B Difference Between Potential and Potential Energy

[sophiecentaur]

An energy has the dimension of an energy, what else? Once more: The potential energy in point-particle mechanics is the potential of a force. That's what I said already in my first posting in this thread...

I still don't get what you are saying about any distinction between P and PE.
Are you prepared to accept that the (potential) Energy in a charged battery is not the Voltage (i.e. potential), but the Watt hours or that the (potential) energy in a suspended mass in a clock is mgh and not gh? How can those pairs be the same?

 

[vanhees71]

Sigh. Is it so difficult to understand what I write? So once more: The potential of the force is the same as potential energy. What else should potential energy be?

A voltage is the difference of a potential of the electromagnetic field. That's not the same as potential energy, which is clear already from the dimensions. In a battery you have no voltage though but an electromotive force, but that's another issue. The energy of a charged battery is in form of internal/chemical energy.

The potential energy in a suspended mass in a clock is given by the potential of the gravitational force on this mass, which is $V=m g z$ (with the $z$ axis pointing "upwards", i.e., against $\vec{g}=-g \vec{e}_z$), while $\Phi=g z$ is the potential of the gravitational field. The force is $\vec{F}=-\vec{\nabla} V=-m g \vec{e}_z=m \vec{g}$ and the gravitational field is $\vec{g}=-\vec{\nabla} \Phi=-g \vec{e}_z=\vec{g}$. Of course, $V=m \Phi$.

I still don't understand what your point really is!

 

[sophiecentaur]

The potential energy in a suspended mass in a clock is given by the potential of the gravitational force on this mass, which is V=mgz (with the z axis pointing "upwards", i.e., against G→), while Φ=gz is the potential of the gravitational field.

"Sigh" are you really saying anything different from me?You say that the Potential Energy depends on the mass and that the Potential is independent of mass. That's what I am saying. What are you arguing about? How did I say it wrong?

 

[vanhees71]

I'm also puzzled, what we discuss about. The only point is that you keep saying "the potential". You have to state which potential you mean, that of the force or the gravitational field. They differ by a factor of $m$ in this example.

 

[sophiecentaur]

The only time I use the term "Potential" is when referring to a unit mass / charge. I think I've been consistent over this thread at least. When using the term "Field", I assume that it's force per unit Mass / Charge.
In " the Sun's Gravitational Potential Well" diagrams, I wouldn't expect the y-axis to be different, depending on what mass of planet we're discussing.

 

[vanhees71]

Well, it would have helped to clearly indicate the potential of what vector field you are talking. That's all I'm saying.