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 $12 c m$ $12 cm$ , how much work would it take to turn the wheel $3 c m$ $3 cm$ ?

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Answer 1 · 2017-10-27T06:01:16

The work is =2.94J#

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

The radius of the axle is $r = 0.24 m$ $r=0.24m$

The radius of the wheel is $R = 0.12 m$ $R=0.12m$

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

$F \cdot 0.12 = 5 g \cdot 0.24$ $F*0.12=5g*0.24$

$F = 5 g \cdot \frac{0.24}{0.12} = 98 N$ $F=5g*0.24/0.12=98N$

The force is $F = 98 N$ $F=98N$

The distance is $d = 0.03 m$ $d=0.03m$

The work is $W = F d = 98 \cdot 0.03 = 2.94 J$ $W=Fd=98*0.03=2.94J$

An object with a mass of 5kg5 kg is hanging from an axle with a radius of 24cm24 cm. If the wheel attached to the axle has a radius of 12cm12 cm, how much work would it take to turn the wheel 3cm3 cm?