# Potential Energy and the Conservation of Energy

Would I be right in saying the following:
Potential energy arises from the conservation of energy. To lift a mass you must exert a force counteracting the force of gravity. As it moved and a force was exerted work was done on it. As it is not moving it has no kinetic energy. Due to the conservation of energy the energy cannot be destroyed so there must be a stored type of energy.....Potential energy.

Drakkith
Staff Emeritus
Sounds good to me.

AlephZero
Homework Helper
As it moved and a force was exerted work was done on it. As it is not moving it has no kinetic energy.

This seems rather confused. Either it is moving, or it isn't. It can't be moving and not moving at the same time.

I would say potential energy has nothing to do with conservation of energy. If you have a situation where the amount of work done on something when it moves between two positions A and B does not depend on the exact path or on the speed that it moves, but only on the positions of A and B, then you can define a "potential energy function" that lets you calculate the amount of work done easily.

Gravity is a good example. If you are working close to the sirface of the earth you can assume gravity is a constant force, and define its potential energy as mgh. Or if you want to consider the inverse square law, you can use a potential energy function that is proportional to 1/r where r is the distance between two objects. (Note, 1/r was not a typo for 1/r2)

You can also define potential energy for other types of force. For example, guess why the voltage between two points in an electrical circuit is sometimes called the "potential difference"...

What I meant by that it was moved up to say a shelf then on the shelf it was not moving. Sorry

This seems rather confused. Either it is moving, or it isn't. It can't be moving and not moving at the same time.

I would say potential energy has nothing to do with conservation of energy. If you have a situation where the amount of work done on something when it moves between two positions A and B does not depend on the exact path or on the speed that it moves, but only on the positions of A and B, then you can define a "potential energy function" that lets you calculate the amount of work done easily.

Gravity is a good example. If you are working close to the sirface of the earth you can assume gravity is a constant force, and define its potential energy as mgh. Or if you want to consider the inverse square law, you can use a potential energy function that is proportional to 1/r where r is the distance between two objects. (Note, 1/r was not a typo for 1/r2)

You can also define potential energy for other types of force. For example, guess why the voltage between two points in an electrical circuit is sometimes called the "potential difference"...

How can you say potential energy has nothing to do with conservation of energy? IMO, potential energy is NECESSARY for conservation of energy. The potential energy + kinetic energy (in your gravitational situation, classically) is the total energy. Sometimes the potential is zero, sometime kinetic is zero, and sometimes neither is zero (and we can actually arbitrarily define the potential to be zero at any point).

Without potential energy, I dont think conservation of energy would not be satisfied.

cepheid
Staff Emeritus
Gold Member
How can you say potential energy has nothing to do with conservation of energy? IMO, potential energy is NECESSARY for conservation of energy. The potential energy + kinetic energy (in your gravitational situation, classically) is the total energy. Sometimes the potential is zero, sometime kinetic is zero, and sometimes neither is zero (and we can actually arbitrarily define the potential to be zero at any point).

Without potential energy, I dont think conservation of energy would not be satisfied.

Amusingly, your last sentence is a double negative. Anyway...

Potential energy only arises in the presence of conservative forces. Total energy of a system is always conserved, even when the forces present are not conservative. Perhaps you are confusing conservation of energy with conservation of mechanical energy (which requires that only conservative forces be present)?

Mechanical energy = kinetic energy + potential energy.

EDIT: AlephZero's second paragraph basically defines what a conservative force is.