Is energy conserved in all inertial coordinate frames?

Question

A body stands on a ramp of height h. After getting a small push, the body slides down. The friction is absent. Potential energy of the body mgh is transformed into kinetic energy of mv^2/2. Consider the same process in the inertial coordinate frame, moving with velocity v=√ 2gh. Initial energy of the body is mgh + mv^2/2, and its final energy is zero.

What happenes with the energy conservation law?

Answer 1

The attorney general argued before the judge that the law must not be repealed.

The ramp of mass M acquired momentum
ΔP = -Δp = -mv.

Kinetic energy acquired by the ramp in the former frame was
ΔKE = 1/2 P²/2M = mgh / M ~ 0
Kinetic energy acquired by the body was +1/2 mv².
Net kinetic energy change in the latter case is +mgh.

In the latter frame:
Kinetic energy acquired by the ramp was
ΔKE' = 1/2 Δ(P'²)/2M ~ Po' ΔP / M =
Po'/M ΔP = (-v) ΔP = mv²
Kinetic energy acquired by the body was -1/2 mv².
Net kinetic energy change in the latter case is the same +mgh.

******************
It is also possible to write conservation of energy not as interaction of two bodies, but single body moving in external potential F(x,t) = -∂/∂x P(x,t). Then, conseravtion of energy becomes
dE/dt = ∂E/∂t
and in case external potantial explicitly depends on time ∂E/∂t ≠ 0, energy E(t) is no longer constant. In this approach, yes, conservartion of energy is replaced by non-conservation of energy.

Answer 2

The energy is relative to a reference. By moving your reference you are negating the energy.

Better example: You -Y are in a car - C at the top of a hill - A. You and the car have potential energy relative to the bottom of the hill - B. When you and the car roll at a velocity relative to B you develop kinetic energy relative to B. However, if we move our frame of reference to C we find that the energy of Y is 0 relative to C. Only when there is acceleration, deceleration or a change in directional vector will there be a differential between Y and C. But the energy between Y and B is always conserved.

Hope that helps put it in perspective.

Answer 3

Assume the height of the ramp is one Earth radius from the surface of the Earth.
We are concerned in this case about Gravitational Energy between mass of the earth M and mass m at the earth surface ,and the Gravitational energy and Power existing at the height of the ramp above the surface of the Earth.

The Gravitational Energy level at height h= r(one earth radius )is as follows;
E1 = GM m/(r+r)

The Gravity energy at the surface level of the earth is as follows:
Eo = GMm/r

The Kinetic energy of mass m when it will collide at the surface of the Earth is as follows=2 x (Eo - E1)

The motional energy of mass m at the earth surface is therefore equal to=GM m/h, where the height =r.

It means that the amount of energy it took to bring it up the ramp is equal to the energy to bringing down the Ramp.This in accordance to the laws of thermodynamics. But in this case it is assumed that no energy is lost due to friction.

Here energy is conserved. However in real life there is friction and in order to do work certain amount of energy has to be lost in space(Energy that cannot be reused to do work). Energy is always lost due to friction.
Therefore Energy input is not equal to the Work out put.
Hence Energy in an open system is not conserved.The energy lost to the surroundings is called Entropy.

Answer 4

pc computers and followers do no longer use a number of power while in comparison with the oven, microwave, AC, and dishwasher. We supply up making use of the dishwasher. substitute your AC clear out each month...the leasing workplace might desire to offer them for you. we've a one mattress room. We run one fan all of the time, which includes interior the mattress room at night. The cooling results of the breeze facilitates us turn the AC thermostat up a level or 2 and nonetheless experience delicate. each a number of months, I carry a experience or a lit candle around the sides of each window and each door searching for air leaks. try this on a windy day. The flame will wiggle or bend while it detects an air leak. we've dark curtains wonderful over those domicile windows that get direct image voltaic, yet there's a sheet of white textile on the curtain dealing with outward, which reflects the image voltaic back out. We went to flourescent easy bulbs...the type that look greater like sunlight hours than the gruesome bluish coloration. We commonly have in basic terms one small lamp lit interior the front room while staring at television, and greater than a number of alternative the time, even it is became off. If we go away for greater desirable than 4 hours, we advance the thermostat 3 or 4 degress. If possible, examine the temperature placing on your water heater. Nudge it down a pair of stages, then attempt it once you bathe. save reducing it till the water is in basic terms too cool while showering.

Answer 5

the inertial coordinate frame,


you said that as if it were an every day term lol