An object with a mass of $2 k g$ $2 kg$ 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 $15 c m$ $15 cm$ , 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 · 2018-03-13T14:17:38

The work is $= 47.3 J$ $=47.3J$

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The load is $L = 2 g N$ $L=2gN$

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

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

$F \cdot 0.15 = 2 g \cdot 0.24$ $F*0.15=2g*0.24$

$F = \frac{2 g \cdot 0.24}{0.15} = 31.36 N$ $F=(2g*0.24)/0.15=31.36N$

The force is $F = 31.36 N$ $F=31.36N$

The distance is $d = 2 π r = 2 π \cdot 0.24 = 0.48 π m$ $d=2pir=2pi*0.24=0.48pim$

The work done is

$W = F \cdot d = 31.36 \cdot 0.48 π = 47.3 J$ $W=F*d=31.36*0.48pi=47.3J$

An object with a mass of 2kg2 kg is hanging from an axle with a radius of 24cm24 cm. If the wheel attached to the axle has a radius of 15cm15 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?