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  2 m from the fulcrum, how far is the second weight from the fulcrum?

Mar 7, 2017

$3.1 m$

Explanation:

A moment is the product of force and the distance over which the force acts.

$M = F d$

In a balanced lever, both moments are equal to each other, so

${M}_{1} = {M}_{2}$

${F}_{1} {d}_{1} = {F}_{2} {d}_{2}$

We can work out the force either side by $F = m a$, where $a \approx 10 m {s}^{-} 2$, so

${F}_{1} = 14 \times 10 = 140 N$

${F}_{2} = 9 \times 10 = 90 N$

and put these values, along with ${d}_{1} = 2 m$ (from the question) into the equation:

$2 m \times 140 N = d \times 90 N$

$d = \frac{280}{90} = 3.1 m$