An object with a mass of 2 kg is hanging from an axle with a radius of 24 cm. If the wheel attached to the axle has a radius of 18 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?

Jun 11, 2017

The work is $= 39.41 J$

Explanation:

Radius of axle $r = 0.24 m$

Radius of wheel $R = 0.18 m$

Taking moments about the center of the axle

$F \cdot R = L \cdot r$

$F \cdot 0.18 = 2 \cdot g \cdot 0.24$

$F = \frac{2 \cdot g \cdot 0.24}{0.18} = 26.13 N$

The force is $= 26.13 N$

The distance is $d = 2 \cdot \pi \cdot 0.24 m$

The work is

$W = F \cdot d = 26.13 \cdot 0.48 \pi = 39.41 J$