0

Let $W$ between two point be defined as: $$W=\int_a^b \vec{F}.\vec{dr}$$

Here $W$ is the work done between two fixed points $a$ and $b$.

Let $U$ at a point be defined as:

$$U_{\text{at } b}=\int \vec{F}.\vec{dr}+ \text{constant}$$

Here is it proper to say that potential energy $(U)$ is the work done between a fixed point $b$ and another arbitrary point. That is, can we say potential energy is work done having many degrees of freedom.

Qmechanic
  • 201,751
Joe
  • 137
  • This related question might have the answer you're looking for. What exactly is your doubt, though? – JM1 Dec 24 '17 at 08:01
  • Sorry it may not be a doubt. But I want to assure whether my final statements are indeed correct. or is there anything wrong in my reasoning. – Joe Dec 24 '17 at 08:07
  • I'm not sure what you mean by "degrees of freedom", but whether or not your statement is correct depends on what force is doing the work. If you're talking about the work done in moving a particle from $a$ to $b$ by the conservative force associated with the potential energy, it should be $W = -\Delta U = -(U_b - U_a)$. The answer to the other question gives a more detailed explanation of this and more. – JM1 Dec 24 '17 at 08:13

2 Answers2

2

Potential at a point is indeed defined relative to an arbitrary reference. Once you define this reference, you should use it for all other points in the system.

Work between two points is the difference between potentials and is not dependent on reference choice.

npojo
  • 1,498
0

Here potential energy of PARTICLES is the work done by me to put the particles one by one where they are. Potential energy of a particles is right

Keshav
  • 49