An object with a mass of 300 kg300kg is hanging from an axle with a radius of 5 cm5cm. If the wheel attached to the axle has a radius of 12 cm12cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?

1 Answer
Nov 10, 2017

The work is =923.6J=923.6J

Explanation:

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The load is L=300gNL=300gN

The radius of the axle is r=0.05mr=0.05m

The radius of the wheel is R=0.12mR=0.12m

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*0.12=300g*0.05F0.12=300g0.05

F=300g*0.05/0.12=1225NF=300g0.050.12=1225N

The force is F=1225NF=1225N

The distance is d=2piR=2pixx0.12=(0.24pi)md=2πR=2π×0.12=(0.24π)m

The work is

W=Fxxd=1225*0.24pi=923.6JW=F×d=12250.24π=923.6J