Potential Energy (1 Viewer)

[dolbinau]

At what altitudes should I start using the gravitational potential energy formula rather than just mgh? (Where g=9.8 of course). I assume as you go higher and higher g becomes less so you can't use mgh anymore.

 

[henry08]

Gravitational potential energy is generally used in space (where g is never 0, hence EP is -), althoguh they can ask for it on Earth between two apples etc. I wouldn't even use the mgh formula.

 

[Continuum]

I was taught within a few kilometers, since its still relatively small compared with the earth's radius.

Henry08, mgh and -(Gmm)/r are 2 different things. mgh has 0 at the surface of the earth, whereas -(Gmm)/r has 0 at infinity. So to the OP, you still might have to use it for some questions.

 

[dolbinau]

If the question was what is the potential energy of a 30kg mass 2,000m above the earth's surface could I just say:

(30)(-9.8)+2000

(do we take acceleration as negative?)

But if it were say a geostat. satellite I would just use GPE using an altitude of 35800km+radius of the earth?

 

[henry08]

I would use the Ep formula for both of those.

 

[henry08]

I.e for that first question, I got -1.88 x 10^9 J. Remeber you must include the mass of the Earth in the calculation, and when you include the Earths radius, add 2000 metres!

 

[me121]

is the mgh one even in the syllabus?

 

[henry08]

is the mgh one even in the syllabus?

No, most textbooks mention it though to make it easier for students to initially understand Ep.

 

[Almatari]

Gravitational potential energy is generally used in space (where g is never 0, hence EP is -), althoguh they can ask for it on Earth between two apples etc. I wouldn't even use the mgh formula.

I think the force between two apples you're talking about is refering to Newton's Law of Universal gravitation and not potential energy. For force between 2 masses, since G is a small constant, small masses (like things on Earth) will produce insignificant F

In E=mgh, E refers to work done to move object from ground to a point. Use it for objects on Earth
In E=-Gmm/r, E refers to work done to move an object from a very large distance away to a point in a gravitational field. Use it for objects on a planetary scale