An object with a mass of $8 k g$ $8 kg$ is hanging from an axle with a radius of $5 c m$ $5 cm$ . 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 · 2017-07-02T06:40:08

The work is $= 2.74 J$ $=2.74J$

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

Radius of axle $r = 0.05 m$ $r=0.05m$

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

Taking moments about the center of the axle

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

$F \cdot 0.45 = 8 \cdot g \cdot 0.05$ $F*0.45=8*g*0.05$

$F = \frac{8 \cdot g \cdot 0.05}{0.45} = 8.71 N$ $F=(8*g*0.05)/0.45=8.71N$

The force is $F = 8.71 N$ $F=8.71N$

The distance is $d = 2 π r = 2 π \cdot 0.05 = 0.1 π m$ $d=2pir=2pi*0.05=0.1pim$

The work is

$W = F d = 8.71 \cdot 0.1 \cdot π = 2.74 J$ $W=Fd=8.71*0.1*pi=2.74J$

An object with a mass of 8kg8 kg is hanging from an axle with a radius of 5cm5 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?