# A balanced lever has two weights on it, one with mass 4 kg and one with mass 8 kg. If the first weight is  9 m from the fulcrum, how far is the second weight from the fulcrum?

Mar 24, 2016

$4.5 m$

#### Explanation:

From the second condition for static equilibrium, the resultant torque (moments) must be zero, ie $\sum \vec{\tau} = 0$, where $\vec{\tau} = \vec{r} \times \vec{F}$.

$\therefore {r}_{1} {F}_{1} - {r}_{2} {F}_{2} = 0$, where $F = W = m g$.

$\therefore \left(9 \times 4 g\right) - \left({r}_{2} \times 8 g\right) = 0$

$\therefore {r}_{2} = \frac{36}{8} = 4.5 m$.