Can kinetic and gravitational potential energy could both be zero and can gravitational potential energy be equal to kinetic energy?
Potential energy is a chimera. The energy is contained in the gravitational field. The energy density W of the gravitational field is given by
W=W0-g²/(8πG). W0 is a background energy density which prohibits an absolute negative energy density value. g is the gravitational acceleration. G is the gravitational constant.
Potential energy cannot have a mass equivalent because the rest mass of elementary particles is exactly defined.
Yes, it is sitting there and not moving. Since it is not moving, it does not kinetic energy. Also, since it is on the ground, it cannot go any lower. In this case, both the potential and kinetic energy are zero. An object can have both kinetic and potential energy at the same time. For example, an object which is falling, but has not yet reached the ground has kinetic energy because it is moving downwards and potential energy because it is able to move downwards even further than it already has. At a start, the potential energy = mgh and kinetic energy = zero because its velocity is zero. Total energy of the object = mgh. As it falls, its potential energy will change into kinetic energy. If v is the velocity of the object at a given instant, the kinetic energy = 1/2mv2. Kinetic energy can only be zero or positive; it cannot be negative. This is due to the fact that kinetic energy is defined as half an object's mass multiplied by its velocity squared. Because mass is a measure of matter, it can never be negative, and velocity is always positive because it is squared. At r = ∞ both gravitational potential and kinetic energy of the object both become zero. Therefore, the total energy also becomes zero. The gravitational potential energy of a very hody is zero when it is at infinity because the force of attraction of earth on the body bod is then zero. Due to the principle of the conservation of energy, the amount of gravitational potential energy lost by the object must be equal to the amount of kinetic energy gained by the object. They are two different forms of energy. Gravitational potential energy is associated with the gravitational interaction between two masses. Kinetic energy is associated with the motion of an object. If we drop a pencil and want to compute its speed upon hitting floor, we equate KE with its loss of PE in falling the 1.1 m. PE = KE v = 4.6 m /sec the height is always the vertical distance (not necessarily the total distance the body may travel) between the starting point and the lowest point of fall. So the reason for that kinetic energy is not greater than the potential energy is, due to motion of the object kinetic energy loses some energy in the form of light energy, heat and friction these things does not happen in the potential energy that's why potential energy is always greater than the kinetic energy. According to the virial theorem, the kinetic energy is half of the negative of potential energy. The potential energy is the double of the negative of kinetic energy. The total energy is equal to the negative of the kinetic energy. The total energy is equal to half of the potential energy. The sum of kinetic energy and potential energy always remain constant at each point of motion and is equal to initial potential energy at height h.
We can easily proof that the energy contained in the gravitational field is given by -g²/(8πG).
To proof it, we look at two masses M,m in airless space. First of all, the masses are so far apart that their gravitational fields practically do not overlap and therefore attract each other almost imperceptibly. We also consider the two masses to be approximately point-like with a very small radius r0 and use that the field energy depends quadratically on the field strength. In the separated state, the field energy W is given by
Wfield= ∫[ r0,∞]4πr²(gm²+gM²) X dr. X is a constant, we want to determine.
The change in field energy is given by the volume integral
∆Wfield= ∫[ r0,∞]4πr²(g(m+M)²-gm²-gM²) X dr=X*4πG²*2Mm/r0.
gm=-mG/r², gM=-MG/r², g(m+M)=-G(m+M)/r².
The mechanical energy ∆Wkin, which is released when the two masses coincide is given by
∆Wkin= ∫[r0,∞]Fdr. F is the attraction. It applies, F=mg. With g=-MG/r² we get ∆Wkin=MmG/r0
From the conservation of energy ∆Wkin+∆Wfield=0 we get
X= -(MmG/r0)/ (4πG²*2Mm/r0)=-1/(8πG) which has to be proven.
“…Can kinetic and gravitational potential energy could both be zero and can gravitational potential energy be equal to kinetic energy?…..”
- to answer to this question it is necessary before to understand that the term “potential energy” is used only if some system of interacting/coupling by some fundamental Nature force, particles, bodies, etc. is considered,
- and, at that – if there exist only one body [including, of course, a particle], then really every body has potential energy always – though this energy is uncertain, and is actualized in concrete systems by concrete ways, and this energy is equal to particles’ energy E=Pc=mc2=γm0c2, P is absolute value of 4D momentum, P, m is inertial mass, γ is the Lorentz factor, m0 is the particle/body rest mass; if rest mass is zero – say, of photon, E=Pc=ћω.
At interactions in coupled systems, including gravitationally coupled systems, energies of interacting particles are redistributed.
That can happen in a point, say, if in an e±pair system electron and positron meet, their energies in a 3D space point completely are transmitted to created photons’ energies; if the interactions in a system are distant, than the system’s elements move in space being impacted by some forces, F, and at that the forces make some jobs A=ʃFds; all that happens really practically always in 3D space.
However in all cases if a system is closed, i.e. doesn’t dissipate energy outside, the energy of the system, Es, because of the energy conservation law always is the same that they had before the coupling;, Es=Σmic2, i=1,2…N are bodies indexes.
So if we consider a system of, say, two bodies, for simplicity let masses of bodies are Mand m, M0>>m0, bodies are at rest in 3D space [their kinetic energies Ek=0], that interact by Gravity Force, then:
- if the bodies are free – in this case on infinite distances, energy of the system Es=M0c2+m0c2, and this energy remains be constant at any motion of bodies, in this case because of momentum conservation law practically motion of only m.
So if after some negligible impact on m m moves toward M, its kinetic energy increases under Gravity force F=GMm/r2, however its energy remains be E=m0c2, i.e. though, as that is in mainstream physics in Newton Gravity, M Gravity field makes the work A=Fs,
- however really – see above - this work so is equal to zero.
I.e. gravitational field doesn’t really directly – as that is in mainstream physics – make a work, really m moves in the M’s field spending own energy – as, say, that a human does if swims in water, but the Gravity Force really acts on this, by specific way, at that:
- all fundamental Nature forces, including Gravity Force, act only between particles – and so further between bodies;
- every particle/body in Matter always constantly radiates some Force’s mediators, which don’t contain/carry energy – and so, in contrast to mainstream physics gravitational filed fundamentally doesn’t contain any energy [at least at statics], but if a mediator hits into a particle of other body, the mediator triggers in the particle specific releasing of its own energy portion, which is transformed into this particle’s motion;
- and, while its current “own’ energy mp0sc2 decreases, and so rest mass decreases, however the whole particle’ energy remains E=mp0c2= mp0sc2+Ek..
At motion from the infinity to a distance r, this portion is equal Eg=GMm/r, and it is, of course equal to Ek. In mainstream gravity Eg is called “potential energy of m in M’s field” – what looks as in sense that potential M’s gravity field action on further after r m falling, but that isn’t so, again, Eg relates to motion before r.
More see the Shevchenko-Tokarevsky’s 2007 initial models of Gravity and Electric Forces in
https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces; and 2023 model of Nuclear Force, though
https://www.researchgate.net/publication/369357747_The_informational_model_-Nuclear_Force
- all at least 3 these fundamental Nature forces in Matter act by the same scheme.
Cheers
As a mass travels away from the centre of a gravitational field, its kinetic energy is converted to gravitational potential energy. Therefore, kinetic energy decreases while gravitational potential energy increases. At r = ∞ both gravitational potential and kinetic energy of the object both become zero. When an object falls toward the ground, it “loses” gravitational potential energy as its height decreases, and “gains” kinetic energy as its speed increases. In reality, it is neither gaining nor losing energy: as the object falls, its gravitational potential energy is transformed into kinetic energy. A node is defined as a point on a string where there is no movement possible, so that both the kinetic and potential energy are zero. Gravitational Potential is equal to the potential energy of the unit mass kept at that point. Kinetic energy and gravitational potential energy are related because they are both forms of energy that an object can possess. When an object falls, its GPE decreases as it gains KE. Conversely, when an object rises, it gains GPE as its KE decreases. There are some well-accepted choices of initial potential energy. As, the lowest height in a problem is usually defined as zero potential energy, or if an object is in space, the farthest point away from the system is often defined as zero potential energy. Gravitational potential energy can be zero but gravitational potential can never be zero. The gravitational potential at a point can be defined as the work done in bringing a unit mass from infinity to that point. The gravitational potential energy could even be negative if the object were to pass below the zero point. However, the case is different when it is in the state of rest, in this case, it does not have any kinetic energy but posses potential energy. Thus, it is not possible for an object that it has kinetic energy but not the potential energy. Yes, it is possible when the object is in state of rest.
Rk Naresh "Kinetic energy and gravitational potential energy are related because they are both forms of energy that an object can possess. When an object falls, its GPE decreases as it gains KE. Conversely, when an object rises, it gains GPE as its KE decreases."
If this would be true, a falling object could not increase its relativistic mass while it gains kinetic energy. It only changes the potential energy, it already has, to the kinetic energy it gets.
The point is that Einstein's energy/mass equivalent reveals the fallacy of the potential energy concept.
No, both cannot be zero at the same instant in SHM. Potential energy is zero at the mean position of SHM of the particle, i.e., the point where displacement of the particle is zero whereas kinetic energy is zero at the extreme point of SHM of the particle, i.e., the point where displacement of the particle is maximum. That is, the sum of the changes in potential and kinetic energies of the object is always zero. This means that if the potential energy of the object increases, then the kinetic energy of the object must decrease by the same amount. If gravitational potential at some point is zero, then gravitational field strength at that point will also be zero. At r = ∞ both gravitational potential and kinetic energy of the object both become zero. Therefore, the total energy also becomes zero.In classical mechanics, two or more masses always have a gravitational potential. Conservation of energy requires that this gravitational field energy is always negative, so that it is zero when the objects are infinitely far apart. Objects can have both kinetic energy and potential energy at the same time. An object can be elevated above the ground and be moving at the same time. The change in Potential Energy is equivalent to the change in Kinetic Energy. The initial KE of the object is 0, because it is at rest. Hence the final Kinetic Energy is equal to the change in KE. Is your question can an object have KE without initially having PE? The answer is yes. Picture a hockey puck sitting on the ice. It does not have any potential energy or kinetic energy. If an object has no forces acting on it, you can consider it to have zero potential energy. A block moving in space at constant velocity would have zero potential energy. Vice versa, the book in the above example has gravitational potential energy with no kinetic energy. Because potential energy is not absolute rather it is relative i.e. when we say “the value of potential energy at a point is 'x' Joule, it means that this value is relative to value at some other reference point. You ask your question in a wrong way: when a body moves in a conservative field, the energy transforms from potential to kinetic and vice-versa. But, at a given time, the two energies are not necessarily equal. Gravitational potential energy may be converted to other forms of energy, such as kinetic energy. If we release the mass, gravitational force will do an amount of work equal to mgh on it, thereby increasing its kinetic energy by that same amount. Objects can have both kinetic energy and potential energy at the same time. An object can be elevated above the ground (have potential energy) and be moving at the same time.
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