An object with a mass of $7 k g$ $7 kg$ is hanging from an axle with a radius of $25 c m$ $25 cm$ . If the wheel attached to the axle has a radius of $35 c m$ $35 cm$ , 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 · 2017-04-25T16:33:21

The work is $= 77 J$ $=77J$

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The load L=(7g)N#

Radius of axle $r = 0.25 m$ $r=0.25m$

Radius of wheel $R = 0.35 m$ $R=0.35m$

Taking moments about the center of the axle

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

$F \cdot 0.35 = 7 \cdot g \cdot 0.25$ $F*0.35=7*g*0.25$

$F = \frac{7 \cdot g \cdot 0.25}{0.35} = 49 N$ $F=(7*g*0.25)/0.35=49N$

Distance is $d = 2 π r = 2 \cdot π \cdot 0.25 = (0.5 π) m$ $d=2pir=2*pi*0.25=(0.5pi)m$

Work is $W = F d = 49 \cdot 0.5 π = 77 J$ $W=Fd=49*0.5pi=77J$

An object with a mass of 7 kg7kg7 kg is hanging from an axle with a radius of 25 cm25cm25 cm. If the wheel attached to the axle has a radius of 35 cm35cm35 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?