An object with a mass of $3 k g$ $3 kg$ is hanging from an axle with a radius of $2 c m$ $2 cm$ . 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 a length equal to the circumference of the axle?

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Answer 1 · 2018-05-10T16:42:20

The work is $= 3.69 J$ $=3.69J$

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The load is $L = 3 g N$ $L=3gN$

The radius of the axle is $r = 0.02 m$ $r=0.02m$

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

$F \cdot 0.12 = 3 g \cdot 0.02$ $F*0.12=3g*0.02$

$F = \frac{3 g \cdot 0.02}{0.12} = 4.9 N$ $F=(3g*0.02)/0.12=4.9N$

The force is $F = 4.9 N$ $F=4.9N$

The distance is $d = 2 π R = 2 \cdot π \cdot 0.12 = 0.75 m$ $d=2piR=2*pi*0.12=0.75m$

The work is

$W = F \times d = 4.9 \cdot 0.75 = 3.69 J$ $W=Fxxd=4.9*0.75=3.69J$

An object with a mass of 3kg3 kg is hanging from an axle with a radius of 2cm2 cm. If the wheel attached to the axle has a radius of 12cm12 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?