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?

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lcmendozaf lcmendozaf · Answer 1 · 2019-09-13T00:18:19+02:00

Answer:

The box should be placed at a distance of [tex]\frac{r}{2}[/tex] from the pivot

Explanation:

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

[tex]T_{m} = T_{2m}[/tex] Replacing the formula for Torque:

[tex]m*r = 2m*X[/tex] where X is the distance we need to find.

Solving for X we get:

[tex]X = \frac{r}{2}[/tex]

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.