An object with a mass of $7 k g$ $7 kg$ is hanging from an axle with a radius of $15 c m$ $15 cm$ . If the wheel attached to the axle has a radius of $75 c m$ $75 cm$ , 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 · 2017-08-09T06:20:13

The work is $= 12.93 J$ $=12.93J$

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The load is $L = 7 g N$ $L=7gN$

The radius of the axle is $r = 0.15 m$ $r=0.15m$

The radius of the wheel is $R = 0.75 m$ $R=0.75m$

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

Taking moments about the center of the axle

$F \cdot 0.75 = 7 g \cdot 0.15$ $F*0.75=7g*0.15$

$F = 7 g \cdot \frac{0.15}{0.75} = 13.72 N$ $F=7g*0.15/0.75=13.72N$

The distance is $d = 2 π r = 2 \cdot π \cdot 0.15 = 0.3 π$ $d=2pir=2*pi*0.15=0.3pi$

The work is

$W = F d = 13.72 \cdot 0.3 π = 12.93 J$ $W=Fd=13.72*0.3pi=12.93J$

An object with a mass of 7kg7 kg is hanging from an axle with a radius of 15cm15 cm. If the wheel attached to the axle has a radius of 75cm75 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?