An object with a mass of 3 kg3kg is hanging from an axle with a radius of 2 cm2cm. If the wheel attached to the axle has a radius of 15 cm15cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?

1 Answer
Oct 30, 2017

The work is =3.69J=3.69J

Explanation:

enter image source here

The load is L=3gNL=3gN

The radius of the axle is r=0.02mr=0.02m

The radius of the wheel is R=0.15mR=0.15m

The effort is =FN=FN

The acceleration due to gravity is g=9.8ms^-2g=9.8ms2

Taking moments about the center of the axle

F*0.15=3g*0.02F0.15=3g0.02

F=3g*0.02/0.15=3.92NF=3g0.020.15=3.92N

The force is F=3.92NF=3.92N

The distance is d=2piR=2pi*0.15=0.3pimd=2πR=2π0.15=0.3πm

The work is W=Fd=3.92*0.3pi=3.69JW=Fd=3.920.3π=3.69J