An object with a mass of 5 kg5kg is hanging from an axle with a radius of 24 cm24cm. If the wheel attached to the axle has a radius of 2 cm2cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?

1 Answer
Jan 30, 2018

The work is =886.7J=886.7J

Explanation:

www.odicis.org

The load is L=5gNL=5gN

The radius of the axle is r=0.24mr=0.24m

The radius of the wheel is R=0.02mR=0.02m

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*0.02=5g*0.24F0.02=5g0.24

F=(5g*0.24)/0.02=588NF=5g0.240.02=588N

The force is F=588NF=588N

The distance is d=2*pi*0.24md=2π0.24m

The work is

W=Fxxd=588*0.48pi=886.7JW=F×d=5880.48π=886.7J