A logical problem about a new system.

[Richlair]

I was thinking of a problem on my own when I came upon an entirely new idea.

Assume that a force(call it air resistance) acts on a body such that it opposes the motion of the body by an acceleration a. If the body is at rest, it doesn't act. I know that it is not possible but just assume such a system. Now, suppose you throw a ball upwards with considerable speed. Let us consider cases and analyse the motion of the ball.

Case I: If a<g.
The ball moves up with deceleration(a+g) and comes to rest and comes down with less acceleration (g-a) on it.

Case II: a=g
The ball moves up with fair deceleration 2g, comes to rest. Now, at the instant when it is at rest, air resistance doesn't act on the ball. But since gravity does, the ball starts coming down but air resistance pulls it up with same force and so, the ball just floats in air neither going up nor coming down.

Case III: a>g
The ball moves up with powerful deceleration (a+g) and comes to rest. Now, consider the instant when it is at rest. Only gravity acts on it and so, it tends to come down. But if it does come down for an instant, air resistance acts upon it pulling it upwards with acceleration more than gravity. So, just as the ball starts moving down, it is pulled forcibly upwards and hence, for an instant, tends to move up. Now, again, air resistance changes its direction(remember that it just tends to oppose the motion like friction), and begins pulling it downwards and gravity also pulls and so, the ball again starts falling down for a fraction of time. Finally, we can see that the ball never moves at all.

My question is, am I right in this analysis of the motion of the ball? Because it seems vague and incorrect(for the third case).

 

[Drakkith]

The problem here is that you are asking us to gauge whether your made up force is going to have X effect. I don't really even understand it. It opposes the acceleration of a body? We have a term for that already, called Inertia. Also, you seem to be neglecting to take into account the acceleration provided by your arm to throw the ball upwards to begin with. I also don't understand your use of A and G. Gravity is a constant acceleration of 9.8 m/s^2 here on earth, no matter the inertia of the object. In case 1 the ball would be hard to toss into the air, and would slowly come to a stop and slowly come back down. In case 2, you couldn't even move the ball since all acceleration would be opposed equally. Case 3 is just crazy, as it seems that it would be pushed opposite of the normal direction.

I think that is what would happen, but since it isn't real its hard to say. You should try to stick to real concepts, they are generally much easier to work through lol.

 

[Richlair]

My force doesn't oppose the acceleration of the body. It just gives acceleration against the instantaneous motion of the body.
Since everything is hypothetical, you can just assume that somehow the ball was just tossed into the air. If you feel the tossing of the ball in the air is absurd, assume such an atmosphere of air(as given in the question) starts from above 2 metres in the ground and goes to a considerable height. So, you can throw the ball from less than two metres height normally and notice the motion of the ball as soon as it reached the special atmosphere.
I know this is completely impossible, but I wanted to analyse the motion in such a case by assuming it exists in another planet.

 

[Drakkith]

So your force is exactly like resistance moving through a fluid, but variable then. Alright, got it. If so, then I think your analysis is correct. Although case 3 might result in a paradox where my grandfather comes out from a singularity and gives birth to an alien bicycle. :)

 

[Richlair]

So your force is exactly like resistance moving through a fluid, but variable then. Alright, got it.

Exactly. I am surprised it didn't cross my mind about viscosity. Anyway, you got the point.

If so, then I think your analysis is correct. Although case 3 might result in a paradox where my grandfather comes out from a singularity and gives birth to an alien bicycle. :)

Oh, thanks for your help.

 

[Drakkith]

Oh, thanks for your help.

Just saying that it makes no sense and would violate conservation of energy and momentum and all kinds of other things.