# A balanced lever has two weights on it, the first with mass 1 kg  and the second with mass 7 kg. If the first weight is  8 m from the fulcrum, how far is the second weight from the fulcrum?

Mar 12, 2018

~1.14 meters

#### Explanation:

When a lever is balanced, the torque exerted on either side of the fulcrum is equal, so the lever is held in equilibrium.

$\tau = r F \sin \theta$ where $\tau$ is the torque on one side of the lever and $\theta$ is the angle that the side makes with the fulcrum.

${\tau}_{1} = \left(1 \cdot 9.8\right) \cdot 8 \cdot 1$
${\tau}_{2} = \left(7 \cdot 9.8\right) \cdot r \cdot 1$

Knowing that ${\tau}_{1}$ and ${\tau}_{2}$ are equal, we can combine the two equations to solve for $r$.

$9.8 \cdot 8 = 68.6 r$
$78.4 = 68.6 r$
$r = 1.14$