An object with a mass of $5 k g$ $5 kg$ is hanging from an axle with a radius of $24 c m$ $24 cm$ . 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 · 2017-07-03T05:00:48

The work is $= 55.4 J$ $=55.4J$

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The load $L = (5 g) N$ $L=(5g)N$

Radius of axle $r = 0.24 m$ $r=0.24m$

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

Taking moments about the center of the axle

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

$F \cdot 0.32 = 5 \cdot g \cdot 0.24$ $F*0.32=5*g*0.24$

$F = \frac{5 \cdot g \cdot 0.24}{0.32} = 36.75 N$ $F=(5*g*0.24)/0.32=36.75N$

The force is $F = 36.75 N$ $F=36.75N$

The distance is $d = 2 π r = 2 π \cdot 0.24 = 0.48 π m$ $d=2pir=2pi*0.24=0.48pim$

The work is

$W = F d = 36.75 \cdot 0.48 \cdot π = 55.4 J$ $W=Fd=36.75*0.48*pi=55.4J$

An object with a mass of 5 kg5kg5 kg is hanging from an axle with a radius of 24 cm24cm24 cm. If the wheel attached to the axle has a radius of 32 cm32cm32 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?