An object with a mass of $3 k g$ $3 kg$ is hanging from an axle with a radius of $2 c m$ $2 cm$ . If the wheel attached to the axle has a radius of $1 c m$ $1 cm$ , 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 · 2017-06-14T04:58:15

The work is $= 7.39 J$ $=7.39J$

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The load $L = (3 g) N$ $L=(3g)N$

Radius of axle $r = 0.02 m$ $r=0.02m$

Radius of wheel $R = 0.01 m$ $R=0.01m$

Taking moments about the center of the axle

$F \cdot R = L \cdot r$ $F*R=L*r$

$F \cdot 0.01 = 3 \cdot g \cdot 0.02$ $F*0.01=3*g*0.02$

$F = \frac{3 \cdot g \cdot 0.02}{0.01} = 58.8 N$ $F=(3*g*0.02)/0.01=58.8N$

The force is $F = 58.8 N$ $F=58.8N$

The distance is $d = 2 \cdot π \cdot 0.02 = 0.04 π$ $d=2*pi*0.02=0.04pi$

The work is $W = F \cdot d = 58.8 \cdot 0.04 π = 7.39 J$ $W=F*d=58.8*0.04pi=7.39J$

An object with a mass of 3 kg3kg3 kg is hanging from an axle with a radius of 2 cm2cm2 cm. If the wheel attached to the axle has a radius of 1 cm1cm1 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?