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 $16 c m$ $16 cm$ , 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 · 2017-07-04T11:29:10

The work is $= 44.3 J$ $=44.3J$

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The load $L = (2 g) N$ $L=(2g)N$

Radius of axle $r = 0.24 m$ $r=0.24m$

Radius of wheel $R = 0.16 m$ $R=0.16m$

Taking moments about the center of the axle

$F \cdot R = L \cdot r$ $F*R=L*r$

$F \cdot 0.16 = 2 \cdot g \cdot 0.24$ $F*0.16=2*g*0.24$

$F = \frac{2 \cdot g \cdot 0.24}{0.16} = 29.4 N$ $F=(2*g*0.24)/0.16=29.4N$

The force is $F = 29.4 N$ $F=29.4N$

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 is

$W = F d = 29.4 \cdot 0.48 \cdot π = 44.3 J$ $W=Fd=29.4*0.48*pi=44.3J$

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 16cm16 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?