An object with a mass of $7 k g$ $7 kg$ is hanging from an axle with a radius of $25 c m$ $25 cm$ . 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 · 2017-03-29T13:18:32

The work done is $= 35.92 J$ $=35.92J$

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The load $= (7 g) N$ $=(7g)N$

Radius of axle $r = 0.25 m$ $r=0.25m$

Radius of wheel $R = 0.75 m$ $R=0.75m$

Taking moments about the center of the axle

$F \cdot 0.75 = 7 \cdot g \cdot 0.25$ $F*0.75=7*g*0.25$

$F = \frac{7 \cdot g \cdot 0.25}{0.75} = \frac{7}{3} g = 22.87 N$ $F=(7*g*0.25)/0.75=7/3g=22.87N$

The distance is $= 2 \cdot π \cdot 0.25 = 0.5 π$ $=2*pi*0.25=0.5pi$

The work done is

$W = F \cdot d = 22.87 \cdot 0.5 π = 35.92 J$ $W=F*d=22.87*0.5pi=35.92J$

An object with a mass of 7kg7 kg is hanging from an axle with a radius of 25cm25 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?