An object with a mass of $5 k g$ $5 kg$ is hanging from an axle with a radius of $12 c m$ $12 cm$ . If the wheel attached to the axle has a radius of $45 c m$ $45 cm$ , 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 · 2017-11-19T08:17:06

The work is $= 36.9 J$ $=36.9J$

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The load is $L = (5 g) N$ $L=(5g)N$

The radius of the axle is $r = 0.12 m$ $r=0.12m$

The radius of the wheel is $R = 0.45 m$ $R=0.45m$

The effort is $= (F) N$ $=(F)N$

The acceleration due to gravity is $g = 9.8 m s^{- 2}$ $g=9.8ms^-2$

Taking moments about the center of the axle

$F \cdot 0.45 = 5 g \cdot 0.12$ $F*0.45=5g*0.12$

$F = 5 g \cdot \frac{0.12}{0.45} = 13.1 N$ $F=5g*0.12/0.45=13.1N$

The force is $F = 13.1 N$ $F=13.1N$

The distance is $d = 2 π R = 2 π \times 0.45 = (0.9 π) m$ $d=2piR=2pixx0.45=(0.9pi)m$

The work is

$W = F \times d = 13.1 \cdot 0.9 π = 36.9 J$ $W=Fxxd=13.1*0.9pi=36.9J$

An object with a mass of 5 kg5kg5 kg is hanging from an axle with a radius of 12 cm12cm12 cm. If the wheel attached to the axle has a radius of 45 cm45cm45 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?