An object with a mass of $8 k g$ $8 kg$ is hanging from an axle with a radius of $18 c m$ $18 cm$ . 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 · 2018-02-02T06:33:24

The work is $= 88.67 J$ $=88.67J$

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The load is $L = 8 g N$ $L=8gN$

The radius of the axle is $r = 0.18 m$ $r=0.18m$

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

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

$F \cdot 0.45 = 8 g \cdot 0.18$ $F*0.45=8g*0.18$

$F = \frac{8 g \cdot 0.18}{0.45} = 31.36 N$ $F=(8g*0.18)/0.45=31.36N$

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

The distance is $d = 2 \cdot π \cdot 0.45 m$ $d=2*pi*0.45m$

The work is

$W = F \times d = 31.36 \cdot 0.90 π = 88.67 J$ $W=Fxxd=31.36*0.90pi=88.67J$

An object with a mass of 8kg8 kg is hanging from an axle with a radius of 18cm18 cm. If the wheel attached to the axle has a radius of 45cm45 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?