# An object with a mass of 7 kg is hanging from an axle with a radius of 8 cm. If the wheel attached to the axle has a radius of 56 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?

May 14, 2016

34.496J

#### Explanation:

The mass of the object lifted = $\left(m\right) = 7 k g$

The radius of the axle $\left(r\right) = 8 c m = 0.08 m$

The radius of the Wheel attached with the axle

$R = 56 c m = 0.56 m$

We are to find out the work done to turn the wheel a length

equal to the circumference of the axle. When turning of axle

equal to its circumference$\left(2 \pi r\right)$ occurs ,the weight is lifted

to the same height$\left(h = \text{circumference of axle}\right)$ against the gravity .

Hence the work done $W = m g h = m \times g \times 2 \pi r = 7 \times 9.8 \times 2 \times \frac{22}{7} \times 0.08 = 34.496 J$