Why does a teeter-totter (see-saw) tend to incline towards the heavier end? Since objects of different mass tend to fall at the same speed (assuming a vacuum), why do then heavier objects push harder on a scale? Why are they heavier? Even though they have different masses, their "resistance" against Earth's pull is proportional. Right?
This seems like a very basic question.
Best Answer
The reason that objects tend to fall at the same rate is because on earth we can approximate the force of gravity to be $F=mg$. In this case, the force is really $$|F|=G\frac{Mm}{r^2}$$ where $r$ is the distance to the center of the earth, $M$ is the mass of the earth, and $G$ is the gravitational constant. Since these things tend to be the same near the earths surface, we approximate $g = \frac{GM}{r^2}$. This we can relate to $F=ma$ (Newton's Laws), and we can infer that for objects of any mass, the acceleration is the same, at $a=g$.
Now, to the point about the see-saw. The accelerations are the same, but the forces are not the same, since they are also proportional to the mass, $m$. Where a see-saw balances at is dependent on the torque, which is given by $\tau = \vec{r}\times\vec{F}$, where $\vec{r}$ is the distance from the pivot point. Now, for masses the same distance away from the pivot point, the torque is greater for the greater force. For objects under the influence of gravity, the greater force belongs to the object with greater mass. Therefore, the see-saw tends to tip toward the side with greater mass.