Energy Definition and 999 Threads

Hi A theorem states that if V(x , t) ≥ V0 then <E> is real and <E> ≥V0 for any normalizable state. The proof contains the following line <E> = (ħ2/2m)∫∇ψ*∇ψ d3x + ∫ Vψ*ψ d3x ≥ ∫ V0ψ*ψ Can anybody explain why that inequality is true ? Thanks

I am not against replacing fossil fuel, but we do NOT have a good solution yet. Why not build safer nuclear power plant? Or get into fusion power plant. I worked for a company as power of the Lawrence Livermore Fusion project back in 1979, still no result. Now they are fighting a losing battle...

I tried using the 109 J to convert to seconds but that didn't work. I also looked through the energy equations but nothing worked. I am not sure how to find time.

Maybe starlink isn't there for WiFi but for gaining energy from it's orbit around the earth. But this would make Earth approach to the sun.

Hello physics researchers, teachers and enthusiasts. I notice one little thing is confusing me in the derivation of Bernoulli's equation in the article, they write:$$dW = dK + dU$$where dW is the work done to the fluid, dK is the change in kinetic energy of the fluid, and dU is the change in...

My sign doesn't check out and I don't get why that'd be the case. Forces that act --> ##F_{fr} and F_g## derivation: ##\Delta K = W_{NC} + W_C (1)## ##\Delta K + \Delta U = W_{NC}## ##\frac 12 mv_2^2 - \frac 12 mv_1^2 + mgy_2 - mgy_1 = W_{NC}## NOTE: ##y_2## assumed to be datum line so ##y_2 ==...

Hello there, I have tried the problem but don't get a different of 6g's as I am supposed to. I am not sure whether I interpreted the problem in the correct way, but I would love some feedback/hints on what went wrong in my solution, thanks in advance. Solution: SITUATION DRAWINGS + FBDS so...

so I haven't looked at the solution yet, but I know that a 100% the velocity needs to be bigger, but analytically, I get a - sign instead of a + sign as you'll see at the final square root. So for the first 15meters of the motion all you should know is that ##v_1 = 10.458 m/s##. for the 2nd...

this is an easy problem but would it be possible to consider car-car system. What I did on paper was carsystem and because they have the same properties(mass en speed) multiply by ##2## solution for car-car-earth system I assume is the following if it is possible? solution for car-car: law or...

I am writing a military SF, and wonder, what could be the most realistic things, that are close to the old SF concept of energy shields. So far, i wrote that a small mecha uses a handheld plasma shield against an incoming missile. Like explosive reactive armor, it meant to shatter the...

So in this picture friction is also assumed, but if we assume friction as an energy don't we need to consider the system to be earth, roller-coaster car, roller-coaster itself(due to friction force)? I actually still had this question from a previous coverage of this material lol... I just...

Electrons flowing through a resistor are dissipating electrical energy. The electrical energy is transported from the battery to the electrons along the curved field lines of the Poynting vector. It seems like a meaningful idea that electrical energy necessarily travels from the source to the...

While reading this thread on Stack Exchange... https://physics.stackexchange.com/questions/113092/why-does-a-system-try-to-minimize-potential-energy ... a question came to mind : - Say an object is launched away from Earth at a velocity greater than the escape velocity. This system will not end...

Hello : i was watching the news , and it was all about how Europe will start the coal factories again for energy generation had a question related to reduction of coal consumption for energy generation 1 ) could we use coal fine particles instead of chunks of coal that will burn more...

A point charge of value q=8uC is released from rest at a point 1.5m away from the center of the axis of a ring with uniform charge density 3uC/m. The ring has a radius of 10 cm. What is the kinetic energy of this charge when it is 4.5 cm from the center of the charge ring, considering that it is...

Canonical ensemble is the statistical ensemble which is applicable for the closed system in contact with the reservoir at constant temperature ##T##. Canonical ensemble is characterized by the three fixed variables; number of particles ##N##, volume ##V## and temperature ##T##. What is said is...

Summary: Request for an example of minimum energy principle usage The minimum energy principle states that, for a system at constant entropy, volume and other extensive quantities, the internal energy is minimized at equilibrium. Can you give me an example in which, using this principle, is it...

The calculation of the vacuum energy density gives us a discrepancy with reality. There should be a mass equivalent of about $10^{96}$ kilograms. I'm wondering if the assumed point-like "structure" of particles could be the cause of this wrong value. Since string theory doesn't assume a...

Hello everyone! I noticed in the derivation of potential energy, Mr Lewin defined the gravitational potential energy of a mass m at point P relative to a much larger mass M. He says the potential energy of m at point P is equal to the work he would have to do to move the mass m from infinity to...

Hello everyone! I've been studying work and energy, and one problem I have is understanding conservation of mechanical energy. If on a rollercoaster you have two points A and B you expect the mechanical energy at A to be equal to the mechanical energy at point B, makes sense to me; but I started...

- design of a micro-turbine based on different scenarios of waterfalls - build a system that involves a battery for storing power - test in the lab I have attached a image. I know the image is not very detailed but wanting some advice on this situation. I have done some water calculations on...

My attempt was to consider spherical shells of radius ##r## (##r\leq R##))and thickness ##dr## and then the potential energy of this shell would be in the field only of the "residual" sphere of radius ##r## (a result also known as shell theorem) $$U_{dr}=G\frac{\rho\frac{4}{3}\pi r^3 \rho 4\pi...

If we have a ball with mass m dropped from a height h down to the ground, how come we can't set the conservation of energy equation just as the velocity of the ball turns 0. mgh = 0 If instead the ball were moving with an initial velocity v, would the equation be ##mgh + \frac{1}{2}mv^2 = 0##...

In generic terms and expressions without going into specificity or nature of fields/forces in order to highlight the same, how exactly could we characterise the distinction between 'Potential' & 'Potential Energy'?

I wondered about this question. According to me, there 2 ways you can look at it. A system can have energy, or a system is energy. Next to that, the idea of energy, the definition of energy seems a bit vague to me. There are so many types of energy, but what is it really? A system can have...

This is a thermodynamics question. A gas absorbs 10 000 J of heat , it releases 3000 J and does 2000 J of work. How much has the internal energy varied? So I did 10 000 - 3000 -2000 = 5000 J so internal energy decreases by 5000 J. But the correct answer is A) it increased by 5000 J . How ?

https://www.physicsforums.com/threads/conservation-of-momentum-and-loss-of-energy-in-inelastic-collisions.311037/post-2182192 If I understand correctly mathematically the momentum of the system remains unchanged but individual momentums decreases always. In an inelastic collision the momentum...

= -3.7298538168*10^13, -2.0594767123*10^13 Ive tried this equation with both masses and my homework keeps coming back with the wrong answer. I've tried checking my arithmetic but I cannot find anything wrong with it please help haven't gotten the chance to try B but I am pretty sure it will be...

Daniel Vasilaky asks do physicists know "how much energy the universe has"? An infinite amount seems absurd - no need for conservation laws and so perpetual motion would be possible. I'd say no to a negative amount also. So it'd be zero (I'd say probably) or a finite, positive amount (maybe)...

Currently, dark energy is described as a being that exerts a negative pressure while having a positive energy density. {\rho _\Lambda } + 3{P_\Lambda } = {\rho _\Lambda } + 3( - {\rho _\Lambda }) = - 2{\rho _\Lambda } However, there seems to be a problem with the negative pressure assertion...

If we insert the values from (2.9), (2.10), (2.11) into (2.5) & (2.6) how can we get (2.13) & (2.14) ?? I need to see the calculations step by step.

As far as I know, if vacuum antigravitates, it makes the light that travels through it redshift, e.g. in a very large empty box with mirror walls, light will just lose energy. I am interested in the reverse effect, if we had a very large box or planet with mirror walls, that is filled with...

Suppose a charged particle is in an electric field and feels an electric potential. Then the particle travels through a wormhole to another electric field and the particle feels a different electric potential. The potential energy of the particle will change. So what will that part of potential...

For reference:

I think the answer is that the elastic potential energy will be a 1/16th of the original value. This is my reasoning: 1) If the diameter doubles, the cross sectional area is 4 times the original value. (from A= πr2). 2) F= stress/area. Force (load is the same). If cross sectional area...

Hamilton’s principle minimises kinetic energy minus potential energy, that is, with a fixed kinetic energy, Hamilton's principle maximises potential energy. What if we consider the limit that the kinetic energy or the mass/the inertia can be ignored then the lagrangian is solely the negative of...

While this was inspired by another thread, I think the question is different enough that it can be asked separately. It's also more suited to this forum than the forum where the question that inspired this one was asked. Wiki gives four possible interactions for interactions of gamma rays with...

Hi, if the force is the derivative of potential energy, does it mean that the force is equal to mg and with a constant gravity, it will be the same at any height? But in real life, F (or mg) would be different on the Earth's surface and 400 km above it (~8 m/s^2). So, this formula is used to...

Hello! Amateur question alert! Please excuse any misuse of terms. Answers gratefully received. :smile: I have a question about the energy that can be drawn from the vacuum through quantum fluctuations. My understanding is there are very strict limits on how much energy can be borrowed for how...

I found that I had an inaccurate understanding of their relationship earlier. After rethinking, I try to express their relationship in a simple and understandable way Nuclear reactions convert energy from form of mass to form of light, and both energy and momentum are conserved during the...

So the potential energy of an object in a gravitational field is pe=hmg where h is the height of the object in the gravitational field in meters m is the mass in kilograms and g is the acceleration in meters per second per second I read on an answer to a question that the force to lift an...

I was reading "Brief answers to big questions" By Hawking, the above pic is from a page of the book, it says that at the time of the big bang there was an equal amount of positive and negative energy, and that the negative energy never went anywhere, the space-time itself is a store of negative...

1. Golf ball initial potential energy uncertainty (110-5kg 0.01 m 0.01m/s2)= 110-9J4.31210-5=4.31210-14j 2. Golf ball initial potential energy calculation (4.4 x10-4kg 9.8 m/s2 0.609 m)= 4.31210-54.31210-14j 3.Golf ball final potential energy uncertainty ( 110-5kg 0.0 m0.01 m/s2)= 0.0 J 4...

I am sure this is an elementary question; I'm just trying to clarify some points that were poorly explained to me years ago in secondary school. I know that a full answer would involve solving Schrödinger's equation etc., but keeping this on the level of valence electrons,...) I was confused by...

a) ##\rho = \frac{I}{c} = \frac{F}{A}## for a perfect absorber ##F = ma## where ##a = \frac{c}{t}## ##\frac{I}{c} = \frac{mc}{tA}## ##I = \frac{I^2 tA}{mc^2} = \frac{P}{A}## ##P = \frac{I^2 tA^2}{mc^2} = \frac{W}{t}## ##W = \frac{I^2 t^2A^2}{mc^2}## I am unsure what A is. I think it should be...

I am having trouble understanding this derivation and need some guidance. 1) I tried solving the algebra from the first equation to the second equation circled in red. Can someone please help with what algebra steps, I cannot solve to the circled solution. 2) What does Ee stand for? Is it...

Will the presence of attractive interactions between gas molecules raise or lower the molar Gibbs energy of a gas relative to its ‘perfect’ value? I would think that these attracting forces result in a lower energy state. A decrease in the energy state implies a decrease in the enthalpy. A...

I want to get the stress energy tensor of a scalar field using the Hilbert method (namely, ##T^{\mu v} = \frac{2}{\sqrt{-g}} \frac{\delta S}{\delta g_{\mu v}}##) $$S = \int \frac{1}{2}(\partial_\mu \phi \partial^{\mu} \phi - m^2 \phi ^2)\sqrt{-g}d^4x$$ $$= \int \frac{1}{2}(\partial^{v} \phi...

Let's arrange the rod's axis parallel to the z axis. ##T_{00} = A/\mu## (since it represents the energy density) ##T_{03}=T_{30} = \frac{F\sqrt{\mu / F}}{A}## (It represents the flow of energy across the z direction) ##T_{33} = F/A## (pressure) It seems that ##T_{33}## i have got has the...

Hi. I'm not sure where to put this question, it concerns particles, mass-energy equivalence and various things. Classical electromagnetism seems to be as sensible a place as any. There is energy stored in an E field. Energy density (at position r, time t) = \frac{1}{2}...