# An object with a mass of 5 kg is hanging from an axle with a radius of 24 cm. If the wheel attached to the axle has a radius of 38 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?

Jul 2, 2016

$\approx 73.85 J$

#### Explanation:

Given

• $\text{The radius of the axle } \left(r\right) = 24 c m 0.24 m$

• $\text{The mass of the object } \left(m\right) = 5 k g$

We are to calculate the work done to lift the object by turning the wheel a length equal to the circumference of the axle.

$\text{Now circumference of the axle} \left(l\right) = 2 \pi r = 2 \times \pi \times 0.24 m$

Actually the work done occurs due to the lifting of the object against the gravitational pull by length $l = 2 \pi r$

So $\text{Work done} \left(W\right) = m \times g \times 2 \pi r$

$= 5 \times 9.8 \times 2 \times 3.14 \times 0.24 J \approx 73.85 J$