An object with a mass of $4 k g$ $4 kg$ 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 $24 c m$ $24 cm$ , how much work would it take to turn the wheel $16 c m$ $16 cm$ ?

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Answer 1 · 2017-11-27T12:25:54

The work is $= 4.7 J$ $=4.7J$

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

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

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

$F \cdot 0.24 = 4 g \cdot 0.18$ $F*0.24=4g*0.18$

$F = 4 g \cdot \frac{0.18}{0.24} = 29.4 N$ $F=4g*0.18/0.24=29.4N$

The force is $F = 29.4 N$ $F=29.4N$

The distance is $d = 0.16 m$ $d=0.16m$

The work is $W = F \times d = 29.4 \times 0.16 = 4.7 J$ $W=Fxxd=29.4xx0.16=4.7J$

An object with a mass of 4kg4 kg is hanging from an axle with a radius of 18cm18 cm. If the wheel attached to the axle has a radius of 24cm24 cm, how much work would it take to turn the wheel 16cm16 cm?