Change in work done is or is not equal to the change in potential energy?

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  • Potential energy is just stored energy. That's all you need to know.

  • Work is added or spent energy. Another quantity that can happen to equal potential energy stored. But not always; only if no energy is lost on the way. They are two different quantities.

Potential energy happens to be "the negative of the work done by conservative forces", and this is how you can store potential energy, yes. But don't confuse the two; have a look at this example:

  • While a ball lies on a shelf, there is potential energy stored. No work is being done at this moment.
  • Work was done in order to get the ball up there. You need to the add energy (in the form of work for example) which you want to store.
  • Work will be done when you "release" this system - meaning, when you let the ball fall down. Then gravity is doing work on the ball, sucking out the energy there was stored in the ball/Earth system.

This is why you can read that work done by conservative forces equals the potential energy they can store. Because for a conservative force, none of the energy is "lost"; it is all stored.

Work done by conservative forces and potential energy can therefore be thought of as equivalent and equal. But keep them seperated in your thinking as different terms and different physical quantities.

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Esha Mukhopadhyay
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Esha Mukhopadhyay

Updated on April 03, 2020

Comments

  • Esha Mukhopadhyay
    Esha Mukhopadhyay over 3 years

    what is potential energy? is it the work done by external forces or internal forces on a body? i searched on the net and it said the the negative of the work done by conservative forces is potential energy. not only that it also said that no energy left or entered the system where there was only potential energy. how is it possible? my textbook on electrostatic forces says that if a test charge is moved without changing the kinetic energy in a constant electric field then the work done according to work energy theorem is 0. then does that mean the change in potential energy is not equal to work done. i m so confused please help

  • Esha Mukhopadhyay
    Esha Mukhopadhyay over 6 years
    i understood clearly what u meant to say. let me repeat it nd please correct me if I am wrong. potential energy is the energy which is present in a body due to its location. be it a spring or a body in a gravitational field or an electrical field. change in potential energy occurs when the internal forces do work. as a result it is the negative of the work done by external conservative forces. this is why whenever there is only potential energy present then no energy is given out or taken in. but i still m confused about the part of change in potential energy
  • Esha Mukhopadhyay
    Esha Mukhopadhyay over 6 years
    how can we change potential energy without changing kinetic energy? not only that how can a change in potential energy result in no absorption or release of energy?
  • Esha Mukhopadhyay
    Esha Mukhopadhyay over 6 years
    nd as my book says that the charge is moved without change in kinetic energy it bcoms more incomprehensible. of course if its moving then there will b a change in mechanical energy. wudnt it b?
  • Steeven
    Steeven over 6 years
    @EshaMukhopadhyay "potential energy is the energy which is present in a body due to its location." Almost, just be careful when saying "in a body". Elastic potential energy in a spring is stored in the body of the spring. (Same for e.g. chemical potential energy.) But gravitational (as well as e.g. electric and magnetic) potential energy is present because two object pull in each other, so it is not stored in one of them alone. It is rather stored in the "system" or "field" between them. A small detail, maybe, but good to be aware of.
  • Steeven
    Steeven over 6 years
    @EshaMukhopadhyay "* change in potential energy occurs when the internal forces do work.*" Yes, internal forces within the system (gravity is an internal force within the ball/Earth-system). "as a result it is the negative of the work done by external conservative forces." Yes, and the reason is pretty obvious: the potential energy only exists because the conservative force (like gravity) pulls. If it didn't there would be no tendency for the object (like the ball) to move when released, and then no energy would be seen as stored.
  • Steeven
    Steeven over 6 years
    @EshaMukhopadhyay "this is why whenever there is only potential energy present then no energy is given out or taken in." Well, yes if you by "only" mean that there are no external forces. If I lift a book to a shelf, then I am doing work (corresponding to gravity doing negative work) on the book in order to add potential energy to this book/Earth-system by seperating them further.
  • Steeven
    Steeven over 6 years
    @EshaMukhopadhyay "how can we change potential energy without changing kinetic energy?" When lifting a book, we do indeed change the kinetic energy along the way. But after moving it, it is staying still and stationary on the shelf. No change in kinetic energy from start to end position. Potential energy has not really gotten anything to do with kinetic energy - it just often happens to convert to it, when released (the ball speeds up while potential energy is reduced, when it falls from the shelf), but potential energy could also very slowly be converted into e.g. heat or work or so.
  • Steeven
    Steeven over 6 years
    @EshaMukhopadhyay "how can a change in potential energy result in no absorption or release of energy?" Doesn't a book falling from a shelf release energy? Potential energy is converted into kinetic. When I'm lifting a book to a shelf, I am also doing work on it; I add energy which is then stored as potential. losing or gaining one type of energy will always come from or go to another type of energy (no energy is every created or disappearing; it is only ever converted from one type to another according to the 1st law of thermodynamics.)
  • Steeven
    Steeven over 6 years
    @EshaMukhopadhyay "nd as my book says that the charge is moved without change in kinetic energy it bcoms more incomprehensible. of course if its moving then there will b a change in mechanical energy. wudnt it b?" A satellite drifting through outerspace experiences no change in any form of energy. Its kinetic energy is never changed or converted - it just continues at constant speed. Same for an electric charge. After it is speeded up, it only slows down again if an electric field pushes it to stop later on. And then that field is doing (negative) work on it. Otherwise it doesn't stop.
  • Esha Mukhopadhyay
    Esha Mukhopadhyay over 6 years
    thanx for ur detailed explanation. i thoroughly understand it now
  • Steeven
    Steeven over 6 years
    @EshaMukhopadhyay You are very welcome; glad I could help.