An object with a mass of $4 k g$ $4 kg$ is hanging from an axle with a radius of $4 c m$ $4 cm$ . 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 $32 c m$ $32 cm$ ?

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Answer 1 · 2017-12-29T09:01:48

The work is $= 2.1 J$ $=2.1J$

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

The radius of the axle is $r = 0.04 m$ $r=0.04m$

The radius of the wheel is $R = 0.24 m$ $R=0.24m$

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

$F \cdot 0.24 = 4 g \cdot 0.04$ $F*0.24=4g*0.04$

$F = \frac{4 g \cdot 0.04}{0.24} = 6.53 N$ $F=(4g*0.04)/0.24=6.53N$

The force is $F = 6.53 N$ $F=6.53N$

The distance is $d = 0.32 m$ $d=0.32m$

The work done is

$W = F \cdot d = 6.53 \cdot 0.32 = 2.1 J$ $W=F*d=6.53*0.32=2.1J$

An object with a mass of 4kg4 kg is hanging from an axle with a radius of 4cm4 cm. If the wheel attached to the axle has a radius of 24cm24 cm, how much work would it take to turn the wheel 32cm32 cm?