if a mass were held above the surface of the earth and released to the earth, then where does that expended energy come from? has that mass of that object been reduced to equal the kinetic energy developed by the object right before impact?
No, Julixa, the relationship between kinetic and potential energy is purel.y classical and is not connected to mass converting to energy via e= mc^2 which is what I think you are asking about. As MRC_Hans said, the potential energy of an object is precisely the work done in raising it to that height.
If you take an object and raise its height then you are giving the object potential energy. More generally, by moving an object with mass m through a gravitational field the work done by the gravitational field is the line integral (between the two points) of F . dl (This is a dot product where F = -G(mM/r^2)r. and dl represents an infinitesimal displacement along the chosen path. Anyway my point is if you integrate this you end up with an equation for the work done by moving an object along some arbitrary path within the gravitational field. An the important concept is that the work only depends on the position of the two points (start and end) NOT the path taken. Now if you use the conservation of energy where the change in potential energy equals the negative of the work done we have: Change in Potential Energy = Potential energy at endpoint - Potential energy at start point. At some point in the G-field (r) the potential energy U(r) depends on four things: 1. The gravitational constant (G) 2. The mass of the object (m) 3. The mass of the Earth (M) 4. The relative distance from the Earth's center (r) U(r) = -G(mM/r) As an object falls to Earth its potential energy decreases (this is from the minus sign, this happens because when we integrate Newton's law of universal gravitation along a line integral a negative constant -GmM is taken out. Hence a minus sign remains with us.). At a point infinitely far away the potential energy of an object is zero. Hence the potential energy of any object in Earth's gravitational field (whether we put it there or it came from somewhere else) is always negative. The energy of the object is conserved since the gravitational field is a conservative force (if I move something in the field then move it back I do not use any work - conservative field). Energy depends on two things: 1) The conservation of energy: E = KE + PE | This must always work. 2) KE = 1/2mv^2 | PE = -G(mM/r) From this, potential energy and kinetic energy are conserved and 100% interchangeable. We lose potential energy at exactly the same rate as we gain kinetic energy. The more kinetic energy an object has the less potential energy it has stored. Once it runs out of potential energy you have to do work on it. The energy is stored in the gravitational field. If you let that object go it will use the potential energy stored in the field and we know that it can do work. We did work on it -> gave it potential energy | it stored this | now it uses the potential energy to fall to Earth -> and can do work by making a dent in the ground when it impacts. Remember that the object has potential energy until it reaches the center of the Earth's gravity. An object sitting on the ground has potential energy to fall further if all of a sudden the ground opened up. I hope this helps.
It is stored as the object's position relative to Earth's center of gravity (COG). Thus, a stone lying on the ground has a potential energy: Dig a hole and dump it into it, and some of that energy is released Please Register or Log in to view the hidden image!. You now removed some energy, and corespondingly, the stone occupies a new position relative to Earths COG. Lift it back up, and you invest some energy. Correspondingly, the stone is in a new position. Its mass never changes. Hans
Think of it like a stretched wire. The wire doesn't 'gain' mass but it has potential energy. I think the problem is in your concept of energy being stored. In many physics textbooks they use the term stored a lot for potential energy as it is the best way of thinking about it sometimes. Energy isn't a thing however and is just a concept (we do not really know what it is). In the case of an object in a gravitational field, the object does not store energy in/on it in any way but it is still said to HAVE energy which can be used later.
Potential energy is always related to the <b>configuration</b> of a system - i.e. the relative positions of parts of the system to each other. In fact, "configuration energy" might be a better name for it.
Mr.James R, Can you pls detail it. Furthur , suppose we grind anything eg. whole wheat to flour. Then if some KE will be transfered to wheat flour & stored as PE, which we applied on grinding the wheat.
That's wrong. grinding wheat will not "impart potential energy". The work done grinding the wheat goes out as heat.
Many thanks. During this grinding, if some exothermic or endothermic(as described above) type considerations are possible.
kineticv and potential energy I appreciate all that has been said, however I sstill dont feel that the storage factor has been adequately explained. If energy has been put into a system, then where is it. To say that it is in a gravitational field is abstract. It has to be physically somwhere and i believe that the energy was converted to increase the mass of the object in a gravitational field and so relinquished when the object returns to earth and impacts to heat.
Re: kineticv and potential energy Energy is a quantitative measure of the ability to do work. In the example of an object above the earth, the ability to do work exists because of the configuration of the system. You seem to be thinking of energy as if it were air or water, and had to be located in some specific place; that isn't the case with energy.
It looks to me that potential energy is not yet researched in details. Homeopathic remedies may contain PE but we are not able to /evaulate/judge/test that??
300 years of researching Potential Energy is just not good enough for some. Go read a Physics Textbook, for 15 year olds.
Homeopathic remedies are prepared by taking one part of say salt & 9 parts of lactose & triturate it for some time say one hour. This become 1X, than one part of 1X+9part of lactose & again trituration for one hour which become 2X & so on...We apply some KE in trituration to mixture of 1+9 parts. This applied KE on mixture is considered as lost as heat. But I feel that some KE might possibily be stored as PE in that mixture which may produce some homeopathic effects. There can be some chemical reaction among mixture, some molecular polar rearrangement,some electrostatic force or some smoothning of molecular friction which probably enable this mixture to store some PE. I think the storage of some PE can only justify the effect of Homeopathic remedies in higher potency say 30X.(the other process is by succussion of 1+99 part of salt+alcohol called 1C and so on..). But I am not finding more referances on this type of PE storage.
thed I told less researched, therefore asking from scholars here. When something do exist with no scientific proof, then we can/should try to find some proof. We come here only because it is not available in books.
