Question about potential energy

In summary: This means that the potential energy of a body is always decreasing as you move further away from the center of the planet.
  • #1
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Let's say we have a mass M at the ground of the Earth with speed U going upwards so its energy is E= kinetic. The speed is enough to surpass Earth's gravitational field so now it has a speed U2<U and its energy now is E= kinetic+potential. So my question now is: Is this potential energy lost? I mean when it's in the gravitational field its kinetic energy converts to potential and potential to kinetic when back down... So when it exits the field potential can no longer convert to kinetic? If this is the case where does potential energy goes ?
 
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  • #2
It never exits the field. The gravitational field of teh Earth is not limited to a finite region of space.
 
  • #3
Like the post above mine says, the body never escapes the field. The potential energy is ##U=-\frac{GM_em}{r}## . As the distance increases, ##U## tends to zero.
For a body to escape the pull of Earth its kinetic energy ##K## must be greater than ##U## i.e., the total energy ##E=K+U## must be positive ( ##E## is constant).
As the distance increases, ##U## goes to zero and ##K## slowly decreases. The total energy ##E## will always remain constant though.
 
  • #4
What about U=mgh ? As far as I know acording to this equation potential energy seems to be positive but also getting bigger as h growing. What's going on?
 
  • #5
Xalkias said:
What about U=mgh ? As far as I know acording to this equation potential energy seems to be positive but also getting bigger as h growing. What's going on?
##U=mgh## is only an approximate relation ( where g doesn't change appreciably with distance). For your case, where the body wants to escape the Earth's attraction, you cannot assume ##g## to be constant. Also, in ##U=mgh##, the potential at the Earth's surface is zero and at a very large distance it's infinity. Compare this to ##-\frac {GM_em}{r}##
 
  • #6
Xalkias said:
What about U=mgh ? As far as I know acording to this equation potential energy seems to be positive but also getting bigger as h growing. What's going on?
Only differences in potential energy are physically meaningful. The actual value at a chosen reference point is irrelevant.

When using ##U\, = \, mgh##, one is implicitly assuming a reference point at ground level, a height measured up from ground level and a potential energy of zero at the reference point.

When using ##U \, = \, - \frac{GM_em}{r}##, one is assuming a reference point at infinity, a radius measured out from the center of the Earth and a potential energy of zero at the reference point.

The difference between potential energy of a mass at a height of 10 meters above the Earth's surface and the potential energy energy of a mass at the Earth's surface is the same, either way. Both formulas give the same answer for the difference.
 
  • #7
Xalkias said:
What about U=mgh ? As far as I know acording to this equation potential energy seems to be positive but also getting bigger as h growing. What's going on?
What's going on is that the gravitational potential on the Earth's surface is Negative (with respect to infinity). Moving upwards is going in the Positive direction (doing work against gravity). It's like climbing up a mineshaft. The whole shaft has negative height but your height is increasing as you move up. I heard the term "Number Line" on the Radio, this morning. Moving right on the number line is always Increasing; going Up through the gravity field is Increasing your Potential.
-GmM/(Greater R) is more than -GmM/(Small R)

As far as gravity is concerned, the absolute potential Everywhere in the Universe is Negative (until they find something with Negative Mass).
 

1. What is potential energy?

Potential energy is the energy stored in an object due to its position or state. It is the energy that an object has the potential to use in the future.

2. How is potential energy different from kinetic energy?

Potential energy is the energy an object has due to its position or state, while kinetic energy is the energy an object has due to its motion. Potential energy can be converted into kinetic energy and vice versa.

3. What are some examples of potential energy?

Some examples of potential energy include a stretched rubber band, a book on a shelf, a compressed spring, and a pendulum at its highest point.

4. How is potential energy calculated?

Potential energy is calculated using the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.

5. What factors affect an object's potential energy?

The factors that affect an object's potential energy are its mass, height, and the strength of the force acting on it. As these factors change, so does the object's potential energy.

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