An object with a mass of $200 k g$ $200 kg$ 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 $24 c m$ $24 cm$ , 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 · 2017-04-24T15:25:48

The work is $= 328.4 J$ $=328.4J$

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The load L=(200g)N#

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

Radius of wheel $R = 0.24 m$ $R=0.24m$

Taking moments about the center of the axle

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

$F \cdot 0.24 = 200 \cdot g \cdot 0.08$ $F*0.24=200*g*0.08$

$F = \frac{200 \cdot g \cdot 0.08}{0.24} = 653.3 N$ $F=(200*g*0.08)/0.24=653.3N$

Distance is $d = 2 π r = 2 \cdot π \cdot 0.08 = (0.16 π) m$ $d=2pir=2*pi*0.08=(0.16pi)m$

Work is $W = F d = 653.3 \cdot 0.16 π = 328.4 J$ $W=Fd=653.3*0.16pi=328.4J$

An object with a mass of 200kg200 kg is hanging from an axle with a radius of 8cm8 cm. If the wheel attached to the axle has a radius of 24cm24 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?