An object with a mass of $5 k g$ $5 kg$ is hanging from an axle with a radius of $24 c m$ $24 cm$ . If the wheel attached to the axle has a radius of $12 c m$ $12 cm$ , 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 · 2017-03-30T05:28:57

The work is $= 147.8 J$ $=147.8J$

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The load $= (5 g) N$ $=(5g)N$

Radius of axle $r = 0.24 m$ $r=0.24m$

Radius of wheel $R = 0.12 m$ $R=0.12m$

Taking moments about the center of the axle

$F \cdot 0.12 = 5 \cdot g \cdot 0.24$ $F*0.12=5*g*0.24$

$F = \frac{5 \cdot g \cdot 0.24}{0.12} = 10 g = 98 N$ $F=(5*g*0.24)/0.12=10g=98N$

The distance is $= 2 \cdot π \cdot 0.24 = 0.48 π$ $=2*pi*0.24=0.48pi$

The work done is

$W = F \cdot d = 98 \cdot 0.48 π = 147.8 J$ $W=F*d=98*0.48pi=147.8J$

An object with a mass of 5kg5 kg is hanging from an axle with a radius of 24cm24 cm. If the wheel attached to the axle has a radius of 12cm12 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?