Regarding GPE

[Spinosaurus75DinosaurFan]

1. I noticed that our Calculations page say that in cases close to the ground and in cases far from the ground use different formulas. But what is "close to the ground", and how high is "far from the ground"?

2. The formula for "far from the ground" is "Ep = |(G*M*m)/r1 - (G*M*m)/r2|". r1 is the distance between the center of mass of the planet and the center of mass of the object before the fall / after being lifted (in meters). So usually it is radius of the planet (in case of earth 6371000 m) + how far the object is away from the ground before the fall / after being lifted. r2 is the distance between the center of mass of the planet and the center of mass of the object after the fall / before being lifted (in meters). So usually it is radius of the planet (in case of earth 6371000 m) + how far the object is away from the ground after the fall / before being lifted. Therefore, r1 > r2. Therefore, (G*M*m)/r2 > (G*M*m)/r1, which means the result I get is going to be negative. Am I misunderstanding something?

Note: Former calc group members, calc group members and Kaltias only

 

[Kaltias]

1) "Close to the ground" means "close enough to consider this formula a good approximation".

Kinda like relativistic KE is needed only when you are "close enough" to light speed.

2) If you are lifting, R2 > R1.

If it's falling, you get a negative result yet (GPE is lowering), you simply need to consider the absolute value as the result

 

[Spinosaurus75DinosaurFan]

No, you are wrong. Lifting is also negative, because R1 is after being lifted and R2 is before being lifted.

 

[Kaltias]

In this case, just use the absolute value.

Otherwise E = GPE1 - GPE2 also works (GPE1 is the GPE when the height is at its maximum value, GPE2 when the height is at its minimum)

 

[Assaltwaffle]

I'm not super versed in potential energy; it is one of the ways of calculation that I haven't used much.

 

[Spinosaurus75DinosaurFan]

@Kaltias Height at its maximum value>Height at its minimum value. We'll get a negative value.

So we should simply swap R1 and R2, you mean?

 

[Kaltias]

The main point is, variation of GPE it can be both negative and positive because gravitational force is a vector, not a pure number

If you get a negative result, take its absolute value. If you get a positive result, that's the result.

 

[Spinosaurus75DinosaurFan]

Ok. But in most cases, it's negative.

 

[ArbitraryNumbers]

I'm not very good with potential energy either. I can only do the simple formula.