Gravitational Potential Energy can be negative?

[RandomMystery]

I have two physics books that state that

U(r) = -GMm/r

What I don't understand,is how can potential energy be negative?

I've done the integral of GMm/r^2 from infinity to r, but I don't quite get the concept of negative potential energy.

I don't understand why using r=infinity as the initial potential energy and as the initial reference point, always makes U negative from that perspective.

For example

E = U + K

E = -GMm/r + [mv^2]/2

I don't understand this infinity perspective system, so instead I use a mass or Earth perspective:

U= GmM/(r+x) + [4piGmpr^2]/6

*[4piGmpr^2]/6 is the integral of 4piGmpr/2 which is an estimation of the force acting on a particle inside Earth.

Here U is always positive. I'm having trouble understanding the value of U from the "infinity" perspective.

 

[jtbell]

I don't understand why using r=infinity as the initial potential energy and as the initial reference point, always makes U negative from that perspective.

When you lift an object upwards (or away from the center of the earth) against gravity, you have to do work. Positive work. If the object starts out at rest and ends up at rest, the work you do goes completely into increasing the potential energy. The (positive) work you do equals the (positive) change in potential energy.

Suppose you have to do a million joules of work in lifting an object from (say) the Earth's surface to infinity. If we define the potential energy to be zero when the object is at infinity, and you have to do a million joules of (positive) work in order to put the object there, what does the initial potential energy have to be?

 

[granpa]

when a positive charge and a negative charge come together they release energy and the resulting neutral particle no longer has any potential. The positive potential energy became positive light energy.

when 2 masses come together they release positive energy but the resulting larger mass has even more potential energy. The only way for this to balance is for gravitational potential energy to be negative.

 

[RandomMystery]

When you lift an object upwards (or away from the center of the earth) against gravity, you have to do work. Positive work. If the object starts out at rest and ends up at rest, the work you do goes completely into increasing the potential energy. The (positive) work you do equals the (positive) change in potential energy.

Suppose you have to do a million joules of work in lifting an object from (say) the Earth's surface to infinity. If we define the potential energy to be zero when the object is at infinity, and you have to do a million joules of (positive) work in order to put the object there, what does the initial potential energy have to be?

What you are saying is that the Mechanical Energy is zero at infinity? Then what would happen if the net mechanical energy positive or negative? If I am doing work against gravity, my potential energy is positive and it increases since my work has contributed to the increase in potential energy (which is positive not negative). Is potential energy the work done by gravity (in this case it would be negative) or the potential energy stored that can be converted into kinetic energy (in this case this would be positive)?

when a positive charge and a negative charge come together they release energy and the resulting neutral particle no longer has any potential. The positive potential energy became positive light energy.

when 2 masses come together they release positive energy but the resulting larger mass has even more potential energy. The only way for this to balance is for gravitational potential energy to be negative.

what is light energy? I don't recall seeing "light" produced by gravitation. When 2 masses come together, they convert gravitational potential energy to kinetic energy, Is that what you mean by "they release postive energy."?



Last thing, (and the original queston) if potential energy is defined as energy that can Potentially be converted into kinetic energy, how can something that is negative be converted to positive kinetic energy?

From the traditional definition (if an object is outside of Earth's surface):

r is the radius of the planet and x is the distance from the object to the surface of the planet.

From the traditional definition (if an object is inside of earth):

The equation with Pi accounts for gravity inside of earth. U is never negative in this equation. So why is U negative in the other equation?

 

[granpa]

the negative potential energy isn't converted to positive energy.
rather, as you create more positive energy you also create more negative potential energy.
the sum of the positive and negative remains constant.

 

[rcgldr]

How can potential energy be negative?

Potential energy is the negative of the work done by a field when an object moves from one point to another point, by definition. In the case of gravity, if an object "falls", the work done is positive, and the change in potential energy is negative, total energy of the system remains constant, so the definition of potential energy makes sense. In the case of a positively charged source generating a field, and there's a positively charged particle in the field produced by the plate, then potential energy will be positive, decreasing with distance from the source.

 

[RandomMystery]

the negative potential energy isn't converted to positive energy.
rather, as you create more positive energy you also create more negative potential energy.
the sum of the positive and negative remains constant.

I think I'm having a definition problem. If potential energy is the energy that you could potentially use. How can you use energy that you don't have, or energy that is negative? Does it have to do about where E mech is?

Potential energy is the negative of the work done by a field when an object moves from one point to another point, by definition. In the case of gravity, if an object "falls", the work done is positive, and the change in potential energy is negative, total energy of the system remains constant, so the definition of potential energy makes sense. In the case of a positively charged source generating a field, and there's a positively charged particle in the field produced by the plate, then potential energy will be positive, decreasing with distance from the source.

So potential energy is the negative work done by a field (or spring) and not the energy it or they store. It's not change that is confusing me. You can have potential energy without moving or "changing." So change does not have to do with it. Is the potential energy zero because our Emech line is at infinity and Emech = zero at infinity?

 

[rcgldr]

You can have potential energy without moving or "changing."

Potential energy is relative, so you need a reference point. For a point source in space, it's convenient to use ∞ as a reference point, since U at -G M m / ∞ = 0 (GPE would be negative at any finite distance from point source). For an infinite plane source or when only considering small heights from the Earth's surface, which approximates the inifinte plane case, GPE = + m g h, and it's convenient to use h=0 as a reference point.