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

May 14, 2016

1.568J

#### Explanation:

The mass of the object lifted = $\left(m\right) = 4 k g$

The radius of the axle $\left(r\right) = 6 c m = 0.06 m$

The Circumference of the axle $\left({C}_{a}\right) = 2 \pi r = 2 \pi \times 0.06 m$

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

The Circumference of the Wheel $\left({C}_{w}\right) = 2 \pi R = 2 \pi \times 0.12 m$

When wheel turns $2 \pi \times 0.12 m$ the axle turns $2 \pi \times 0.06 m$

So When wheel turns $8 c m \mathmr{and} 0.08 m$ the axle turns

$\frac{2 \pi \times 0.06 m}{2 \pi \times 0.12 m} \times 0.08 = 0.04 m$

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

the weight against gravity by $h = 0.04 m$

So work done $w = m g h = 4 \times 9.8 \times 0.04 = 1.568 J$