An object with a mass of $3 k g$ $3 kg$ 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 $44 c m$ $44 cm$ , 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 · 2017-12-06T07:25:29

The work is $= 5.54 J$ $=5.54J$

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

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

The radius of the wheel is $R = 0.44 m$ $R=0.44m$

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

$F \cdot 0.44 = 3 g \cdot 0.03$ $F*0.44=3g*0.03$

$F = \frac{3 g \cdot 0.03}{0.44} = 2 N$ $F=(3g*0.03)/0.44=2N$

The force is $F = 2 N$ $F=2N$

The distance is $d = 2 π R = (0.88 π) m$ $d=2piR=(0.88pi)m$

The work is $W = F \times d = 2 \cdot 0.88 π = 5.54 J$ $W=Fxxd=2*0.88pi=5.54J$

An object with a mass of 3 kg3kg3 kg is hanging from an axle with a radius of 3 cm3cm3 cm. If the wheel attached to the axle has a radius of 44 cm44cm44 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?