Consider a teeter-totter that is made out of pine, shown below. A pineapple sits on one side of the teeter-totter, a distance 1.23 m from the pivot point, while an apple
(non-pine) sits on the other side, a distance of 2.95 m from the pivot. If the
pineapple has a mass 121 g, what must the mass of the apple be in order to balance
the teeter-totter (ie, to maintain rotational equilibrium)?

Approximately (rounded to three significant figures.)

Explanation:

Let and denote the mass of the pineapple and the apple, respectively.

Let denote the distance between the pineapple and the pivot. Let denote the distance between the apple and the pivot.

Because of gravity, both the pineapple and the apple would exert a normal force on the seesaw. The magnitude of that force is equal to the weight of the fruit. Let denote the gravitational field strength.

Since these two forces are perpendicular to the seesaw, the magnitude of the torque exerted by the pineapple and the apple would be:

For the seesaw to maintain a rotational equilibrium, these two torques need to balance each other. Thus:

.

Rewrite and simplify this equation to find an expression for the unknown mass of this apple, :

.

Substitute in the values , , and and evaluate:

.

Thus, the mass of the apple should be approximately .

b.

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