Can Elastic Potential Energy Be Negative:Detailed Facts And FAQs


We are familiar with the term elastic potential energy, which can be defined as the energy possessed by an elastic body due to the virtue of a change in its orientation.

By the definition of elastic potential energy, the orientation is responsible for its change in the shape of the body. Then can an object have a negative orientation? Then can elastic potential energy be negative if its orientation is negative? What does it mean?

The term negative potential energy is discussed in the earlier post. Now let us discuss negative elastic potential energy.

The potential energy possessed by an elastic body is given by the equation.

Where k is the elastic constant, and x is the amount of deformation.

PE=(1/2)kx2

By the above expression, the potential energy stored in the elastic body cannot be negative as the elastic constant is a quantity that is always positive, and the deformation can be increased or decreased. Still, we are taking the square value of the deformation; the square of a negative number is also positive. Thus, an elastic body can’t possess negative potential energy while dealing with the elastic potential energy in classical theory.



Image credits: Image by Peggy und Marco Lachmann-Anke from Pixabay

So if you plot the graph of elastic potential energy as a function of displacement, you will get a quadratic function, which is maximum at x=0.

A graph of Potential energy Vs. displacement

Can elastic potential energy be negative? This is a question with lots of confusion; this can be answerable by considering Schrodinger’s cat’s very famous quantum theory.

Schrodinger’s cat says that any potential energy is free to accept the arbitrary constant, which does not change its physical entity.

For every elastic body, we need to do the work to make them stretch or compress. The work done on the body is responsible for the amount of deformation of the body.

In quantum mechanics, the reference zero energy state-level always balances the change in potential energy and kinetic energy. At that instance, the elastic potential energy after stretching can be negative.

So it is crucial to choose a system to describe a physical quantity as negative or positive.

When can elastic potential energy be negative

There is a contradiction for the above statement; in some particular materials like spring, the elastic potential energy be negative.

When the spring resists itself stretching, then the potential energy stored inside the spring can be negative.

Stretching and compressing is the leading property of the spring. A spring is compressed when an external force is applied to it. A compressed spring must regain its original shape by stretching because an elastic force is a restoring force.

But, when spring is restricted to regain its original shape, the potential energy stored in the spring becomes negative.

Another consequence that may cause elastic potential energy to be negative is when the reference point possesses more potential energy than the actual point where the elastic body is located; then, the elastic body possesses the negative potential energy.

How can elastic potential energy be negative

The reference point energy plays a vital role in the negative potential energy. At the reference point, every object possesses a certain amount of potential energy. Considering the reference point, we can get the answer for how can elastic potential energy be negative.

can elastic potential energy be negative
An illustration to show how can elastic potential energy be negative

The elastic body compresses only when an external force is triggered on them. If the elastic body is compressed and it makes certain displacement from its original position below the reference point energy, the potential energy stored after compressing the body will be negative.

Frequently Asked Questions

What are the differences between elastic and gravitational potential energy?

Elastic and gravitational potential energy are the two types of potential energy; there are some differences between them, listed in the below table.

Elastic Potential EnergyGravitational Potential Energy
The object influences elastic potential energy due to elongation or compression.Gravitational potential energy is influenced by the object which is placed vertically.
Elastic potential energy is unaffected by the object’s height and mass.Gravitational potential energy is primarily influenced by the height at which the object is placed and the mass that the object possesses
Elastic potential energy depends on the displacement, which defines the amount of compression and elongation.Gravitational potential energy is not disturbed by the displacement when the object moves horizontally. But if the object is moving vertically against gravity, the amount of displacement is considered height.
In order to explain negative elastic potential energy, along with the zero-point energy, the quantum theory has to be involved in the process.The zero-point state is large enough to explain the negative gravitational potential energy as the center of mass in the gravitational field is considered the reference point.

Does negative potential energy affect the elasticity of the material?

Elasticity depends only on the nature of the material, like how much the body is compressed or elongated.

When the body is stretched or compressed, the potential energy is maximum as long as the body is in a deformed state. If you keep stretching or compressing it, the body never stretches or compresses when it reaches its saturation level. So the elasticity is not affected by the negative or positive potential energy.

The elastic potential energy increases quadratically; why?

Elastic energy is a type of energy that varies with elongation and compression.

The property of not being constant is due to its nature. For an elastic body, if you apply a small force to exert motion, there will be stored energy which causes double pull-back distance on the elastic body. So for a slight pull, the body travels double the distance; this is responsible for the quadratic increase of elastic potential energy.

Does the stiffness of an elastic body affect the elastic potential energy?

Yes, the stiffness and potential energy are two proportional quantities.

If an elastic body is stiffer means it is pretty harder to compress or stretch it. In order to stretch the stiffer body, more force has to be exerted on the body. It means that the stored potential energy is more. Hence it is clear that stiffness affects the potential energy. Whenever the stiffness is more, the elastic body has more potential energy.

Does the elastic potential energy is conserved?

The elastic potential energy changes its form after the application of external force. Sometimes the potential energy is lost due to the release of heat caused by the work.

Since the application of external agency causes the potential energy to change its form to kinetic energy, the total energy will be conserved because kinetic energy and wok always compensate for the loss of potential energy. Hence even though elastic potential energy is non-conservative, the total elastic potential energy is conserved.

Keerthi Murthi

I am Keerthi K Murthy, I have completed post graduation in Physics, with the specialization in the field of solid state physics. I have always consider physics as a fundamental subject which is connected to our daily life. Being a science student I enjoy exploring new things in physics. As a writer my goal is to reach the readers with the simplified manner through my articles. Reach me – keerthikmurthy24@gmail.com

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