Question

A bicycle wheel has a diameter of 64.2 cm and a mass of 1.82 kg. Assume that the wheel is a hoop with all of the mass concentrated on the outside radius. The bicycle is placed on a stationary stand and a resistive force of 116 N is applied tangent to the rim of the tire. (a) What force must be applied by a chain passing over a 9.04-cm-diameter sprocket in order to give the wheel an acceleration of 4.56 rad/s2? N (b) What force is required if you shift to a 5.61-cm-diameter sprocket?

Answer 1

here,

the mass of wheel , m = 1.82 kg

the diameter , d = 64.2 cm = 0.642 m

the resistivie force applied at tangent , Ft = 116 N

a)

the diameter of first spocket , d1 = 9.04 cm = 0.0904 m

let the force applied by chain be F

the angular acceleration , alpha = (Ft * (d/2) - F * ( d1/2))/(m * (d/2)^2)

4.56 = (116 * (0.642/2) - F * ( 0.0904/2))/(1.82 * (0.642/2)^2)

solving for F

F = 804.8 N

the force applied by the chain is 804.8 N

b)

the diameter of second spocket , d2 = 5.61 cm = 0.0561 m

let the force applied by chain be F

the angular acceleration , alpha = (Ft * (d/2) - F * ( d2/2))/(m * (d/2)^2)

4.56 = (116 * (0.642/2) - F * ( 0.0561/2))/(1.82 * (0.642/2)^2)

solving for F

F = 1297 N

the force applied by the chain is 1297 N