Is it possible to have negative potential energy

As I see it, if the body A never had any potential energy to begin with, then this not present energy cannot change into kinetic energy, otherwise we would be creating kinetic energy out of nothing. Why does it make any physical sense to say that the body is in "potential energy debt", ie the potential energy is reduced to negative when it was zero to begin with?

It's not a good idea to bring in the infinities which arise when modeling objects as classical points. It's well known and understood that things like point charges and point masses are extremely useful tools in classical physics, but lead immediately to nonphysical infinities if you ask the wrong questions about them. Nobody says this. If you adopt the "grain" picture I mentioned above, however, you're free to set the zero point wherever you wish, at least in the context of non-relativistic physics.

You are assigning a bit too much physicality to potential energy, I think. The physical thing is the potential energy difference between two points in space, not the actual value of the potential energy at any particular point.

Your mistake is in assuming that the value of potential energy is relevant, like when you say that if two bodies don't interact there should be zero potential energy. In fact, what matters is not how much potential energy a body has, but whether it could have less by moving somewhere else.

In the standard convention, the gravitational potential between two bodies is negative, and by moving closer this potential energy will be more negative; the energy lost is converted into kinetic energy. As the objects move farther and farther away their potential energy increases towards zero, but this is not very important; what matters is that the curve becomes flatter.

That is, they would lose less potential energy by moving a fixed distance, so the force is smaller. So what value does the potential energy have now?

Is it negative? Yes it is. What does that mean? It only means that the ball will rather want to be in this hole than at the floor. In the same way that it rather wants to be at the floor than on the shelf. The value of potential energy is irrelevant. Only the difference is important. Because objects always want to move towards a situation of lower potential energy.

The scale just happens to be in the negative range in the first case. And that is irrelevant and not important. It seems you are excluding conservation of energy considerations from your question. Thus the potential energy may be in debt but the kinetic energy is not, and the total energy remains constant. There's a few things here.

First off, your approach of having the potential be zero when the distance between the object is zero, and infinite as it approaches infinite distance has a flat: this would make the potential energy of any two objects at any finite distance infinite.

In the astronomical world, there's not always an obvious place to put this reference point. When it comes to activities on the Earth, we often put the reference point at the ground, but that reference is terribly Earth-centric. For astronomical work, that's not convenient. So the interesting question is why we put the reference point on the ground for Earth based activities.

The trick is to choose a convenient point. If we want to convert any more of the gravitational potential energy into kinetic energy, we need to dig a hole. A lot of extra terms in the equations cancel out by doing so. When it comes to astronomy, we're far less interested in things hitting the surface of Earth and when they do, they tend to dig their own holes! The surface of the Earth is no longer a convenient reference point. Because it's the one reference point that every object in the system can agree with.

The side effect is that all potential energies here are negative, as you noticed. This is quirky, for sure, but for general astronomical uses, it's an acceptable quirk. The numbers are just tools in a model. It is up to us to understand how they should work and what they should mean. A kg hiker ascends from the base to the summit. What is the gravitational potential energy of the hiker-Earth system with respect to zero gravitational potential energy at base height, when the hiker is a at the base of the hill, b at the summit, and c at sea level, afterward?

The altitudes of the three levels are indicated. First, we need to pick an origin for the y -axis and then determine the value of the constant that makes the potential energy zero at the height of the base. Then, we can determine the potential energies from Figure , based on the relationship between the zero potential energy height and the height at which the hiker is located.

Besides illustrating the use of Figure and Figure , the values of gravitational potential energy we found are reasonable. The gravitational potential energy is higher at the summit than at the base, and lower at sea level than at the base.

Gravity does work on you on your way up, too! It does negative work and not quite as much in magnitude , as your muscles do. But it certainly does work. Similarly, your muscles do work on your way down, as negative work. The numerical values of the potential energies depend on the choice of zero of potential energy, but the physically meaningful differences of potential energy do not. Check Your Understanding What are the values of the gravitational potential energy of the hiker at the base, summit, and sea level, with respect to a sea-level zero of potential energy?

In Work , we saw that the work done by a perfectly elastic spring, in one dimension, depends only on the spring constant and the squares of the displacements from the unstretched position, as given in Figure. Therefore, we can define the difference of elastic potential energy for a spring force as the negative of the work done by the spring force in this equation, before we consider systems that embody this type of force. The potential energy function corresponding to this difference is.

Then, the constant is Figure is zero. Other choices may be more convenient if other forces are acting. When the spring is at its unstretched length, it contributes nothing to the potential energy of the system, so we can use Figure with the constant equal to zero.

The value of x is the length minus the unstretched length. Calculating the elastic potential energy and potential energy differences from Figure involves solving for the potential energies based on the given lengths of the spring.

When the length of the spring in Figure changes from an initial value of Using 0. A simple system embodying both gravitational and elastic types of potential energy is a one-dimensional, vertical mass-spring system. This consists of a massive particle or block , hung from one end of a perfectly elastic, massless spring, the other end of which is fixed, as illustrated in Figure.

Assuming the spring is massless, the system of the block and Earth gains and loses potential energy. We need to define the constant in the potential energy function of Figure.

Note that this choice is arbitrary, and the problem can be solved correctly even if another choice is picked. We must also define the elastic potential energy of the system and the corresponding constant, as detailed in Figure. The equilibrium location is the most suitable mathematically to choose for where the potential energy of the spring is zero.

Therefore, based on this convention, each potential energy and kinetic energy can be written out for three critical points of the system: 1 the lowest pulled point, 2 the equilibrium position of the spring, and 3 the highest point achieved. We note that the total energy of the system is conserved, so any total energy in this chart could be matched up to solve for an unknown quantity. The results are shown in Figure. The block is pulled down an additional [latex] 5.

In parts a and b , we want to find a difference in potential energy, so we can use Figure and Figure , respectively. Each of these expressions takes into consideration the change in the energy relative to another position, further emphasizing that potential energy is calculated with a reference or second point in mind. By choosing the conventions of the lowest point in the diagram where the gravitational potential energy is zero and the equilibrium position of the spring where the elastic potential energy is zero, these differences in energies can now be calculated.

In part c , we take a look at the differences between the two potential energies. The difference between the two results in kinetic energy, since there is no friction or drag in this system that can take energy from the system.

Even though the potential energies are relative to a chosen zero location, the solutions to this problem would be the same if the zero energy points were chosen at different locations. Suppose the mass in Figure is in equilibrium, and you pull it down another 3. Does the total potential energy increase, decrease, or remain the same? View this simulation to learn about conservation of energy with a skater! Build tracks, ramps and jumps for the skater and view the kinetic energy, potential energy and friction as he moves.

You can also take the skater to different planets or even space! Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics.

It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. With respect to both gravity and electromagnetism, to the best of my understanding potential energy is added or subtracted from a system based on the distance between two objects such as charged or massive objects. It can clearly be seen that this is always negative. The key thing is that the absolute value of potential energy is not observable; there is no measurement that can determine it.

The only thing that can be measured is differences in potential energy. So actually there is a redundancy in the equation above: if I add any constant to it, the difference in potential energy for two given separations is the same. The idea of redundancies in physical descriptions is very important in theoretical physics, and is known as gauge invariance. EDIT: following some comments by the original poster, I've added some more to this answer to explain the effect on total energy of a system of attracting objects at very short distances.

We can rearrange this inequality to give a condition on the radius for negative total energy:. The distance at which the Newtonian energy becmes negative is less than the Schwarzschild radiusif two point masses were this close they would be a black hole. In reality we should be using GR to describe this system; the negative energy is a symptom of the breakdown of our theory.

The classical electron radius is the scale at which quantum fluctuations must be taken into account, so again the negative energy is a symptom of the breakdown of the theory.

Definition : The change in potential energy of the system is defined as the negative of work done by the internal conservative forces of the system. By this definition we can conclude that we are free to choose reference anywhere in space and define potential energy with respect to it. For ex : Consider a system of 2 oppositely charged particles which are released from rest.

Under the action of their mutual electrostatic forces they move towards each other. The internal electrostatic forces are doing positive work which results into the decrease in potential energy of the system.