An object with a mass of $300 k g$ $300 kg$ is hanging from an axle with a radius of $5 c m$ $5 cm$ . 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 · 2017-11-10T06:26:32

The work is $= 923.6 J$ $=923.6J$

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The load is $L = 300 g N$ $L=300gN$

The radius of the axle is $r = 0.05 m$ $r=0.05m$

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

$F \cdot 0.12 = 300 g \cdot 0.05$ $F*0.12=300g*0.05$

$F = 300 g \cdot \frac{0.05}{0.12} = 1225 N$ $F=300g*0.05/0.12=1225N$

The force is $F = 1225 N$ $F=1225N$

The distance is $d = 2 π R = 2 π \times 0.12 = (0.24 π) m$ $d=2piR=2pixx0.12=(0.24pi)m$

The work is

$W = F \times d = 1225 \cdot 0.24 π = 923.6 J$ $W=Fxxd=1225*0.24pi=923.6J$

An object with a mass of 300 kg300kg300 kg is hanging from an axle with a radius of 5 cm5cm5 cm. If the wheel attached to the axle has a radius of 12 cm12cm12 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?