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 $15 c m$ $15 cm$ , 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 · 2017-10-30T12:22:57

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 $R = 0.15 m$ $R=0.15m$

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

$F \cdot 0.15 = 3 g \cdot 0.02$ $F*0.15=3g*0.02$

$F = 3 g \cdot \frac{0.02}{0.15} = 3.92 N$ $F=3g*0.02/0.15=3.92N$

The force is $F = 3.92 N$ $F=3.92N$

The distance is $d = 2 π R = 2 π \cdot 0.15 = 0.3 π m$ $d=2piR=2pi*0.15=0.3pim$

The work is $W = F d = 3.92 \cdot 0.3 π = 3.69 J$ $W=Fd=3.92*0.3pi=3.69J$

An object with a mass of 3 kg3kg3 kg is hanging from an axle with a radius of 2 cm2cm2 cm. If the wheel attached to the axle has a radius of 15 cm15cm15 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?