An object with a mass of $5 k g$ $5 kg$ is hanging from an axle with a radius of $24 c m$ $24 cm$ . If the wheel attached to the axle has a radius of $2 c m$ $2 cm$ , 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 · 2018-01-30T14:02:35

The work is $= 886.7 J$ $=886.7J$

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The load is $L = 5 g N$ $L=5gN$

The radius of the axle is $r = 0.24 m$ $r=0.24m$

The radius of the wheel is $R = 0.02 m$ $R=0.02m$

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

$F \cdot 0.02 = 5 g \cdot 0.24$ $F*0.02=5g*0.24$

$F = \frac{5 g \cdot 0.24}{0.02} = 588 N$ $F=(5g*0.24)/0.02=588N$

The force is $F = 588 N$ $F=588N$

The distance is $d = 2 \cdot π \cdot 0.24 m$ $d=2*pi*0.24m$

The work is

$W = F \times d = 588 \cdot 0.48 π = 886.7 J$ $W=Fxxd=588*0.48pi=886.7J$

An object with a mass of 5 kg5kg5 kg is hanging from an axle with a radius of 24 cm24cm24 cm. If the wheel attached to the axle has a radius of 2 cm2cm2 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?