When a ball is tossed straight up, does it experience momentary equilibrium at top of its path?

Question

This question has been asked many times all over the Internet and answers can be found on places such as yahoo and ask.com, but I'm not satisfied with those answers and I don't trust the validity of those places. This seems like a more appropriate place to ask. So, here's my train of thought and I would like to ask you if you think I'm right or wrong. Even though most of the answers point to the fact that the ball does not achieve equilibrium because the force of gravity is constantly acting upon it, thus causing an acceleration, I still think there's a moment of equilibrium and here's why: When the ball is traveling up, it's accelerating towards the ground and eventually reaches a point at which its speed reaches 0. At this moment, isn't the reason the speed is 0 is due to the fact that net force is 0? The force that made the ball travel in the upward direction was canceled out by the gravitational force. So, the sum of forces at that brief moment is equal to 0, otherwise the ball would be moving. I don't think gravity is the only force acting on the ball at that moment, since the throwing force was acting on it as well, until both canceled each other out for that brief moment. Am I right or wrong?

Answer 1

I am sorry, but your analysis is incorrect. Once the ball leaves the person's hand, it is never in equilibrium until it lands on the ground or the person catches it again. In particular, it is definitely not in equilibrium when it reaches the top of its path, where the velocity is momentarily zero.

Here's why:

The definition of equilibrium is that there is no net force acting on the object, as you state correctly. But, according to Newton's Second Law of Motion, a net force imparts an acceleration onto an object, NOT a velocity. So, the fact that the object's velocity is zero tells us nothing about whether there is or is not a force acting on the object. Notice that even though the velocity is momentarily zero, the change in velocity at that moment is most definitely NOT zero. How do we know that? Because the velocity is zero only for an instant in time, which means that it was not zero the instant prior and it will not be zero the instant after. Thus, the velocity is clearly NOT constant. As a result, the acceleration is NOT zero, and so the net force is NOT zero. And, therefore, the object is NOT in equilibrium.

Of course, this conclusion is based on the assumption that air resistance is negligible, and can therefore be ignored. If, on the other hand, you include air resistance, it is possible for an object in free fall to reach an equilibrium if you drop the object from a high enough starting point. At this equilibrium, the object is falling fast enough that the drag force caused by air resistance is exactly equal and opposite to the force of gravity, so that the net force is zero. But this equilibrium does not happen at the highest point in the object's trajectory, but rather at a point where the object is falling very rapidly.

BTW, once the object reaches this equilibrium, it is said to be traveling at its so-called "terminal velocity".