An object with a mass of $3 k g$ $3 kg$ is hanging from an axle with a radius of $2 c m$ $2 cm$ . If the wheel attached to the axle has a radius of $16 c m$ $16 cm$ , 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 · 2017-04-23T06:02:56

The work is $= 0.46 J$ $=0.46J$

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The load L=(3g)N#

Radius of axle $r = 0.02 m$ $r=0.02m$

Radius of wheel $R = 0.16 m$ $R=0.16m$

Taking moments about the center of the axle

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

$F \cdot 0.16 = 3 \cdot g \cdot 0.02$ $F*0.16=3*g*0.02$

$F = \frac{3 \cdot g \cdot 0.02}{0.16} = 3.675 N$ $F=(3*g*0.02)/0.16=3.675N$

Distance is $d = 2 π r = 2 \cdot π \cdot 0.02 = 0.04 π m$ $d=2pir=2*pi*0.02=0.04pim$

Work is $W = F d = 3.675 \cdot 0.04 π = 0.46 J$ $W=Fd=3.675*0.04pi=0.46J$

An object with a mass of 3 kg3kg3 kg is hanging from an axle with a radius of 2 cm2cm2 cm. If the wheel attached to the axle has a radius of 16 cm16cm16 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?