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Absolute potential energy is defined with reference to infinity.

There is a disconcerting aspect of potential energy. In the earlier module titled “Potential energy”, we defined “change in potential energy” – not the potential energy itself!

We assigned zero gravitational potential reference for Earth’s gravitation to the ground level and zero elastic potential energy to the neutral position of the spring. The consideration of zero reference potential energy enabled us to define and assign potential energy for a unique position – not to the difference of positions. This was certainly an improvement towards giving meaning to absolute value of potential energy of a system. In this module, we shall broaden the reference and aim to define absolute potential energy for a particular configuration of a system in general.

Reference at infinity

The references to ground for gravitation or a neutral position for a spring are essentially local context. For example, gravitation is not confined to Earth system only. What if we want to refer potential energy value to an object on the surface of our moon? Would we refer its potential energy in reference to Earth’s ground?

We may argue that we can have moon’s ground as reference for the object on its surface. But this will also not serve purpose as there might be occasions (as always is in the study of the motions of celestial bodies) where we would need to compare potential energies of systems belonging to Earth and moon simultaneously. The point is that the general concept of potential energy can not be bounded to a local reference. We need to expand the meaning of reference, which is valid everywhere.

Now, we have seen that change in potential energy is equal to negative of work by conservative force. So existence of potential energy is related to existence of conservative force. Can we think a situation in which this conservative force is guaranteed to be zero. There is no such physical reference, but there is a theoretical possibility of such eventuality. Let us have a look at the Newton’s law of gravitation (this law will be discussed subsequently). The force of gravitation between two particles, “ m 1 ” and “ m 1 ” is given by :

F = G m 1 m 2 r 2

As r , F 0 . As there is no force on the particle, there is no work involved. Hence, we can conclude that a system of two particles at a large (infinite) distance has zero potential. As infinity is undefined, we can think of system of particles at infinity, which are separated by infinite distances and thus have zero potential energy.

Theoretically, it is also considered that kinetic energy of the particle at infinity is zero. Hence, mechanical energy of the system of particles, being equal to the sum of potential and kinetic energy, is also zero at infinity.

Infinity appears to serve as universal zero reference. The measurement of potential energy of any system with respect to this zero reference is a unique value for a specific configuration of the system. Importantly, this is valid for all conservative force system and not confined to a particular force type like gravitation.

Questions & Answers

how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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what is energy?
James Reply
can anyone tell who founded equations of motion !?
Ztechy Reply
n=a+b/T² find the linear express
Donsmart Reply
Quiklyyy
Sultan Reply
Moment of inertia of a bar in terms of perpendicular axis theorem
Sultan Reply
How should i know when to add/subtract the velocities and when to use the Pythagoras theorem?
Yara Reply
Centre of mass of two uniform rods of same length but made of different materials and kept at L-shape meeting point is origin of coordinate
Rama Reply
A balloon is released from the ground which rises vertically up with acceleration 1.4m/sec^2.a ball is released from the balloon 20 second after the balloon has left the ground. The maximum height reached by the ball from the ground is
Lucky Reply
work done by frictional force formula
Sudeer Reply
Torque
Misthu Reply
Why are we takingspherical surface area in case of solid sphere
Saswat Reply
In all situatuons, what can I generalize?
Cart Reply
the body travels the distance of d=( 14+- 0.2)m in t=( 4.0 +- 0.3) s calculate it's velocity with error limit find Percentage error
Clinton Reply
Explain it ?Fy=?sN?mg=0?N=mg?s
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Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
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