# Biophysics Problem 20

A teeter-totter is $20\; kg$ in mass. Assume it is a uniform plank of length $2 \;m.$ The pivot point is placed $0.2 \;m$ from the midpoint. What weight must be added to the short end to balance the teeter-totter?

(Hint: Think a moment about the pivot - the uniform plank can be assumed to be a single weight concentrated at its midpoint. Can you justify this?)

#### First Step

There are 3 vertical forces here, of which we know only one (the weight of the plank). I hope you realize that if you take moments about the pivot point you will get an equation that does not contain one of the unknowns(the upward force through the pivot point). The equation will contain the only other unknown, which is the weight of the mass added to the short end.

First, add to the diagram the vectors representing the two downward forces. Also indicate their distances from the pivot point.

#### Diagram

Now use the principle of rotational equilibrium and take moments about the pivot point to solve for $W.$

#### Calculations

You should have:

$W \times 0.8\;m = (20 \times 9.8) \times 0.2\;m \\ W = 49 \;N$