An object with a mass of $2 k g$ $2 kg$ 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 $8 c m$ $8 cm$ , 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 · 2018-03-23T18:06:00

The work $= 2.46 J$ $=2.46J$

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The load is $L = 2 g N$ $L=2gN$

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

The radius of the wheel is $R = 0.08 m$ $R=0.08m$

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

$F \cdot 0.08 = 2 g \cdot 0.02$ $F*0.08=2g*0.02$

$F = \frac{2 g \cdot 0.02}{0.08} = 4.9 N$ $F=(2g*0.02)/0.08=4.9N$

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

The distance is $d = 2 π R = 2 π \cdot 0.08 = 0.16 π m$ $d=2piR=2pi*0.08=0.16pim$

The work done is

$W = F \cdot d = 4.9 \cdot 0.16 π = 2.46 J$ $W=F*d=4.9*0.16pi=2.46J$

An object with a mass of 2kg2 kg is hanging from an axle with a radius of 2cm2 cm. If the wheel attached to the axle has a radius of 8cm8 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?