Why is potential energy negative?

In summary, the potential energy of a particle is negative because it is less than if the particle was an infinite distance from the source of the potential energy. The sign of potential energy depends on the direction of work done on or by the object, and in the case of an attractive force, the work is negative. This is commonly seen in objects near the Earth's surface, where the positive value for increasing height is actually the difference between two values of absolute (negative) potential energy relative to infinity.
  • #1
Big L
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If a particle is moving with kinetic energy T(x) in a potential field of energy V(x), why is the total energy E(x) = T(x) - V(x), i.e. why is potential energy negative?

The way I have seen it explained is that the potential energy is less than if the particle was an infinite distance from the source of the potential energy (e.g. an electron experiencing an attractive force to its nucleus).

This does not make sense to me. If you throw a ball, the total energy of the ball is its kinetic energy plus its potential energy due to gravity.
 
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  • #2
Big L said:
If a particle is moving with kinetic energy T(x) in a potential field of energy V(x), why is the total energy E(x) = T(x) - V(x)

It's not, at least not with the usual definition of potential energy. Can you point us to where you saw this, so we can see what it's actually saying, instead of trying to guess?
 
  • #3
The sign of the Potential Energy depends upon whether work is done on or 'by' the object when it was taken to that position from infinity (or another suitable reference). With an attractive force, the work is negative (you get work out). For a repulsive force, the sign of the potential is different and you have to put positive work into bringing the object in from infinity.

The common use of Potential Energy is when considering objects near the Earth's surface. In that case, it is common to use height relative to the ground as a positive quantity so work is put in as the x value increases. This gives a positive value for increasing height. But this positive value is actually the difference between two values of absolute (negative) Potential, relative to infinity. This can be confusing until you actually do some calculations, when it will start to make sense.
 

FAQ: Why is potential energy negative?

Why is potential energy negative?

1. What is potential energy and how is it related to negative values?

Potential energy is the energy that an object possesses due to its position or configuration. Negative potential energy typically refers to the potential energy of a system in a state of lower energy compared to its reference state. This can occur when the system is bound, as in the case of a molecule or an object in a gravitational field.

2. How is potential energy calculated and why does it result in negative values?

Potential energy is calculated by multiplying the force acting on an object by the distance it is displaced. The negative value arises from the choice of reference point or state, which is usually chosen to be when the object is at rest or at a state of minimum energy. This reference point allows for a meaningful comparison of energy between different states of a system.

3. Is negative potential energy always a bad thing?

No, negative potential energy is not inherently bad. It simply indicates that the system is in a state of lower energy compared to its reference state. This can be useful, for example, in understanding the stability of a chemical bond or the motion of an object in a gravitational field.

4. Can potential energy ever be positive?

Yes, potential energy can also be positive. This occurs when the object or system is in a state of higher energy compared to its reference state. For example, when a spring is compressed, it has positive potential energy, which is converted into kinetic energy when the spring is released.

5. How does negative potential energy relate to the laws of thermodynamics?

The first law of thermodynamics states that energy can neither be created nor destroyed, but can only be converted from one form to another. Negative potential energy is a form of stored energy, and according to the first law, it can be converted into other forms of energy, such as kinetic energy. The second law of thermodynamics also applies to potential energy, as it states that in any energy conversion process, some energy will be lost as heat, resulting in a decrease in overall potential energy.

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