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 1 cm1cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?

1 Answer
Jun 14, 2017

The work is =7.39J=7.39J

Explanation:

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The load L=(3g)NL=(3g)N

Radius of axle r=0.02mr=0.02m

Radius of wheel R=0.01mR=0.01m

Taking moments about the center of the axle

F*R=L*rFR=Lr

F*0.01=3*g*0.02F0.01=3g0.02

F=(3*g*0.02)/0.01=58.8NF=3g0.020.01=58.8N

The force is F=58.8NF=58.8N

The distance is d=2*pi*0.02=0.04pid=2π0.02=0.04π

The work is W=F*d=58.8*0.04pi=7.39JW=Fd=58.80.04π=7.39J