An object with a mass of #3 kg# is hanging from an axle with a radius of #3 cm#. If the wheel attached to the axle has a radius of #28 cm#, how much work would it take to turn the wheel a length equal to the circumference of the axle?

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Answer 1 · 2017-11-15T14:06:59

The work is #=5.54J#

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The load is #L=3gN#

The radius of the axle is #r=0.03m#

The radius of the wheel is #R=0.28m#

The effort is #=FN#

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

Taking moments about the center of the axle

#F*0.28=3g*0.03#

#F=3g*0.03/0.28=3.15N#

The force is #F=3.15N#

The distance is #d=2piR=2pixx0.28=(0.56pi)m#

The work is

#W=Fxxd=3.15*0.56pi=5.54J#