An object with a mass of $4 k g$ $4 kg$ is hanging from an axle with a radius of $6 c m$ $6 cm$ . 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 · 2016-05-14T13:06:08

1.568J

The mass of the object lifted = $(m) = 4 k g$ $(m)=4kg$

The radius of the axle $(r) = 6 c m = 0.06 m$ $(r)=6cm=0.06m$

The Circumference of the axle $(C_{a}) = 2 π r = 2 π \times 0.06 m$ $(C_a)=2pir=2pixx0.06m$

The radius of the Wheel attached with the axle $(R) = 12 c m = 0.12 m$ $(R)=12cm=0.12m$

The Circumference of the Wheel $(C_{w}) = 2 π R = 2 π \times 0.12 m$ $(C_w)=2piR=2pixx0.12m$

When wheel turns $2 π \times 0.12 m$ $2pixx0.12m$ the axle turns $2 π \times 0.06 m$ $2pixx0.06m$

So When wheel turns $8 c m or 0.08 m$ $8cmor0.08m$ the axle turns

$\frac{2 π \times 0.06 m}{2 π \times 0.12 m} \times 0.08 = 0.04 m$ $(2pixx0.06m)/( 2pixx0.12m)xx0.08=0.04m$

So the work done to turn the wheel by 8cm is to work done to lift

the weight against gravity by $h = 0.04 m$ $h=0.04m$

So work done $w = m g h = 4 \times 9.8 \times 0.04 = 1.568 J$ $w =mgh=4xx9.8xx0.04=1.568J$

An object with a mass of 4 kg4kg4 kg is hanging from an axle with a radius of 6 cm6cm6 cm. If the wheel attached to the axle has a radius of 12 cm12cm12 cm, how much work would it take to turn the wheel 8 cm8cm8 cm?