A*sin(theta)

hence

v = sqrt(2mg/Cd*rho*A*sin(theta)) = 128.90265 m/s

c. as mass is increased, terminal velocity also increases

d. v = 65.5782709

drag force = mg = 784.8 N

e. d = 40,000 m

work = -40,000*mg = -31392000 J

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