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 $5 c m$ $5 cm$ , 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 · 2017-11-26T09:09:33

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 $R = 0.05 m$ $R=0.05m$

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

$F \cdot 0.05 = 3 g \cdot 0.02$ $F*0.05=3g*0.02$

$F = 3 g \cdot \frac{0.02}{0.05} = 11.76 N$ $F=3g*0.02/0.05=11.76N$

The force is $F = 11.76 N$ $F=11.76N$

The distance is $d = 2 π R = 2 \cdot π \cdot 0.05 = (0.1 π) m$ $d=2piR=2*pi*0.05=(0.1pi)m$

The work is $W = F \times d = 11.76 \times 0.1 π = 3.69 J$ $W=Fxxd=11.76xx0.1pi=3.69J$

An object with a mass of 3kg3 kg is hanging from an axle with a radius of 2cm2 cm. If the wheel attached to the axle has a radius of 5cm5 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?