The concept of potential energy is best understood with examples, so let me give an example:    There lies a mass of $1~\mathrm{kg}$ on ground, I lift the mass to a height of $1~\mathrm m$. Since I have done a work (force times displacement) against the gravity, therefore, I have given potential energy to the mass.    Well, how can I know that the mass has gained any energy, if you say that “Let it fall and it will gain kinetic energy”. This argument shows that potential energy that I gave to the mass during the lift is now converting into kinetic energy, but I see it as the gravity doing work on the mass and therefore its kinetic energy is increasing.    Gravity is a force, so it can provide kinetic energy to a body by setting it in a motion and that’s exactly what’s happening in the above argument. Just imagine that I lifted that mass of $1~\mathrm{kg}$ and at when I reached to a height of $1~\mathrm m$ I just switched off the gravity. Now, will the potential energy convert into kinetic energy if I let the mass to fall (the word fall here refers only to my leaving it there). I think no, it will just remain there. So, it can be argued that energy-conservation is violated and hence the thought experiment is sloppy, but this contradiction of energy-conservation has come only from axiom of potential energy (the axiom that working against a field lets the object to gain some kind of energy called potential energy) So, why there is a concept of potential energy when it can be understood as the field is doing the work and supplying the kinetic energy rather than potential energy is getting converted to kinetic energy?    A Second View of the Situation: Let's take magnetic field  instead of gravitational field, imagine that I have two wires with current flowing in both of them in same direction, like this  According to the principles of magnetism, the two wires will attract each other, now if I take the violet wire far away (all I mean is doing the work against the attractive field) and then suddenly switching off the current in the red wire, would my violet wire accelerate towards the red one? If not where the potential energy has gone which I supplied it during taking it away.    We can also imagine this situation using electrostatic field (as @FGSUZ has said in his comment) by using parallel plate capacitors. We can do same thing in this setup too.     Thank you. Any help will be much appreciated.    Explanation of why I don’t think that my question is a duplicate: The question which was suggested to me as of which mine is a duplicate, I think that question is basically on work-energy theorem, there OP’s main problem was why potential energy came when work is defined as change in kinetic energy. My question is why do we say that potential energy converts into kinetic energy when it is the force(the gravitational force) which is supplying the kinetic energy?    Another defense against duplication: The question, to which my question is seemed to be of duplicate, says clearly in the last second paragraph above the EDIT as  "Secondly, the force done by us (the external agency), is along the direction of the displacement, the work done is positive and so the change in kinetic energy should be positive (by the work energy theorem?)" It says clearly that the OP wants to understand things in terms of energy theorem and doubts within it. My question deals with the interpretation of conversion of PE into KE and the work done by the field to supply KE.
122843
So the title's a bit irrelevelant. And I'm having a tough time thinking how to describe my doubt but I'll try my best. Apologies if it is vague, do let me know in the comments.   So I just finished reading the work energy theorem and was moving on to the concept of potential energy (which my book explains poorly, or I'm missing something).   I understand that by the work energy theorem the change in the kinetic energy of a body is the work done by an external force force on the body. ✓Got it, the change in the kinetic energy of a body is equal to the work done by the net force  So I moved on to potential energy, where my book tries to explain stuff by starting off with an example in which we're elevating the book of mass $m$ by doing work $mgh$ on it, where $h$ is the height to which it is raised. My first doubt is, since the force we applied is $mg$ (equal to the gravitational force of attraction in magnitude yet opposite in direction), the resultant force on the book is 0. Since the resultant force is zero, the work done by the resultant force on the book should be 0, and there should be no change in the kinetic energy.   Secondly, the force done by us (the external agnecy), is along the direction of the displacement, the work done is positive and so the change in kinetic energy should be positive (by the work energy theorem?)  What am I messing up? Mixing the two concepts (potential energy and work energy theorem)? Yet after the work we do, potential energy increases, not the kinetic energy? What am I confusing?  Edit   So the given answers helped me understand where I was going wrong (somewhat). The change in the kinetic energy of a particle is equal to the work done on it by the net external force (if the particle is the system)   Now I'm having trouble interpreting the work energy theorem for a system of particles. A book explains it by considering a system of two charges (one positive and one negative; attracting each other). It says:     Because of mutual attraction, the particles are accelerated towards each other and the kinetic energy of the system increases   Firstly, how can we consider something which isn't fixed as our system (the charges move...).   Secondly, there is no net force on the system, so how is the kinetic energy even increasing.   PS: I'm still all confused about potential energy. Before my book starts about potential energy it goes on to talk about the work energy theorem for a system of particles, and that's where I'm confused now.
25589
From Wikipedia: The work done by a constant force of magnitude F on a point that moves a displacement d in the direction of the force is the product: $$W = Fd.$$  If I lift some object from a ground, the force to be put in above equation is the gravitational force $mg$.   But while I am moving the object upwards, against the gravity, I must pull the object with greater force than $mg$, right? So the net force is $F_{myforce}-mg$ which results in object being lifted. But this is not the case. Why? Does it matter how strongly I pull the object?  What work will I do if I move this object in absence of gravity (in space)? Will work done be zero or not?
69037
I (as a middle-school student) was wondering how virtual particles even conserve energy of the entire system? I don't mean just the particle's energy, but conservation with respect to the surroundings?  Let me explain more, Einstein proved that $E = mc^2$ and equivalently, we can say $m = \frac{E}{c^2}$ . We however know mass causes curvature in space-time (gravity well). Now that statement being completely valid we can use Quantum Fluctuation, implying energy and time can be related by the relation:  $\Delta{E}\Delta{t}\approx\frac{\hbar}{2}$ and by that simple relation we can make the following points:   As the energy increases, the time allowed to be "borrowed" decreases, before it gives it back to the universe. As time increases, the energy allowed to be "borrowed" decreases.    These are completely satisfactory points I've made, I believe.  Now, I have read that the vacuum is filled with constantly bubbling virtual particles that get created from the energy "borrowed" by the above relation and is destroyed again, which satisfies the energy conservation laws.   This seems to imply that  in the short time the virtual particle exists, they must have a very small mass which is: $m_{1} = \frac{\Delta{E}}{c^2}$ and using basic classical mechanics rather than GR (for sake of simplicity) we calculate that the gravitational force mediated by this short-lived virtual particle;  $F_{g}= G\frac{m_1 * m_x}{r^2}$   where $m_x$ is an particle\mass in question. Nevertheless since we know the force set upon an object moves the object in a direction, we can say it would increase its kinetic energy by this factor: $F_g = \frac{1}{2}mv^2$ which is equal to $G\frac{m_1 * m_x}{r^2} = \frac{1}{2}mv^2$.  Surely, this implies that every time quantum fluctuations happen, energy of real-particles\masses increases and therefore violates energy conservation, but what prevents this violation from taking place?  If virtual particles are not really present and interact with objects like I thought, how can Hawking radiation (currently a large concept in black hole physics) then be accepted in physics community?
51551
Since Newtonian gravity is analogous to electrostatics shouldn't there be something called negative mass? Also, a moving charge generates electric field, but why doesn't a moving mass generate some other field?
88422
In all the places I've looked kinetic energy is derived from the definition of work, but I don't understand how the definition of work was developed with out the concept of kinetic energy. My question really is:  What is the logic behind the definition of  without referring to kinetic energy?  OR  What is the logic behind the definition of  without referring to work?
16956
First of all, I have a confusion about the definition and idea of Tension. For example, in my Physics Textbook, the idea of tension is written like this: &quot;Let's say there is a wire with a cross-section area of A and its length is $L_o$. If I hang the wire from a point and hang a weight of W on the other end of the wire, it will generate a repulsive force of T. This T is called the Tension Force.&quot; For me, this only explains to me what force will we call tension force, but it doesn't quite explain to me what is exactly this Tension force or where it originates from. Also, I have been doing pulley problems (Figuring out the acceleration of weights hanging from pulleys)  by first labeling all of the tension forces by $T_1$, $T_2$, and then doing some math with them to get my answer. But It bugs me that I am using these tension force values without even knowing where they came from or what they are. My idea was, maybe Tension force comes from the intermolecular bonds between the molecules of the rope, rubber or wire, etc. But even then, I have some different situational questions. For example:  Why you can't push a rope, copper wire against a wall?  What happens when I pull on two ends of a wire with 2 different forces?  Does the force increase proportionally to the applied force? Why does the wire break after a certain amount of force is exceeded.?  Does the idea of tension apply to everyday objects,(for example, a coffee mug, glass pane, etc). If it does, can I use something like a heat map or 3D equation to describe the tension in every point of the object? [Edit: more concisely, is there a mathematical way to show the various amounts of tension forces on a 2D (like a metal sheet) and 3D objects (like a football ) instead of a 1D object(like a string)].  If I take a metallic object like a paperclip or a thin wire. I can bend It multiple times and it eventually breaks into two pieces. I used to do this to pull of capacitors from old circuit boards. But does it happen with things like ropes or paper? If not, why it doesn't happen? ( Maybe it has something to do with intermolecular forces and the various internal stresses?)  Let's say I have an iron bar and I have thrown it out into space. Does that iron bar have equal stress distribution or still uneven or will the stress on all points become zero? (Is there even such thing as zero stress?)
116336
An electric potential difference is created when two charges are separated. In a capacitor, there is a clear accumulation of opposite charges on the two separated plates, therefore work has to be done in moving an unit charge from one plate to another, against the electric field.   But, , a potential difference is created in a resistor due to the heat produced by the collision and increased lattice vibrations. So there is an energy loss across the resistor, yes, but how does this energy loss due to heat create an electric potential difference. In other words, do electrons accumulate on one or both sides of the resistor? If not, why should we do electric work in moving from one end of the resistor to another. If the difference in energy is not due to electric work, then that's not electric potential, is it?
79901
The topic which haunted me for two years until I gave up on it. But now I am doing engineering and this topic suddenly popped out of my textbook from nowhere. I seriously need to understand this topic because I wasn't able to do so in the past. I have read many book on 'energy' and it came to nothing. Maybe just because the many books I have read all said 'energy' is something which doesn't 'exist'! It is 'abstract'! It is just a number which represents the state or orientation of a system. But then I see so many examples that 'uses' energy to do 'work'. But the question here is that if anything doesn't exist in this universe, then how can the same thing be used to do something that exist?  My problem is that I didn't understood the topic 'energy' and all the other topics related to it (work, power etc.)
14142
I'm interested in what kind of energy has electric current ?. For everything I taught in school should have kinetic energy because electrons are on a certain potential within the electric field when the switch is closed then the electrons move and the electric current is "generated" which then should have the kinetic energy. And so I was thinking all the time until I came across this article  which actually tells me that everything I know about the electric current is wrong On the other hand, I wonder if so many books from college ,schools, are spoken in the wrong way It's just a little weird that a huge number of scientists and engineers are actually talking nonsense all the time and so I hope that you can help me clarify my dilemma.  thanks in advance.
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Say that I have a vertical thermally insulated cylinder which contains an ideal monoatomic gas under a weightless piston and the system is initially in equilibrium.   Now if a load of weight $W$ is kept on the piston,the piston would fall by some distance and the system would attain a new equilibrium. It is intuitive that the sum of the work done by gravity and the work done by atmospheric pressure would change into internal energy of the gas.   However, my book mentions that only the work done by gravity goes into the increase in internal energy of gas. It does not say anything about where the atmospheric work would go. Why is it so?
27623
In high school I was taught energy was conserved. Then I learned that nuclear reactions allow energy to be converted into mass. Then I also heard that apparently energy can spontaneously appear in quantum mechanics. So, are there any other caveats with the conservation of energy?
33453
For a constant force, $P=Fv$. I understand the mathematical derivation of this, but this seems to me, intuitively, to be nonsense. I feel that my discomfort with this comes from a fundamental misunderstanding of force and Newton's Second Law, so I'm not really looking for any mathematical explanation. So, to begin:  How is it that a constant force does not add energy to a system at a fixed rate? Consider a rocket burning a fuel at a constant rate. The chemical potential energy should be converted to kinetic energy at a constant rate, that is, $(1/2)mv^2$ should be increase linearly. The magnitude of the velocity of the rocket would then increase at a less than linear rate, implying a nonconstant acceleration and therefore, a nonconstant force/thrust (F=ma).  If force is indeed a "push or a pull," shouldn't that constant rate of burning of fuel yield a constant "push or pull" as well? Clearly not, so I would have to think that, somehow, a given force applied to a certain object at rest would in some way be different than that a force of the same magnitude being applied to that same object in motion. In this sense, is force merely a mathematical construct? What does it tangibly mean, in physical terms? Would a given force acting upon me "feel" differently to me (in terms of tug) as I am moving at differing velocities?  Force being defined as a "push or pull," which is how it has been taught in my high school class, seems rather "handwavy," and maybe that's the issue. It's been troubling me for a couple of weeks and my teacher hasn't really been able to help, so thanks!
40063
My questions mostly concern the history of physics. Who found the formula for kinetic energy $E_k =\frac{1}{2}mv^{2}$ and how was this formula actually discovered?  I've recently watched Leonard Susskind's lecture where he proves that if you define kinetic and potential energy in this way, then you can show that the total energy is conserved. But that makes me wonder how anyone came to define kinetic energy in that way.  My guess is that someone thought along the following lines:     Energy is conserved, in the sense that when you lift something up   you've done work, but when you let it go back down you're basically   back where you started. So it seems that my work and the work of   gravity just traded off.   But how do I make the concept mathematically rigorous?  I suppose I need functions $U$ and $V$, so that the total energy is their sum $E=U+V$, and the time derivative is always zero, $\frac{dE}{dt}=0$.   But where do I go from here? How do I leap to either   a) $U=\frac{1}{2}mv^{2}$ b) $F=-\frac{dV}{dt}$?    It seems to me that if you could get to either (a) or (b), then the rest is just algebra, but I do not see how to get to either of these without being told by a physics professor.
122502
With respect to both gravity and electromagnetism, to the best of my understanding potential energy is added or subtracted from a system based on the distance between two objects such as charged or massive objects.  Would this then imply that when oppositely charged objects or two massive objects are brought together within a small enough radius that the drop in potential energy would be greater than the combined mass of the two objects making the net mass/energy of the system negative?
63036
I know work done is negative of change in potential energy, I.e., $W=-(∆U)$.  It means that Work done against a force (or work done on a system) increases its potential energy. And Work done by a force (or work done by the system) decreases its potential energy.  But why this is so that an internal force (by internal force I mean that a force created under a system) will always tend to decrease the potential energy of the system while the external force increase the potential energy of the system?
1492
If a spring is stretched by a weight of mass m, (so the extension is $\Delta x$) then $ k = \frac W{\Delta x} = \frac {mg}{\Delta x}$. So $ k\Delta x= mg $.  When the Spring is stretched by distance $\Delta x$ (by the weight) then it looses gravitational potential enegry. ($ \Delta GPE= mg\Delta x$)  But, when we calculate the change in elastic potential energy, We get  $ U = \frac 12 k(\Delta x)^2 $. Since $ k\Delta x = mg$, $U=\frac 12 mg\Delta x$  At, equilibrium we have no kinetic energy $E_k = 0$  Doesn't that violate Energy Conservation?  Where does the rest of lost GPE goes?  Here's a illustration
16279
I understand the energy and mass can change back and forth according to Einstein. It is fluid; it can go from one to the other. So, what keeps mass from just turning into energy? Is there some force holding a subatomic particle together? What keeps mass in it's state? I hope this is not a silly question but I am clueless. Thanks