To be able to analyze the equation of systems undergoing rol

To be able to analyze the equation of systems undergoing rolling resistance. If a rigid cycle of weight W rolls at a constant velocity along a rigid surface and does not encounter any frictional resistance from the air or the ground, its motion will continue indefinitely. In reality, no materials are perfectly rigid and, therefore, the surface upon which the cylinder rolls with deform due to the cylinder\'s weight. This deformation increases the amount of the cylinder\'s surface area that is in contact with the deformed surface and causes the normal force to distribute over a larger area of the cylinder. Rolling resistance is primarily a Part A A bicyclist is riding a bicycle on a flat road(Figure 2). The combined weight of the bicyclist and the bicycle is W = 220 lb. the radius of each wheels is R = 13.0 in. and the coefficient of rolling resistance between the tyros and the rod is a = 6.60 times 10^-2 in. The pedaling power of the chain that allows the bicycle to maintain a constant velocity when the chain is on the gear with a radius r = 1.50 in? consider he combined weight to be evenly distributed between the two wheels. Express your answer to three significant figures and include the appropriate units. Part B The bicyclist encounters a theta = 10.0 degree incline in the rod. (Figure 3) To maintain a constant velocity, the bicyclist shifts into a larger gear and all piles a force on the pedals that results in a tendon of T= 17.0 lb in the chain. Given the same coefficient of rolling resistance of alpha = 6.60 times 10^-2. What is r, the radius of the gear used by the bicyclist to maintain the same velocity?

Solution

a)

Weight on each tire = 220/2 = 110 lb

Rolling friction force F = c*W/R

= 6.6*10^-2 * 110 / 13

F = 0.5585 lb

Now, torque = F*R = T*r

T = F*R/r

= 0.5585*13/1.5

T = 4.84 lb

b)

Normal force from the road = W*cos10 = 110*cos10 = 108.33 lb

F = 6.6*10^-2 * 108.33 / 13 = 0.55 lb

F*R = T*r

r = (F/T)*R

= (0.55 / 17) * 13

r = 0.42 in