An object with a mass of $4 k g$ $4 kg$ is hanging from an axle with a radius of $16 c m$ $16 cm$ . If the wheel attached to the axle has a radius of $12 c m$ $12 cm$ , how much work would it take to turn the wheel $8 c m$ $8 cm$ ?

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Answer 1 · 2018-04-04T11:24:34

The work is $= 4.18 J$ $=4.18J$

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The load is $L = 4 g N$ $L=4gN$

The radius of the axle is $r = 0.16 m$ $r=0.16m$

The radius of the wheel is $R = 0.12 m$ $R=0.12m$

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

$F \cdot 0.12 = 4 g \cdot 0.16$ $F*0.12=4g*0.16$

$F = \frac{4 g \cdot 0.16}{0.12} = 52.3 N$ $F=(4g*0.16)/0.12=52.3N$

The force is $F = 52.3 N$ $F=52.3N$

The distance is $d = 0.08 m$ $d=0.08m$

The work is

$W = F \times d = 52.3 \cdot 0.08 = 4.18 J$ $W=Fxxd=52.3*0.08=4.18J$

An object with a mass of 4kg4 kg is hanging from an axle with a radius of 16cm16 cm. If the wheel attached to the axle has a radius of 12cm12 cm, how much work would it take to turn the wheel 8cm8 cm?