An object with a mass of #5 kg# is hanging from an axle with a radius of #12 cm#. If the wheel attached to the axle has a radius of #38 cm#, how much work would it take to turn the wheel a length equal to the circumference of the axle?

1 Answer
Apr 23, 2016

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As shown in the figure
The radius of the Wheel #R=38cm#
The radius of the Axle #r=12cm#
The mass of the object #m=5kg#
The Weightof the object #W=mg=5xx9.8N#
P is the applied force.
The Displacement of Applied force(P)=Circumference of the axle #=d=2xxpixx12cm=24pixx10^-2m#
The working principle of wheel -axle system may be compared with the working principle of First Kind of lever

So
#PxxR=Wxxr=>P=Wxxr/R=5xx9.8xx12/38N#

Hence the Work done #=Pxxd=5xx9.8xx12/38xx24pixx10^-2J=11.7J#