An object with a mass of $300 k g$ $300 kg$ is hanging from an axle with a radius of $3 c m$ $3 cm$ . If the wheel attached to the axle has a radius of $96 c m$ $96 cm$ , 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 · 2018-02-22T17:13:08

The work is $= 554.2 J$ $=554.2J$

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

The radius of the axle is $r = 0.03 m$ $r=0.03m$

The radius of the wheel is $R = 0.96 m$ $R=0.96m$

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

$F \cdot 0.96 = 300 g \cdot 0.03$ $F*0.96=300g*0.03$

$F = \frac{300 g \cdot 0.03}{0.96} = 91.875 N$ $F=(300g*0.03)/0.96=91.875N$

The force is $F = 91.875 N$ $F=91.875N$

The distance is $d = 2 π R = 2 \cdot π \cdot 0.96 m$ $d=2piR=2*pi*0.96m$

The work done is

$W = F \cdot d = 91.875 \cdot 2 \cdot π \cdot 0.96 = 554.2 J$ $W=F*d=91.875*2*pi*0.96=554.2J$

An object with a mass of 300kg300 kg is hanging from an axle with a radius of 3cm3 cm. If the wheel attached to the axle has a radius of 96cm96 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?