Question

A student sets a board to pivot about its center. The student then places a box with mass m at some position r from the pivot point. The student plans to place a second box with mass 2 m on the other side of the board. In terms of r, where should the box be placed in order to maintain static equilibrium?

Answer 1

Answer:

The box should be placed at a distance of $\frac{r}{2}$ from the pivot

Explanation:

In order to be in static equilibrium, both Torques have to be the same magnitude, so:

$T_{m} = T_{2m}$   Replacing the formula for Torque:

$m*r = 2m*X$   where X is the distance we need to find.

Solving for X we get:

$X = \frac{r}{2}$

As we can see, the distance does not depend on the actual value of the mass but on the fact of one being twice as much as the other one.