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 $33 c m$ $33 cm$ , 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 · 2017-08-12T05:41:34

The work is $= 134.3 J$ $=134.3J$

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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 $R = 0.33 m$ $R=0.33m$

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

Taking moments about the center of the axle

$F \cdot 0.33 = 200 g \cdot 0.06$ $F*0.33=200g*0.06$

$F = 200 g \cdot \frac{0.06}{0.33} = 356.4 N$ $F=200g*0.06/0.33=356.4N$

The distance is $d = 2 π r = 2 \cdot π \cdot 0.06 = 0.12 π$ $d=2pir=2*pi*0.06=0.12pi$

The work is

$W = F d = 356.4 \cdot 0.12 π = 134.3 J$ $W=Fd=356.4*0.12pi=134.3J$

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 33cm33 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?