Question

During a testing process, a worker in a factory mounts a bicycle wheel on a stationary stand and applies a tangential resistive force of 125 N to the tire's rim. The mass of the wheel is 1.50 kg and, for the purpose of this problem, assume that all of this mass is concentrated on the outside radius of the wheel. The diameter of the wheel is 60.0 cm. A chain passes over a sprocket that has a diameter of 8.50 cm. In order for the wheel to have an angular acceleration of 4.50 rad/s2, what force, in Newtons, must be applied to the chain

Answer 1

896.647 N

Step-by-step explanation:

Given data:

Tangential resistive force ( Fr )= 125 N

mass of the wheel ( M ) = 1.50 kg

diameter of wheel ( D1 )= 60 cm

R1 = 30 cm = 0.3 m

diameter of chain ( D2 ) = 8.5 cm

R2 = 0.0425 m

Angular acceleration ( ∝ ) = 4.50 rad/s^2

Determine the Force to be applied to Chain

First ; calculate for the moment of Inertia of the wheel

I = M*R1 ^2 = 1.50 * (0.3)^2 = 0.135 kg*m^2

Next determine the net force on the wheel due to torque

τ = F*R2 - Fr *R1 = F (0.0425) - 125 * 0.3 ---- ( 1)

note that Torque ( τ ) = I * ∝ ----- ( 2 )

Equate; equation ( 1 ) and equation ( 2 )

F( 0.0425 ) - 37.5 = 0.135 * 4.5

∴ F = 38.1075 / 0.0425 = 896.647 N ( force to be applied to chain )