An object with a mass of $5 k g$ $5 kg$ is hanging from an axle with a radius of $18 c m$ $18 cm$ . If the wheel attached to the axle has a radius of $42 c m$ $42 cm$ , how much work would it take to turn the wheel $9 c m$ $9 cm$ ?

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Answer 1 · 2017-10-23T05:56:20

The work is $= 1.89 J$ $=1.89J$

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The load is $L = 5 g N$ $L=5gN$

The radius of the axle is $r = 0.18 m$ $r=0.18m$

The radius of the wheel is $R = 0.42 m$ $R=0.42m$

The effort is $= F N$ $=FN$

The acceleration due to gravity is $g = 9.8 m s^{- 2}$ $g=9.8ms^-2$

Taking moments about the center of the axle

$F \cdot 0.42 = 5 g \cdot 0.18$ $F*0.42=5g*0.18$

$F = 5 g \cdot \frac{0.18}{0.42} = 21 N$ $F=5g*0.18/0.42=21N$

The force is $F = 21 N$ $F=21N$

The distance is $d = 0.09 N$ $d=0.09N$

The work is $W = F d = 21 \cdot 0.09 = 1.89 J$ $W=Fd=21*0.09=1.89J$

An object with a mass of 5kg5 kg is hanging from an axle with a radius of 18cm18 cm. If the wheel attached to the axle has a radius of 42cm42 cm, how much work would it take to turn the wheel 9cm9 cm?