Can Potential Energy Be Negative:Detailed Facts,Examples And FAQs

Generally, think about can a body possess negative energy? If yes, then what is meant by negative energy and is it possible to get negative energy?

The total energy of a system can be negative if the magnitude of potential energy is greater than the magnitude of the kinetic energy. Knowing this, a question now arises: Can potential energy be negative? The answer to this question is given in detail in this article.

How can potential energy be negative

The negative potential energy is a relative concept depends on the frame of reference.

The potential energy can be negative when the body is kept at the reference-point possessing zero energy. If the object is kept below the earth’s surface, it possesses negative potential energy.

Let us consider an object at three different heights. If A is a point below the earth’s surface, then B is the point on the earth’s surface. C is the point above the earth’s surface. Now the object is at point B; since point B is on the earth’s surface, it has zero potential energy.

can potential energy be negative
Illustration to show potential energy can be negative

When the object is lifted and reaches point C, it has the maximum potential energy because of its height. As long as the object is at point C, its potential energy will be maximum. Suppose the object falls back to point B, its potential energy decreases, and I gain becomes zero.

If the object at B falls to point A, which is below the earth’s surface, the object possesses some potential energy. The potential of the object at point A is negative because the reference energy below the earth’s surface is zero. So we can say that the work done by the gravitational field brings the mass from infinity to the earth’s surface, the potential energy is negative. Similarly, when a ball is thrown into the air, the ball acquires positive potential energy as the ball is moving against the gravitational force.

Image credits: Image by OpenClipart-Vectors from Pixabay

As the ball falls back to the ground due to the gravitational attraction, the kinetic energy possessed on the object is maximum. Ideologically we can say that now the ball has acquired negative potential energy.

Can spring potential energy be negative

How can potential energy be negative in spring? This is a fundamental question that arises while talking about the spring since the total energy of the spring is always positive.

  • A spring can possess negative potential energy depending on the position of the spring.
  • Spring possesses potential energy when it is compressed or elongated.

Generally, a spring has two extreme positions and an equilibrium position. Spring possess zero potential energy at the extreme position.  

If we place the spring in the reference zero point as the equilibrium position, the spring possess negative potential energy as

Where; k is the spring constant; x is the displacement of the spring. However, if the spring is released from the compression, it regains its original position. During the process, spring lost its potential energy. When the spring comes back to its initial position, it regains its lost potential energy. But there will be a slight difference in the potential energy.

can potential energy be negative
Illustration to show spring potential energy be negative

Now the change in the potential energy be

In order to compensate for the potential energy, we are free to add a constant. Let V0 be a constant; then the potential energy will be

From the above expression, we know that even though the spring has negative potential energy, the change in the spring’s potential energy is always positive, because the force corresponding to change in the potential energy of the spring is equal to the simple harmonic motion.

Can gravitational potential energy be negative?

If the body has to pass below the reference energy level or it is kept at a greater height away from the gravity, the gravitational potential energy is negative.

Suppose the body is moving at a certain height; gravity wants to attract the body towards it. But the body needs a certain amount of gravitational potential energy to travel against gravity by making the work done by the gravity negative. Hence the gravitational potential energy becomes negative as the body travels towards infinite height.

Normally, when the body is lifted up either it possesses zero or maximum amount of potential energy. But in case of gravitational potential energy, the work done by the gravity will always be negative.

By the equation of gravitational potential energy,

Similarly, PE2 = -Fd cosθ = mgh

The PE1 and PE2 both are in a different frame of reference, so the gravitational potential energy is both positive and negative value.

Frequently Asked Questions

Does the negative potential energy affect the kinetic energy?

The kinetic energy is possessed by a moving body due to work done on the body by the potential energy.

The kinetic energy is always positive because the quantity involved in the kinetic energy, i.e., mass and velocity, are always positive because the square of any number is always positive. Hence the kinetic energy remains positive, even if the potential energy negative.

What caused the negative work done on the object?

The work done by the object is said to be negative only when the object is displaced against the applied force.

The friction force is one reason for the negative work done. The friction force is always retards the motion in the opposite direction of the applied force, which causes the work done on the object to be negative. Another reason is the force of gravity; if the object is moving away from the gravitational pull, then gravity causes work done on the object negative.

Give examples of negative potential energy.

Some of the examples for negative potential energy are listed below:

  • If we consider the reference point as a table, then the book on the floor has negative potential energy.
  • The planets on the solar system possess negative potential energy.
  • A rat in a hole inside the ground possesses negative potential energy.

What is meant by negative spring potential energy?

The negative spring potential energy is defined in terms of direction of the restoring force and the applied force.

In an elastic body, the work done on the object caused by the restorative force is opposite to the force of application, then stored potential energy is said to be negative spring potential energy.

What factor affects the spring potential energy?

The potential energy of the spring is affected by the factors such as;

  • Deformation – compression or elongation of the spring gives the how much potential energy spring has acquired.
  • Spring constant –the force exerted to stretch or compress the spring is called spring constant, which always has a positive value, which influences the potential energy.
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