Four Conceptual Questions as I Teach Myself Physics

[Addem]

So I'm just reading through a high school Physics text, essentially, and I have these four general question as I learn the basics of Classical Mechanics.

1. If acceleration has units distance/time^2, then I would expect, between two different objects accelerating over the same distance but with one taking twice as long, it would have a quarter the acceleration. However, when I try to draw out tables of time, position, velocity, and acceleration, this seems not to come out. Can someone give a toy example which would demonstrate the proportionality between acceleration and the inverse square of time?

2. I feel uneasy about the nature of potential gravitational energy. It is supposedly 0 for an object at rest on the ground ... unless that ground happens to be a trap door? And then it has some non-0 PE? Can anyone say some things to clarify this idea? Is potential energy not intrinsic to an object and the gravitational field surrounding it? (I just use the word "gravitational field" only due to the understanding of it which I've gained from science fiction--I don't truly and totally understand what that is.)

3. When something falls, it loses PE but gains KE. But what happens when its at rest on the ground? Does it have both 0 PE and 0 KE? Has all of the energy which it once had, in one of those forms, now distributed into the ground? In the form of heat and some small measure of mechanical energy (denting the ground)?

4. If in space you apply a force on an object and, in response, the object travels infinite distance, does that imply that the force has done infinite work?

Thank you for any help.

 

[Dale]

1. If acceleration has units distance/time^2, then I would expect, between two different objects accelerating over the same distance but with one taking twice as long, it would have a quarter the acceleration. However, when I try to draw out tables of time, position, velocity, and acceleration, this seems not to come out. Can someone give a toy example which would demonstrate the proportionality between acceleration and the inverse square of time?

If you accelerate at 2 m/s^2 for 1 s you will travel a distance of 1 m. If you triple that to 3 s then you will travel 9 times as far, or 9 m.

2. I feel uneasy about the nature of potential gravitational energy. It is supposedly 0 for an object at rest on the ground ... unless that ground happens to be a trap door? And then it has some non-0 PE? Can anyone say some things to clarify this idea? Is potential energy not intrinsic to an object and the gravitational field surrounding it? (I just use the word "gravitational field" only due to the understanding of it which I've gained from science fiction--I don't truly and totally understand what that is.)

The 0 point is completely arbitrary, and it is OK for gravitational PE to be negative. In fact, one common convention is to put 0 at infinity, so that gravitational PE is always negative.

3. When something falls, it loses PE but gains KE. But what happens when its at rest on the ground? Does it have both 0 PE and 0 KE? Has all of the energy which it once had, in one of those forms, now distributed into the ground? In the form of heat and some small measure of mechanical energy (denting the ground)?

Yes.

4. If in space you apply a force on an object and, in response, the object travels infinite distance, does that imply that the force has done infinite work

The important distance is the distance it moves while the force is being applied.