Your Day

Pet_Sounds · 08-24-2019, 10:22 PM

Quote:

Originally Posted by Doug McClasky

I mean that the air pressure is adding permanent change to velocity that if removed would stop changing velocity. Like what's the difference between a ball hanging in midair and a ball sitting on the ground with air pushing down on it when if that air were removed would change/add velocity?

The forces on the ball hanging in midair aren't balanced. That's why it is only instantaneously at rest.
I think I'm interpreting your question right?

~~jwb~~ · 08-24-2019, 10:26 PM

Quote:

Originally Posted by Pet_Sounds

No, in that case the forces would balance so that the acceleration would be zero. The point with the ball is that its velocity is changing, even when it is instantaneously at rest at the top of its motion.

If the ball were sitting at rest on the earth, however, then its acceleration would be zero. Even though gravity pulls down on it, there's a corresponding upward force exerted by the ground that balances it out.

Being "at rest" (i.e., zero velocity) with nonzero acceleration only happens instantaneously.

That makes sense, I think.

Basically at the peak the ball is already set to move back towards the earth. So even though for an instant it isn't moving it will have a non zero velocity because at any given moment later it will have moved?

The Batlord · 08-24-2019, 10:31 PM

Quote:

Originally Posted by Pet_Sounds

The forces on the ball hanging in midair aren't balanced. That's why it is only instantaneously at rest.
I think I'm interpreting your question right?

Is there a describable difference between balanced and not balanced though?

Pet_Sounds · 08-24-2019, 10:33 PM

Quote:

Originally Posted by jwb

That makes sense, I think.

Basically at the peak the ball is already set to move back towards the earth. So even though for an instant it isn't moving it will have a non zero velocity because at any given moment later it will have moved?

At the peak its velocity (change in position) is zero because, as you said, it's not moving. Its acceleration (change in velocity) is nonzero because the velocity is still changing (it's only zero for an instant).

Crash course in calculus.

OccultHawk · 08-24-2019, 10:33 PM

Everything on earth is being pulled to the center of the earth same as a ball in transition from rising to falling so why isn’t everything at rest considered to have nonzero acceleration?

Pet_Sounds · 08-24-2019, 10:34 PM

Quote:

Originally Posted by Doug McClasky

Is there a describable difference between balanced and not balanced though?

When forces aren't balanced, something is or is about to accelerate. When forces are balanced, no acceleration occurs.

Pet_Sounds · 08-24-2019, 10:35 PM

Quote:

Originally Posted by OccultHawk

Everything on earth is being pulled to the center of the earth same as a ball in transition from rising to falling so why isn’t everything at rest considered to have nonzero acceleration?

The surface of the earth exerts a force upward that balances out gravity. No such force acts on a ball in midair that is about to plunge downward.

Newton's second law basically.

EDIT: Should we move this to the spam thread or something so it doesn't clog this thread up?

The Batlord · 08-24-2019, 10:39 PM

Like I'm basically asking if it's a difference in "philosophy" or if there's a measurable difference in equations. Like, is a thing that's not moving in mid-air because it's reached its zenith mathematically different from something that is sitting still simply because of gravity and air pressure that are working against each other but keeping said thing still?

The Batlord · 08-24-2019, 10:41 PM

Quote:

Originally Posted by Pet_Sounds

EDIT: Should we move this to the spam thread or something so it doesn't clog this thread up?

I don't think anyone is worried about clogging the Your Day thread.

Pet_Sounds · 08-24-2019, 10:47 PM

Quote:

Originally Posted by Doug McClasky

Like I'm basically asking if it's a difference in "philosophy" or if there's a measurable difference in equations. Like, is a thing that's not moving in mid-air because it's reached its zenith mathematically different from something that is sitting still simply because of gravity and air pressure that are working against each other but keeping said thing still?

Yeah, there's a difference in equations. Calculus was invented basically for this question. You need an "open interval" (which can be arbitrarily small) of time around a given point to discuss instantaneous rate of change, and the difference comes down to the behaviour of the object in that open interval as it approaches the point you're interested in. In the case of the ball in mid-air, its motion changes immediately before and after the point in time at which its velocity is zero; the ball on the ground doesn't move at all.

Sorry I'm not explaining this very well, it's hard without math.

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