An object with a mass of $5 k g$ $5 kg$ is hanging from an axle with a radius of $8 c m$ $8 cm$ . If the wheel attached to the axle has a radius of $32 c m$ $32 cm$ , 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 · 2017-07-17T06:14:55

The work is $= 6.16 J$ $=6.16J$

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

Radius of axle $r = 0.08 m$ $r=0.08m$

Radius of wheel $R = 0.32 m$ $R=0.32m$

Taking moments about the center of the axle

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

$F \cdot 0.32 = 5 g \cdot 0.08$ $F*0.32=5g*0.08$

$F = \frac{5 \cdot g \cdot 0.08}{0.32} = 12.25 N$ $F=(5*g*0.08)/0.32=12.25N$

The force is $F = 12.25 N$ $F=12.25N$

The distance is $d = 2 π r = 2 \cdot π \cdot 0.08 = 0.16 π m$ $d=2pir=2*pi*0.08=0.16pim$

The work is

$W = F d = 12.25 \cdot 0.16 π = 6.16 J$ $W=Fd=12.25*0.16pi=6.16J$

An object with a mass of 5kg5 kg is hanging from an axle with a radius of 8cm8 cm. If the wheel attached to the axle has a radius of 32cm32 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?