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

The box should be placed at a distance of
`(r)/(2)` from the pivot

Step-by-step 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 = (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.