# An object with a mass of 7 kg is hanging from an axle with a radius of 36 m. If the wheel attached to the axle has a radius of 9 m, how much force must be applied to the wheel to keep the object from falling?

Feb 22, 2016

#### Answer:

This is a similar case to a lever: the torque on both sides need to be the same for balance. ${\tau}_{1} = r F = r m g = 36 \cdot 7 \cdot 9.8 = 2469.6$ $N m$. ${\tau}_{2} = r F \to F = {\tau}_{2} / r$ but ${\tau}_{1} = {\tau}_{2}$ so $F = \frac{2469.6}{9} = 274.4$ $N$.

#### Explanation:

I think the explanation above is clear, but it's worth pointing out that the force acting one the $7$ $k g$ mass is its weight force, $F = m g$ where $g$ is the acceleration due to gravity, $9.8$ $m {s}^{-} 2$.