A boy on a bicycle is pedaling along a straight and level roadat 8 m/s. When he

Question

A boy on a bicycle is pedaling along a straight and level roadat 8 m/s. When he stops pedaling to coast he finds that he travelsat a distance of 250 meters before coming to rest. Assuming thatthe boy and bicycle have a total mass of 65 kg, find: a. the acceleration; b. the rolling force of friction; and c. the coefficient of rolling friction. A boy on a bicycle is pedaling along a straight and level roadat 8 m/s. When he stops pedaling to coast he finds that he travelsat a distance of 250 meters before coming to rest. Assuming thatthe boy and bicycle have a total mass of 65 kg, find: a. the acceleration; b. the rolling force of friction; and c. the coefficient of rolling friction.

Explanation / Answer

Working formula is Vf^2 - Vo^2 = 2as where Vf = final velocity = 0 (when bicycle stops) Vo = initial velocity = 8 m/sec. (given) a = acceleration s = stopping distance Substituting values, 0 - 8^2 = 2(a)(250) Solving for "a" a = -64/500 a = -0.128 m/sec^2 NOTE that the negative sign indicates that the bicycle was slowingdown as it was coasting. Using Newton's 2nd Law of Motion, F = ma where F = net force acting on the bicycle m = mass of the boy/bicycle = 65 kg (given) a = acceleration = -0.128 m/sec^2 (as calculated above) Substituting values, F = 65(-0.128) F = - 8.32 N NOTE that the negative sign on the force merely indicates that thenet force acting on the body is the friction force whose directionis opposite that of the bicycle's motion. By definition, the frictional force is F = µN where µ = coefficient of friction N = normal force = 65 * 9.8 = 637 newtons hence 8.32 = µ(637) and solving for µ, µ = 0.013

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