# An object with a mass of 8 kg is hanging from an axle with a radius of 32 m. If the wheel attached to the axle has a radius of 24 m, how much force must be applied to the wheel to keep the object from falling?

##### 1 Answer
Dec 9, 2017

This is effectively a moments question.

#### Explanation:

The mass exerts a moment in one direction (we can assume it is clockwise) equal to the product of its weight (m x g) and the perpendicular distance (d). In this case the clockwise moment (taking g = 9.8 N/kg) will be:

${M}_{c} = m \times g \times d = 8 \times 9.81 \times 32$

${M}_{c} = 2500 N m$ (to 2 s.f as given in the data)

To balance this and attain equilibrium there must be an equal and opposite moment. We are told that the distance on the other side must be 24m and asked to solve for the weight, w ( = m x g)

$w = \frac{{M}_{a}}{d} = \frac{2500}{24}$

$w = 104.64$N which I’d probably quote as 105N