Difference In Potential Energy

[Bashyboy]

Hello,

Whenever I read about potential energy, whether its in the case of gravitational, spring, or electric, I invariably come across the phrase, "...only differences in potential energy matter," and, "...the initial potential energy is arbitrarily chosen to be zero," or phrases to that effect. Why is it that differences in potential energy only matter? Why is our choice of the zero configuration arbitrary?

EDIT: Also, the same goes for electric potential.

 

[jtbell]

Consider gravitational potential energy. Assume the gravitational field is practically uniform, that is, we don't move far enough that the 1/r² thing becomes significant.

A table top is about 1 m above the floor. The ceiling of my room is about 3 m above the floor.

1. Define PE = 0 at the floor. Then a 1 kg object on the table top has PE = mgh = 9.8 J. The same object at the ceiling has PE = 29.4 J. If I drop the object from rest at the ceiling, when it hits the table it has kinetic energy KE = PE(ceiling) - PE(table top) = 29.4 - 9.8 = 19.6 J.

2. Define PE = 0 at the table top. Then the 1 kg object has PE = 19.6 J at the ceiling (which is 2 m above the table top). If I drop the object from rest at the ceiling, when it hits the table it has KE = PE(ceiling) - PE(table top) = 19.6 - 0 = 19.6 J.

3. Define PE = 0 at the ceiling. Then the object has PE = -19.6 J at the table top, which is 2 m below the ceiling. If I drop the object from rest at the ceiling, when it hits the table it has KE = PE(ceiling) - PE(table top) = 0 - (-19.6) = 19.6 J.

4. (Exercise) Define PE = 0 at the floor of the basement, which is 4 m below the floor that we've been talking about so far. For the same 1 kg object, what are PE(ceiling) and PE(table top), and if we drop it as before, what is its KE when it hits the table top?

 

[Khashishi]

The answer depends on how fundamental you want to go. The zero point of potential energy is important when you consider annihilation and creation of particles and general relativity. However, in classical mechanics, potential energy is pretty much just a book-keeping mechanism. You only consider changes in states of objects, and you never really consider the destruction of the object altogether.

If you destroy a spring and you want to know how much energy comes out in the pieces, then the potential energy certainly matters!