Understanding Gravitational Potential Energy

[Riogho]

Today in physics class we talked of Gravitational Potential Energy. We talked about how K1 + U1 = K2 + U2 etc etc.

But the idea of potential energy makes no sense to me. They say if you lift something off of the ground I.E. a phone. If i lift the phone up and put it on a table, the energy I used to lift it up is turned into potential energy after it is at rest. And the potential energy of that will be released into Kinetic energy.

But what IS potential energy. What exactly is it? What about my phone is changed when I sit it on the table except now it has 'potential energy'.

 

[Doc Al]

What about my phone is changed when I sit it on the table except now it has 'potential energy'.

Nothing changes with the phone. The potential energy is not a property of the phone, but of the phone-earth system. (You can say that the energy resides in the gravitational field.)

 

[Dale]

What about my phone is changed when I sit it on the table

It is further away from the earth.

 

[jambaugh]

Here is a way to think about potential energy...

Start with the idea of conservation of energy and just think about kinetic energy. In some cases kinetic energy is conserved (if there are no forces or if all forces are perpendicular to the direction of motion then the speed doesn't change and so neither does the kinetic energy).

In some cases the kinetic energy of the system is not conserved because energy of the object we are looking at gets transferred to or from another object by the action of a force (say when one ball hits another so it stops but the other one flies off). If we consider a bigger system we may see that again kinetic energy is conserved. Sometimes the energy is not transferred to kinetic energy elsewhere but say stored in the tension of a spring. (This is actually stored in the electromagnetic fields between the molecules that make up the spring.)

Now suppose you don't want to keep track of all the other bits and pieces where the energy gets temporarily stored but just the object in question and how much energy it might draw from its surroundings. That is its potential energy. By adding in the potential energy we get more cases where the total energy is conserved.

As I mentioned this potential energy of the system may not be (and generally isn't) kinetic energy stored elsewhere. It is usually energy stored in the strength of the surrounding electromagnetic or gravitational fields. The critical point is that we can keep track of the energy stored in the environment of the physical object which can potentially be returned to the object as kinetic energy. In those cases the total kinetic plus potential energy is still conserved as the object moves around. We can in fact use this fact to work out what the forces must be since only a force can change kinetic energy and a change in kinetic energy must in such cases correspond to an opposite change in potential energy.

Even when the energy can't be restored it must go somewhere in the form of say heat and it appears that we can always account for changes in energy in terms of kinetic plus potential plus thermal. Total energy appears to always be conserved.

In any case where an object can have potential energy stored in say the surrounding gravitational or electro-magnetic field it appears that we can also see that these fields can carry energy away in the form of waves. So we do know that there is real energy stored in the fields themselves. The difference in cases is usually a matter of speed. Move two charged spheres around and their potential energies change. Do this fast enough and e-m waves will be generated to the degree that we observe some energy in the system being lost.

For example we observe binary star systems in very fast orbits around each other loosing energy at about the rate that theory predicts gravity waves would carry it off into space.

In the simple case of say an elevator lifting a weight thus increasing its potential energy you can in principle calculate the gravitational fields of our planet plus this weight in the two cases when it is lowered or raised. The differences in the energies of the two fields will equal the differences in potential energies of the two cases. That's where this energy is stored.

In relativity we find that energy and momentum are parts of a total energy-momentum vector or stress-energy tensor. We find that momentum is also conserved. In electromagnetism for example we define a vector potential which (when multiplied by charge) gives us potential energy-momentum which we can add to the kinetic energy-momentum (4-vectors). We then find that this total energy-momentum is conserved by the electromagnetic field though the kinetic energy and kinetic momentum are changed as the particle moves through the e-m field.

 

[Riogho]

Thanks

 

[Gerenuk]

But what IS potential energy. What exactly is it? What about my phone is changed when I sit it on the table except now it has 'potential energy'.

Nothing changed with your phone. But the laws of physics tell you that *conservation of energy only works if* to the kinetic energies you add a potential energy term for each pair of objects.

So you need to write
kinetic energies: Ea+Eb+Ec+Ed+
potential energies: Eab+Eac+Ead+Ebc+Ebd+Ecd
=const.

One thing you can imagine that between each pair of objects there is a rubber string that acquires more tension when attracting objects are further apart. So basically this rubber string *in between* the phone and the Earth changes.