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 $32 c m$ $32 cm$ , 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 · 2017-05-10T06:03:27

The work is $= 246.3 J$ $=246.3J$

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The load L=(200g)N#

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

Radius of wheel $R = 0.32 m$ $R=0.32m$

Taking moments about the center of the axle

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

$F \cdot 0.32 = 200 \cdot g \cdot 0.08$ $F*0.32=200*g*0.08$

$F = \frac{200 \cdot g \cdot 0.08}{0.32} = 490 N$ $F=(200*g*0.08)/0.32=490N$

The work done is

$W = F d$ $W=Fd$

The distance is $d = 2 \cdot π \cdot 0.08 = 0.16 π m$ $d=2*pi*0.08=0.16pim$

Work is

$W = 490 \cdot 0.16 π = 246.3 J$ $W=490*0.16pi=246.3J$

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 32cm32 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?