# A balanced lever has two weights on it, the first with mass 6 kg  and the second with mass 5 kg. If the first weight is  9 m from the fulcrum, how far is the second weight from the fulcrum?

Dec 20, 2016

Place the smaller mass at 10.8 m from the fulcrum to get a balance.

#### Explanation:

What must "balance" here called the torque on each side of the fulcrum. Specifically, torque is the product of the force on the lever multiplied by the distance this force is from the fulcrum.

The force is found by multiplying the mass by $g$, the strength of gravity (9.8 N/kg).

$\tau$ = $m \times g \times r$

So, write this expression for each mass and its distnce from the fulcrum and set them equal.

${m}_{1} \times g \times {r}_{1} = {m}_{2} \times g \times {r}_{2}$

However, in this case, the $g$ appears on both sides of the equation, it can be cancelled:

${m}_{1} \times {r}_{1} = {m}_{2} \times {r}_{2}$

Put in the values:

$6 k g \times 9 m = 5 k g \times {r}_{2}$

${r}_{2} = \frac{54 k g m}{5 k g}$ = $10.8 m$