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 $42 c m$ $42 cm$ , 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 · 2017-04-09T07:23:03

The work done is $= 4.69 J$ $=4.69J$

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

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

Radius of wheel $R = 0.42 m$ $R=0.42m$

Taking moments about the center of the axle

$F \cdot 0.42 = 5 \cdot g \cdot 0.08$ $F*0.42=5*g*0.08$

$F = \frac{5 \cdot g \cdot 0.08}{0.42} = 9.33 N$ $F=(5*g*0.08)/0.42=9.33N$

The distance is

$d = 2 \cdot π \cdot 0.08 = 0.16 π$ $d=2*pi*0.08=0.16pi$

The work done is

$W = F d = 9.33 \cdot 0.16 π = 4.69 J$ $W=Fd=9.33*0.16pi=4.69J$

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 42cm42 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?