An object with a mass of $300 k g$ $300 kg$ is hanging from an axle with a radius of $3 c m$ $3 cm$ . If the wheel attached to the axle has a radius of $90 c m$ $90 cm$ , 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 · 2017-10-29T07:00:10

The work is $= 554.2 J$ $=554.2J$

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The load is $L = 300 g N$ $L=300gN$

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

The radius of the wheel is $R = 0.90 m$ $R=0.90m$

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

$F \cdot 0.9 = 300 g \cdot 0.03$ $F*0.9=300g*0.03$

$F = 300 g \cdot \frac{0.03}{0.9} = 98 N$ $F=300g*0.03/0.9=98N$

The force is $F = 98 N$ $F=98N$

The distance is $d = 2 π R = 2 π \cdot 0.9 = 1.8 π m$ $d=2piR=2pi*0.9=1.8pim$

The work is $W = F d = 98 \cdot 1.8 π = 554.2 J$ $W=Fd=98*1.8pi=554.2J$

An object with a mass of 300kg300 kg is hanging from an axle with a radius of 3cm3 cm. If the wheel attached to the axle has a radius of 90cm90 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?