An object with a mass of $5 k g$ $5 kg$ is hanging from an axle with a radius of $8 c m$ $8 cm$ . If the wheel attached to the axle has a radius of $56 c m$ $56 cm$ , 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 · 2018-05-09T08:08:32

The work is $= 24.63 J$ $=24.63J$

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

The radius of the axle is $r = 0.08 m$ $r=0.08m$

The radius of the wheel is $R = 0.56 m$ $R=0.56m$

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

$F \cdot 0.56 = 5 g \cdot 0.08$ $F*0.56=5g*0.08$

$F = \frac{5 g \cdot 0.08}{0.56} = 7 N$ $F=(5g*0.08)/0.56=7N$

The force is $F = 7 N$ $F=7N$

The distance is $d = 2 π R = 2 \cdot π \cdot 0.56 = 3.52 m$ $d=2piR=2*pi*0.56=3.52m$

The work is

$W = F \times d = 7 \cdot 3.52 = 24.63 J$ $W=Fxxd=7*3.52=24.63J$

An object with a mass of 5 kg5kg5 kg is hanging from an axle with a radius of 8 cm8cm8 cm. If the wheel attached to the axle has a radius of 56 cm56cm56 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?