# How to decide the sign of a potential

• laharl88
In summary, the individual terms in a potential have their own independent signs. When dealing with a spring potential, the sign should be positive for the displacement from the unstretched position. However, for a centrifugal force potential, the sign should be negative due to the outward force. It is important to consider the direction of the force when determining the sign of a potential, as it can greatly impact the stability of equilibrium points.
laharl88
Hi! I'm a new user of this forum, although I've been reading a few threads for a while...
Mi question is this: in rational mechanics, how do i decide the sign of a potential?
Let me explain better: in some exercises it may happen that a mass particle is subject to both gravity and, for example, the force of a spring. If by hypothesis, the two forces are always perpendicular, how should i write the potential?

V= mgy -1/2*k*x^2 or V=mgy + 1/2*k*x^2

Let me underline that this question is not trivial! In fact that mere sign can change everything, including the stability of equilibria points!
I'd be really grateful to anyone who can answer this question.
If i wasn't clear in explaining my doubts, please fell free to tell me.

In the case of spring PE, x is displacement from the unstretched position and the PE is 1/2kx² not -1/2kx².

I know that, i just want to know if the two potentials must have the same sign, or the opposite sign. Suppose, instead of a spring, the plane in which the motion happens to rotate with a constant w. In this case there would be a potential, due to the centrifugal force, given by
V1= 1/2*m*w^2*x^2
In this case, do the two potentials have the same sign or the opposite?
By the way, thanks for answering :)

laharl88 said:
I know that, i just want to know if the two potentials must have the same sign, or the opposite sign.
I guess I don't understand your question then. Each term in the potential has its own sign, independent of the other terms.

Suppose, instead of a spring, the plane in which the motion happens to rotate with a constant w. In this case there would be a potential, due to the centrifugal force, given by
V1= 1/2*m*w^2*x^2
Since the centrifugal force is outward, that potential must be negative, assuming x is the distance from the center: V = -1/2mω²x²

Just think of the force that the potential represents. The potential must always increase in the direction opposite the force.

Doc Al said:
I guess I don't understand your question then. Each term in the potential has its own sign, independent of the other terms.

Since the centrifugal force is outward, that potential must be negative, assuming x is the distance from the center: V = -1/2mω²x²

DaleSpam said:
Just think of the force that the potential represents. The potential must always increase in the direction opposite the force.

Ok,i think i understand now, thanks a lot guys :)

## What is the definition of potential?

Potential is a measure of the energy of a system, specifically the energy of a particle or a collection of particles in a given location. It is typically denoted by the symbol V and is expressed in units of joules (J) or electron volts (eV).

## How is potential related to the sign of a charge?

The sign of a potential is determined by the sign of the charge that creates it. A positive charge will create a positive potential, while a negative charge will create a negative potential. This is because like charges repel each other and opposite charges attract, so the energy of a system will be higher when there are like charges and lower when there are opposite charges.

## What is the difference between positive and negative potential?

Positive potential represents a higher energy state, while negative potential represents a lower energy state. This is because a positive potential is associated with like charges, which repel and require more energy to overcome, while a negative potential is associated with opposite charges, which attract and require less energy to overcome.

## How can you determine the sign of a potential experimentally?

The sign of a potential can be determined experimentally by measuring the direction of the electric field. A positive potential will create an electric field that points away from it, while a negative potential will create an electric field that points towards it. Alternatively, the sign of a potential can also be determined by measuring the direction of the force on a test charge placed in the potential field.

## Can the sign of a potential change?

In most cases, the sign of a potential remains constant. However, in some situations, the sign of a potential may change due to the presence of different charges or a change in the distance between charges. For example, if a positive charge moves closer to a negative charge, the potential between them will become more negative.

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