# An object with a mass of 3 kg is hanging from an axle with a radius of 2 cm. If the wheel attached to the axle has a radius of 15 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?

Oct 30, 2017

The work is $= 3.69 J$

#### Explanation:

The load is $L = 3 g N$

The radius of the axle is $r = 0.02 m$

The radius of the wheel is $R = 0.15 m$

The effort is $= F N$

The acceleration due to gravity is $g = 9.8 m {s}^{-} 2$

Taking moments about the center of the axle

$F \cdot 0.15 = 3 g \cdot 0.02$

$F = 3 g \cdot \frac{0.02}{0.15} = 3.92 N$

The force is $F = 3.92 N$

The distance is $d = 2 \pi R = 2 \pi \cdot 0.15 = 0.3 \pi m$

The work is $W = F d = 3.92 \cdot 0.3 \pi = 3.69 J$