Falling objects

When you toss a ball straight up in the air, does it stop for a split second before it begins it descent?

No, it’s travel path is continually unbroken; it does achieve zero velocity, though, at the apex of said travel path.

The statement of the question is perhaps a bit unclear: The ball does, indeed, reach zero velocity, but it does not stay at zero velocity for any finite length of time. It’s not a matter of it reaching the top, stopping a waiting a little bit, and then falling down.

Agreement comes on my part, if my Physics class was accurate (and I think it was). It’s just that the human eye can’t perceive such negligible movements for the last few moments of the balls’ travel.

Here’s something to help you understand the concept of an infinitesimal amount of time, an instant if you will. (I know it’s easy for some people, but not so easy for others, okay?) Suppose you’re, for instance, rolling a ball down the sidewalk, and there’s a line painted on the walk. A very very thin line, that the ball crosses. Is the ball ever exactly on top of this line? Sure it is, for a split second. It can’t get from one side to the other without crossing it. But if you took a photograph at any time, and zoomed in a zillion times, you could always say that the ball was more on one side than the other. So, how long is the ball actually on the line? A split second. The same way with something moving - you can’t be going one direction, then be going in the other direction, without stopping for some tiny amount of time in between.

You have to distinguish between an infinitesimal amount of time and a very small amount of time. These are very different concepts. According to classical physics the ball has zero velocity not for a split second or tiny amount of time (small but finite numbers) but for an infinitesimal (infinitely small) amount of time.

Of course, Quantum Mechanics denies the absolute continuum; any measurement of time smaller than (IIRC) 10^-35 second doesn’t have meaning. And if you could measure the exact velocities of all the atoms in the ball extremely precisely, then its energy would become so uncertain it would either disappear or explode!

This brings to mind a physics-esque ‘riddle’ I heard a long time ago. If

is a true statement, then what happens when you throw a ball at an oncoming train? When the ball hits the train it (the ball) changes direction. To do so, the ball must, for an instant, come to a complete stop. Yet at the same time it is in contact with the moving train. How is it possible to have to objects in contact with each other moving at different speeds? What am I missing?

Thanks,

Rhythmdvl

The gov has planes, they fly up & turn down. If you are in them when they turn, you experience no gravity, in otherwords, you stop going up before you turn down. weird.

It depends a little on whether you’re talking about what the ball really does or a mathematical model of what the ball does.

Physically, ignoring quantum uncertainty, the ball and the train deflect at their contact point. It’s pretty likely that the ball deflects more than the body of the train, so let’s ignore the train’s deformation. In at least one sense, the ball does indeed spend an infinitesimal time not moving. The interface between the ball and the train may be moving, as the ball deflects, in the direction of the train’s motion; and other parts of the ball may still be moving towards the train; but the center of gravity of the ball is actually standing still.

Mathematically, the function that describes the ball’s velocity is always (let’s say) negative before the collision, no matter what time interval you consider, and always the opposite sign (positive) after the collision (no matter what interval you consider). If you include the ball’s deformation in your model, then the function that describes the ball’s velocity is also continuous (roughly speaking, no jumps or discontinuities). There’s a well-known (to some {grin}) theorem that says that, in this case, the function that describes the ball’s velocity must pass through zero at some time, and therefore the ball’s velocity is indeed zero at some time.

Geez, you’re trying to explain a relatively simple concept in Mechanics, and someone has to go and bring up Quantum Theory and weird paradoxes. I suppose you deserve to be told the truth, then, madd1. The truth to you original question is No, because nothing can ever truly be still. If it’s still, then its Kinetic Energy (the energy it has because it is moving) is equal to 0, and Quantum Mechanics has this big thing against a KE of 0. (Someone check me on this if I’m wrong.) Yeah, I know, just when you thought it was making sense. How can a ball start going up, which it clearly does, and then come down, which it clearly does, without stopping at some point in between? Well, remember the ball rolling on the sidewalk example? Quantum Theory says that the ball can go from one side of the line to the other without ever being on top of the line. If you ever decide to start working with Quantum stuff, just don’t expect anything to make sense.

PS: And where, SingleDad, did you get the idea that a “split second” is a finite amount of time? I’ve never seen it defined in any physics texts, and I think it’s about darn time we had a term for this concept.

This reminds me of a humiliating experience in Physics class when I did not realize that dx/dt was > 0, even when x=0.

Actually, Achernar, it’s not that complicated. Even with quantum mechanics, the vertical component of the ball reaches zero at at least one point in time, but it’s still wiggling other ways. A particle’s position can tunnel, but I don’t think that its velocity can.

And by the way, I’ve also personally welcomed aha, somewhere or another in MPSIMS, (Tim), Billythekid over in Comments on Cecil’s Columns, and a few others. Don’t feel too bad, though, there’s always the hope of something from Cecil :slight_smile: .

Thanks for correcting me there, Chronos, but I think I’ve been misread. I totally agree that the vertical component of the velocity will be 0, but that’s not what the OP asked, is it, and the OP is what I was attempting to answer. (Though now I feel like I’m just going to confuse myself, and others.) It would seem to be implied from the original question that the ball’s motion is restricted to one dimension, which is not a bad assumption in Classical Physics, but when people try to apply Quantum Physics to that, well, we’ve seen what ugly results can ensue. I should have known better than to try to tackle a setup I knew was inherently paradoxical, er, paradoxian, er, paradox-like.

I hope my new signature line strikes you as more accurate. I should have stuck with something like this at first, rather than meticulously looking through all your previous posts for four hours last night, just to get the count wrong. :rolleyes:

I think the question has been answered, but for fun (since things like quantum mechanics are being injected into this discussion) let me add that the ball’s velocity would have to be measured relative to the person or to the ground (since it is still moving along with the Earth’s rotation, orbit, etc. even when the person sees it at “zero” velocity) :slight_smile: