Hi I can understand how once an object is falling in converts PE to KE. My question is how does it move in the first place. I know if we assume a gravitaional force that is fine. However from the perspective of energy it seems if an object starts with no KE it can not lose PE by moving into an area of lower potential as it cannot have any velocity to enable the move. If no PE is lost how can there be a gain in KE. If there is no gain in KE how can it accelerate. Again I can clearly see that once the object is moving it is losing PE which converts to KE and it is accelerating. But from energy principles how can it start to move. Where does the KE come from to move into a lower gravitational potential.
Since a force is a gradient of the potential, I don't know why you wouldn't just accept the force explanation. Since the gradient is not zero, the position is not an equilibrium position. That is the same as saying there is a force on the object. I think you have the idea of KE and acceleration backwards. It can't gain KE unless it accelerates. It accelerates because $$\frac{dV}{dx}\neq0$$ where [itex]V[/itex] is the potential energy. But that is just the force. If you want to find another explanation, you use the principle of least action. If you integrate KE-PE over any given time (giving the action), the path that the particle takes will minimize this. That path is the one for which it falls. While I think this is exceptionally interesting, I don't know if it will really make you feel better. Why do you want an explanation that doesn't use force? I don't know if I'm really able to answer your question, because I don't think I really understand what is confusing you.
At some point any object has gained PE in the first place. This gain cannot (According to classical daily life physics) occour from nothing - but it appearently has anyways in spite of what physical laws we know of; The big bang. First it was nothing, then it exploded... So from somewhere, any object has gained PE. Therfor it can lose PE as KE increase. No matter where an object is locating in a gravity field, it was put there by increasing or decreasing PE from its previous loction. I'm not sure if one have to understand gravity first in order to explain WHY the object gained PE - appearently PE is a function of gravity and mass, and both are two sides of the same thing. Vidar
Choose a different reference frame where it is already moving and has KE. See how pointless it is to ask for "reasons from energy principles"? KE is just a number assigned to the object by an observer. It is not some invisible fuel, that needs to be filled into the tank of the object before it can start moving.
Hi A big thanks for your replies. My problem is once a body is in motion relative to a gravitational field I can describe the motion by using energy or mechanics, but This does not work for a stationary object Energy as a body moves to an area of lower gravitational it loses gravitational potential energy which is converted into KE and hence it moves faster hence accelerates Mechanics there is a force due to the gravitational field acting on the mass this makes the object accelerate Perfect harmony as physics should be However the the two views are not in harmony if the object is stationary. Energy the body has no KE relative to the gravitational field/massive object therfore it cannot move to reduce its PE and hence gain momentum/KE. The body does not move Mechanics no change I believe this is never observed as what newton calls a stationary object has KE as it has molecules vibrating. We call this internal energy or heat. This explains why mechanics and energy models agree. Interestingly an object at absolute zero which is unobservable would not move hence no inertial mass. Further possibilities are a quark which I assume has no internal energy would have no mass. Other effects would be a stationary object at absolute zero will not fall. I have done some very crude drawings on my blog that might help. Please remember at no time does my blog use mechanics only the conservation of energy principle.
Thanks for your post Not sure what you mean if I observe from a different frame of reference both the large mass creating the gravitational field and the object move in the same way there is no difference in their relative positioning hence no acceleration. Sorry a bit confused. I do understand that my use of terms is not very good. KE is not a vector. It is the velocity relative to the large masss/gravitational field creating the KE that is a vector.
I think your problem has nothing to do with energy or gravity. You can construct the same apparent paradox for any object starting to move from rest: In order to move away from the initial position it needs some velocity, but it has no velocity in the initial position, so how does it ever get away from the initial position? It's a problem of intuitive human reasoning vs. math of limits.
Thanks for the comment it is very thought provoking :) but I do not think that is the paradox. I am happy for a warm object to start moving. Simply if it gains KE it will move form rest For example one snooker ball hitting another or a car being towed. both get EPE? which gives them KE so they move. They get that energy without moving as other things are moving. A free object by definition does not get anything from anywhere it is free. So how can it move. I think gravitational force causes me problems as I can see you need a force to stop a body accelerating we call this the reaction to the weight. My problem is all the observations we do are for warm objects so we will never see what I am theorising about. I am trying to just stick to the energy model. In our mind I think we see gravity as an invisible elastic band pulling things together but there is no elastic bands just areas of different potentials which you need movement to access. I think my problem is a stationary object has zero velocity but it has KE (except at absolute zero) we ignore this by calling it internal energy. however the indivdual molecules ( or quarks) have no internal energy they have KE.
@ Adeste A couple of points. Firstly, what has the movement of an 'attracting' object got to do with the field it is producing at the point where you put your test object? At that point, there is just a Field, which will interact with the test object. If the attracting object happens to be moving, then the field may be changing in time but we are considering what happens at one particular point in time. Secondly, there is nothing special about a velocity of Zero, because the velocity depends upon the frame of the observer but the field at that point does not. There is, therefore, no "paradox". You seem to be using macroscopic and microscopic terms interchangeably here. Forget Temperature; it is not relevant here. Your mention of a "free body" is not relevant here, either. Free Body is a concept which is used in calculations, which add the effects of all relevant forces. If equilibrium is the result then these forces add to zero but, in your case, there is no equilibrium because (obviously) the object will be accelerated. You seem to have a bit of a jumble of ideas here which are causing confusion. Take one thing at a time and it should resolve itself.
many tanks for your input I am trying to give an explanation of movement due to a gravitaional field for example earth. An object moving towards earth clearly is losing PE and gaining KE no forces are required for the effect. It is simple energy conservation. This agrees with the model that fields create? forces hence momentum. I am saying fields create acceleration if you move through them and hence a force is required to stop them. Further if they are not moving through a field there is no acceleration hence no force required. I know this can never be observed as all objects are moving unless at theoretical absolute zero. The increase in velocity is relative to the field in fact the increase in velocity has to be in the direction of the field. In my model you have to move to a lower potential to gain KE and hence velocity. My apologies if I am not explaining this too well. My explaination is totally in terms of energy and potentials which should exactly match fields and forces. This match is perfect except if there is no initial velocity to create the change in distance required to change the potential to create the loss in PE to create the gain in KE I hope this is clearer again a big thanks for trying to help me sort out my model.
Then how would you resolve the apparent contradiction I posed? Why not the other way around? If it moves form rest it gains KE. Does it make any difference? Both are just models, or rather parts of the same model.
Work is being done, PE and KE are changing. Of Course force is involved. I really can't see your point, here. There are forces involved, changes of energy and fields. The velocity - whether zero or not - is irrelevant. What "explanation"? You just seem to be asking a question, involving some random ideas. The 'correct' bits of your 'model' are correct but what's new?
I do think that A.T.'s comment is the actual paradox that you are looking at. If you can solve it for his example then the same reasoning should apply for your situation. However, I think that your reasoning from energy principles is wrong even for a moving object. An object with KE could be moving up, down, or horizontally, and your reasoning as presented cannot distinguish those situations. Furthermore, if it is moving horizontally then it is not moving into a region of lower PE, and yet it falls also. The proper way to reason from energy principles is called the Lagrangian formulation of mechanics. In Lagrangian mechanics you use the "action" which is KE - PE, so it is purely based on energy considerations. The other major difference is that in Newtonian mechanics you specify the position and velocity at one point and then solve for the trajectory using the forces, while in Lagrangian mechanics you specify the position at the beginning and the position at a later time and solve for the trajectory using the action. Specifically, the trajectory which the system takes is the trajectory which minimizes the action (most PE least KE). So, as an example, say that the position is the same at the beginning and at the end. If it goes down then it will be increasing KE and decreasing PE, which would maximize the action, so it goes up. How high does it go? Well, if it just stayed level, then its KE would be 0, but its PE would also be 0. The higher it goes the higher its PE but the higher its KE also, so there is a trade off. It wants to go as high as possible to increase PE, but not too high that the KE goes up too much. The parabolic path that it takes winds up being the exact optimal path, it is the highest PE it can get without allowing too much KE. That is how you reason out an actual specific trajectory from energy principles.
A ball thrown up in the air stops moving in order to turn back towards earth (unless you have a really good arm). This is an example of acceleration when there is no motion. This is not true according to classical mechanics which has proven to be a very good description of reality. One part does not precede the other. The motion and the gain of KE are simultaneous. If you want to use a purely energy description of reality, you need to either postulate the principle of least action or the fact that a gradient in a potential field induces acceleration. Again, the second one is equivalent to a force. You don't need to explicitly talk about forces, but conservation of energy is not enough information to describe our world. If it were, you would be correct, objects at rest in a field would not move, but this is not the case. You commented that a particle with no internal degrees of freedom would not move, but this is not the case either. Electrons in an electric field accelerate despite having no internal temperature.
I would like to point out one other flaw in the reasoning presented here for the moving object, and how that same flaw causes the confusion in the stationary case. You have presented the exchange of energy in terms of a chain of cause and effect. 1) Cause: object moves, Effect: object loses PE. 2) Cause: object loses PE, Effect: object gains KE. 3) Cause: object gains KE, Effect: object accelerates. The problem with this is that causes always preceed effects. So if a loss of PE causes a gain in KE then there is some time between the cause and the effect where energy is not conserved. So, since energy is conserved, the loss in PE and the gain in KE must happen at the same time and therefore one cannot cause the other. They simply happen together. So the correct way to state it is that as it moves down it loses PE and gains KE. This is all you can say. Without additional information you cannot say whether or not it is moving down in either case. So the exact same reasoning applies in both cases, as well as the exact same limitation in what you can conclude. Without doing a full Lagrangian analysis you cannot work out the actual trajectory from energy principles. And things get worse for the naive energy analysis if you move to non-uniform gravity. How can you explain a circular orbit with it? According to the naive energy analysis it should simply travel in a straight line slowing down as its PE increases. But the Lagrangian analysis works it out correctly from energy principles.
I assume you mean in the general case... in the simple case of an object falling from rest in a uniform gravitational field the trajectory q(t) can be derived from conservation of energy. To my mind that constitutes a solution of the original problem: energy conservation dictates the relationship between the velocity and position, which in this case uniquely determines q(t) given zero initial speed and a known starting position. (Not sure if this is what the OP had in mind, though.)
Hi first of all big big thank you for your reply I am in trouble with the moderators for having a personal theory. Thanks for the cause an effect discussion you may have sorted out my confusion however I seem to remember at uni some 40 years ago that you can break energy conservation rules as long as the time is short enough it was a formula involving h (plank's constant). Does this not apply. I will look it up if needed.
That's not true. Energy conservation gives many possible solutions. If a ball were to float in the air without moving, it would have the same potential and kinetic energy. In order to pick out the correct path, you need the idea of forces or the least action.
Heisenberg uncertainty relation. ΔE.ΔT <h/2∏ Surely this allows causality as I suggest as Δt can be made as small as you wish
Only because it is moving ie Δx>0. An electron to be not moving would have to be at absolute zero as if not it will be moving by the momentum change caused by infrared photons hitting it a little like brownian motion. sorry if that sounds a little patronizing it was not meant to be Is there any experimental evidence that such a electron starts to move.?