An object with a mass of $4 k g$ $4 kg$ is hanging from an axle with a radius of $14 c m$ $14 cm$ . If the wheel attached to the axle has a radius of $27 c m$ $27 cm$ , how much work would it take to turn the wheel $6 c m$ $6 cm$ ?

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Answer 1 · 2018-05-17T08:08:55

The work is $= 1.22 J$ $=1.22J$

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The load is $L = 4 g N$ $L=4gN$

The radius of the axle is $r = 0.14 m$ $r=0.14m$

The radius of the wheel is $R = 0.27 m$ $R=0.27m$

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

$F \cdot 0.27 = 4 g \cdot 0.14$ $F*0.27=4g*0.14$

$F = \frac{4 g \cdot 0.14}{0.27} = 20.33 N$ $F=(4g*0.14)/0.27=20.33N$

The force is $F = 20.33 N$ $F=20.33N$

The distance is $d = 0.06 c m$ $d=0.06cm$

The work done is

$W = F d = 20.33 \times 0.06 = 1.22 J$ $W=Fd=20.33xx0.06=1.22J$

An object with a mass of 4kg4 kg is hanging from an axle with a radius of 14cm14 cm. If the wheel attached to the axle has a radius of 27cm27 cm, how much work would it take to turn the wheel 6cm6 cm?