A balanced lever has two weights on it, the first with mass 14 kg  and the second with mass 9 kg. If the first weight is  4 m from the fulcrum, how far is the second weight from the fulcrum?

Feb 15, 2016

$\frac{18}{7} \approx 2.57 m$

Explanation:

This is an application of Archimedes' Law of th eLever, which states that when a lever is in balance the ratio of the masses must equal the ratio of the distances from the fulcrum.

If the two masses are ${m}_{1}$ and ${m}_{2}$ and the two distances are ${d}_{1}$ and ${d}_{2}$ then ${m}_{1} : {m}_{2} = {d}_{1} : {d}_{2}$

$: 14 : 9 = 4 : {d}_{2}$

$\frac{14}{9} = \frac{4}{d} _ 2$

${d}_{2} = \frac{4 \cdot 9}{14} = \frac{18}{7} \approx 2.57 m$