An object with a mass of #8 kg# is hanging from an axle with a radius of #5 cm#. If the wheel attached to the axle has a radius of #25 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 · 2017-10-03T08:24:50

The work is #=24.6J#

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The load is #L=8gN#

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

The radius of the wheel is #R=0.25m#

The effort is #=FN#

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

Taking moments about the center of the axle

#F*0.25=8g*0.05#

#F=8g*0.05/0.25=15.68N#

The force is #F=15.68N#

The distance is #d=2piR=2*pi*0.25=(0.5pi)m#

The work is #W=Fd=15.68*0.5pi=24.6J#