An object with a mass of $8 k g$ $8 kg$ is hanging from an axle with a radius of $27 c m$ $27 cm$ . If the wheel attached to the axle has a radius of $45 c m$ $45 cm$ , 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 · 2017-04-04T06:22:10

The work done is $= 79.8 J$ $=79.8J$

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The load $= (8 g) N$ $=(8g)N$

Radius of axle $r = 0.27 m$ $r=0.27m$

Radius of wheel $R = 0.45 m$ $R=0.45m$

Taking moments about the center of the axle

$F \cdot 0.45 = 8 \cdot g \cdot 0.27$ $F*0.45=8*g*0.27$

$F = \frac{8 \cdot g \cdot 0.27}{0.45} = 47.04 N$ $F=(8*g*0.27)/0.45=47.04N$

Circumference of the axle, $d = 2 π \cdot 0.27 m$ $d=2pi*0.27m$

Work done $= F \cdot d$ $=F*d$

$= 47.04 \cdot 2 π \cdot 0.27$ $=47.04*2pi*0.27$

$= 79.8 J$ $=79.8J$

An object with a mass of 8kg8 kg is hanging from an axle with a radius of 27cm27 cm. If the wheel attached to the axle has a radius of 45cm45 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?