An object with a mass of $200 k g$ $200 kg$ is hanging from an axle with a radius of $6 c m$ $6 cm$ . If the wheel attached to the axle has a radius of $36 c m$ $36 cm$ , 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 · 2017-10-24T16:54:10

The work is $= 738.9 J$ $=738.9J$

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The load is $L = 200 g N$ $L=200gN$

The radius of the axle is $r = 0.06 m$ $r=0.06m$

The radius of the wheel is $R = 0.36 m$ $R=0.36m$

The effort is $= F N$ $=FN$

The acceleration due to gravity is $g = 9.8 m s^{- 2}$ $g=9.8ms^-2$

Taking moments about the center of the axle

$F \cdot 0.36 = 200 g \cdot 0.06$ $F*0.36=200g*0.06$

$F = 200 g \cdot \frac{0.06}{0.36} = 326.7 N$ $F=200g*0.06/0.36=326.7N$

The force is $F = 326.7 N$ $F=326.7N$

The distance is $d = 2 π R = 0.72 π$ $d=2piR=0.72pi$

The work is $W = F d = 326.7 \cdot 0.72 π = 738.9 J$ $W=Fd=326.7*0.72pi=738.9J$

An object with a mass of 200kg200 kg is hanging from an axle with a radius of 6cm6 cm. If the wheel attached to the axle has a radius of 36cm36 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?