Can an object be accelerating and yet -not- moving?

What bothers me about this, Con, is that after you toss the ball straight up,

and yet during its entire flight its speed is changing

Correct me if I'm wrong Con, but is this based on the notion that the instant of zero acceleration, that's at the top of its trajectory, is of zero duration

Yet somehow Intuition insists at the moment of zero acceleration the object was still. Since I can't remember having been tossed into the air myself, isn't there an instant at the top when the ball "feels" weightless

Your intuition is never going to accept this. But it is scientifically correct. In fact human beings are feeling this exact feeling of weightlessness right now.

The ball "feels" weightless, not just for the instant when it reaches the top, but for the entire trip. Well ... actually balls don't feel anything. But, if you have tiny little people inside the ball, they will be "weightless" from the instant the ball leaves your hand, to the instant it lands.

Why do you think the astronauts in the space shuttle feel weightless?

Your intuition does not conform to that of a very large number of people. Moreover you appear to resist comprehending that time is composed of instances of zero duration, just as a line is composed of points of zero extent, and just as any interval on the scale of real numbers is composed of an infinity of other real numbers.

Consider that we live our lives under the constant acceleration due to earth's gravity. That is the basis for our "normal" intuition of zero acceleration.

If one is in an aircraft in level flight and pushes the stick forward enough he will experience weightlessness or, if he pushes harder, negative "g" - that is his mass will be bearing on his shoulder straps, and not on his seat or butt. The fact is, all the while, he is acelerating, because the direction (and perhaps the magnitude) of his velocity is changing.

The essence of Newton's law is that, absent a force or acceleration, a body will remain in uniform motion (direction and speed), and that any change in that motion (magnitude or direction) will require application of a force proportional to the acceleration (=rate of change of velocity) that occurs.

What you are calling intuition is merely the stubborn refusal to think. That of course affects many people, but apparently not often to the degree it apparently affects you.

Well said!

There is no instant of zero acceleration. When you throw a ball up in the air, you have given the ball an initial velocity in the positive (up) direction. From the second the ball leaves your hand, the acceleration due to gravity constantly pulls the ball downward, slowing the upward velocity by 9.8 m/s every second. Thus, as the ball is travelling upward, the distance travelled per second continually gets shorter since the ball is slowing down. Once acceleration has slowed the ball down enough, it will stop travelling upward and start to fall back to earth. It is at this point that velocity has changed direction, as a result of the downward acceleration overpowering the upward motion of the ball.



This concept of an "instant" is what is troubling you, I feel. You yourself offered the example of a sine wave earlier. Consider a graph of a sinusoidal alternating voltage (like household AC) , whose value smoothly changes between peaks of opposite polarity. Imagine the graph is on the screen on an oscilloscope, or even better on a piece of magic graph paper that you can zoom inwards indefinitely. Suppose someone asked how long it the voltage remains at each positive peak. You look at one of them on the graph. The line is a smooth curve. It doesn't get up to peak voltage and then go along flat for a bit, and then head back down again. You would expect it to vary smoothly because the alternating current is generated by a rotating magnetic field in an alternator driven by a steam turbine.

Consider two points in time, the first is one millisecond before the peak instant, the second is one millisecond after. In between those points, if you look at the line on the graph with sufficient magnification, you will see that it is a curve that passes through the peak value. If you now reduce the interval before and after from one millisecond to one microsecond, you will still see the same thing. In fact you can reduce the interval as much as you please and it will always be thus. That is what we mean by an instant of infinitely short duration. This is calculus stuff, in fact, and goes right back to Newton.

Your 'intuition' seems to be that the thrown ball arrives at the top of its trajectory and then sits there motionless for a measurable, if short, amount of time before heading back down again.

Sorry max, no offense but I can't make sense out of this statement since I'm not sure whether you're talking about all of us down here or those guys up there in space ships

Okay, like I said, I can't remember, so I'll have to take your word for it

This is becoming very interesting indeed (at least to me). What you seem to be saying is that at this very moment except for the force of my chair on my butt, I'd feel exactly the same floating around in a spaceship

Okay, but it's all getting very complex (to me anyhow). Intuition (mine to be sure) suggests that I'd feel ever-so-slightly different on the way up than on the way down. Mind you, I'm only speculating but let's say you're right

So, what you seem to be saying, my graph of acceleration (including of course throw and catch) isn't a sine wave, but after the first quarter cycle it drops instantaneously to zero (air resistance of course notwithstanding), then stays there for, say, what I had imagined as the next quarter-cycle til I catch it, whereupon we get that last half-cycle

(Still one cycle of a sinewave but with the second quarter missing, so to say)

Then what you mean is, because the drop to zero in acceleration when you let go of the ball is instantaneous, that is the reversal in acceleration, is instantaneous, and therefore there was no "moment of motionlessness": but that's what bothers the Intuition (oh yes, again, mine), that instantaneousness, seems to somehow defy commonsense

I had supposed the centrifugal force equalled the gravitational pull, am I wrong

….but what does that have to do with the ball

NO NO NO! It doesn't "stay" anywhere!



There are occasions when you have to dump "commonsense".

Con you fellas have to get together. I don't know for sure myself, but somebody else above asserted that once released its acceleration is zero throughout the ball's flight

Who was that? Quote please.

Yea Con and thank you for taking so much trouble. Yes I hear what you're saying, and from a purely theoretical, mathematical point of view of course I can see why it's said to be accelerating throughout. Still I can't help feeling there's something unique about that moment of zero

I think also what everyone else has been saying suggests that the term "acceleration" has different meanings. One has to do with a change of velocity and the other a "feeling"? Thus am I not being advised that the although ball is, say, positively accelerating on the way up and negatively on the way down, once it has left my hand it feels no acceleration (nor de- of course) until it falls back into my hand

So my problem is semantic: Where I was thinking of it as a sensation you guys meant a change in velocity. So looking it it from your point of view, then, but viewing the entire event, are we back to the (approximate) sinewave cycle where its leading edge is where I'm tossing it and the its negative tip where I catch it

That's an admission followed by a q

……a qualified admission

Still, from an everyday point of view by the Average Clod (me), somehow there's a difference between a straight line passing through a zero axis and the situation at the peak of the wave. No excuse you understand, but if you stretch the graph horizontally the two lines will appear more nearly coincident, better justifying the notion that moment has duration, even though theoretically it doesn't

georgeob1 wrote:
No, Geo, I hear ya but you're being too judgmental. For instance even though mathematical theory confirms its duration to be zero, Intuition might have been thinking about the rate at which it approaches zero, making my assertion true at least in everyday terms (see directly above) by which we regularly communicate

Remember we live in a real world where nothing is entirely anything while everything is partly something else. Court battles are won and lost, huge sums transferred, on the basis of statements not "technically" true

1. "more nearly"... you're getting there!
2. If it is justifiable to mentally stretch the graph horizontally it is therefore justifiable (in fact consistency demands it) to stretch it vertically and then no matter how close you zoom in, you will see that the line touches zero (or the peak or whatever) for an "infinitesimal" amount of time. Likewise a circle touches a straight line at an infinitesimal point. Also ask yourself what the smallest nonzero real number (of the form 0.00001) might be.

Okay Con, point well taken. However our old buddy Intuition says that somehow the curved line approaches the parallel condition to the axis in a more significant way than the straight line passing through it

So at that instant of zero duration they are parallel

I can't justify this judgment either because it too is merely intuitive

Been a real pleasure, and I did really learn something

The people feeling weightless right now are the people orbiting the earth in the International Space Station (ISS).

A ball thrown in the air is in free-fall. This means that it is under the influence of gravity and nothing else significant.

The reason the people inside the ISS feel weightless is that they are in a ball (in this case big enough for humans) that is in free-fall. The ISS is under the influence of nothing but gravity. The people inside the ISS are also in free-fall which is why if they aren't touching anything, they will take the same path as the walls around them. This is how they float around.

We do the same thing with an airplane. This is done for training or at times for sport. We put it high in the air and then cut all power so the plane is in free-fall. Sure enough the people inside feel weightless.

Seeing how the orbit of the space station is the same as the path of that ball you threw is a little counter-intuitive (but absolutely scientifically correct). However the airplane example you should see is a little different.

So tiny people inside that ball you are throwing would feel weightless. As do people in spacecraft while orbiting feel weightless. People in a falling elevator would also feel weightless (for a couple of seconds unfortunately).

Anytime you are in free-fall (as the thrown ball is in free-fall) you will experience weightlessness.

That's not what was said. What was said is that the acceleration is CONSTANT through the entire flight, not ZERO through the entire flight.

Yea, Max, I follow that perfectly. Furthermore I agree that no matter how one magnifies it, the peak of the ball's acceleration trajectory is nowhere flat so theoretically it's moving and accelerating through the entire trip

1) However, and now this is just speculation, I'm not expressing a scientific principle, at the peak if its slope is zero even for an instant of zero duration, can't the ball be said to have stopped

So maybe the entire issue is one of semantics

But 2) let's move on to the real world where the upward motion of the ball produces a slight updraft which keeps that peak flat even for a microsecond. For all practical purposes of human intercourse the peak is flat

Of course extreme magnification will show it oscillating slightly above and below the horizontal reference but remember we're now in a real world using everyday terms to describe actual situations

In a jury trial where Don's conviction is dependent upon this flatness, he will be executed with the approval of judge, jury, and audience if not defense counsel

Point well taken, Ros, as I thought I had admitted somewhere above

If you're sitting in your car at a red light, and it turns green, how does your car start to move?

Your speed is zero, your acceleration is zero. You lift your foot from the brake and press the accelerator. There is a point in time when your speed is still zero, but your acceleration is some amount greater than zero.

My immediate reaction is that (theoretically) they'd happen at the same instant. However if acceleration is defined as a change in velocity then your implication is, that moment isn't of zero duration

Very interesting

But then what is its duration