# Energy in different F.O.R

• Dweirdo
In summary, the conversation discusses energy in different frames of reference and the concept of energy conservation. The topic is sparked by the observation that, in a certain frame of reference, a body can appear to gain energy without any work being done on it. The participants discuss the role of inertia and non-inertial frames of reference in energy conservation, and give examples to illustrate their points. They also question whether energy can truly be conserved in all frames of reference and how to calculate the efficiency of an engine in different frames.

#### Dweirdo

This is an interesting topic.
Energy in different Frames of reference.
Assume
There is a body moving with a velocity of 5 m/s on a flat surface,and I'm running with the same speed, I see that the initial kinetic energy of the body is 0.
I stop moving now so my velocity is 0, relative to me the body has a speed now of 5m/s
means he as kinetic energy!
How is that possible? energy came from anywhere?how is that possible?
The only thing i can think off is D'lambert's principle doing work on the body cause i had to stop.but with another example it can easily show that it has nothing to do with it.
anybody suggestions ?
I guess there has to be work done on the body in the frame reference of me moving(and stopping) but I can't spot a force in the right direction ( normal force is perpendicular to the displacement thus no work) surface is frictionless and I stop with a pole hitting my head.
Maybe air friction(Drag)??

Thank You in advanced,
Dweirdo

BTW
This is not an HW question , just something I was thinking about.

Energy is conserved in any given inertial frame, but the value can be different in different frames. There's no contradiction here. It's the same with momentum.

I know what You mean,
but In the frame of the running person, he sees the body getting energy from nothing.
how can that be??
I know energy is conserved, but how can You prove it here? what is so special in this F.O.R that a body has increased his velocity without any work done on him??

thanks

A frame of reference attached to the running person is not inertial if he is not moving uniformly. So during the time he decelerates to zero speed, his frame is not inertial.

Oh great! so I can operate my car with my power of mind by just making my self a non inertial frame? That's easy!
So energy is not conserved in a "non inertial" frame of reference ? Are we inertial? is our galaxy movement inertial?
Sorry for my cynical comments but I'm trying to show that it's either I'm a total idiot/can't understand , or the solution is not satisfying enough.
I think It's worth discussion.

Thanks

B.T.W there are many examples for this kind of problems without involving acceleration, so i doubt this is the solution..

What dx is trying to explain is that energy is only conserved in an inertial frame of reference.

If you look at an object co-moving with you, that means it has 0 velocity with respect to you. If you now stop moving and the object does not, it does NOT suddenly gain energy from anywhere that makes it shoot away from you. Energy is NOT conserved.

The object may have 0 J of kinetic energy with respect to you if you are co-moving with the object, and it may have 39539 J of kinetic energy with respect to you after you stop moving. These are two different cases.

EDIT
Also, yes, you could say that you could power your car with your mind! However, it will move with respect to you, not with respect to the ground. If you run away from your car, your car is moving away from you too! Wow, you are powering your car with your mind by simply running away from it! But it isn't very useful...

Ok Let's drop "inertial"-"non inertial" thing, this is something i don't agree with as well, what is the definition of inertial frame?(I know the answer I'm just not satisfied by it)
so let's drop it.
Lets say I move with a velocity of 40 m/s , and Nick89 moves with a velocity of 900 m/s
they both observer a fantastic invention, A robot that uses all his kinetic energy for a HUGE explosion, he moves on a friction less surface (It's actually not moving,but me and You see it move) , so in my frame the explosion is small, in your frame it's bigger?

glad to see more people join this discussion :}

Thank You.

I'm not sure if I understand your question correctly, but I don't think you can say that your robot uses all his kinetic energy to create an explosion. Does it use all the kinetic energy it has in my frame of reference, or your frame of reference? You must specify one, you cannot use both at the same time. With that, your final conclusion is wrong; it uses a fixed amount of energy to create the explosion, either the KE in my FOR, or the KE in your FOR (but not both), so the explosion will be the same for us both.

Furthermore, how does your robot convert all his kinetic energy to an explosion? Maybe he crashes into a wall? Well, in that case, it is his velocity with respect to that wall that matters, not his velocity with respect to either of us.

ok robot and explosion was a bad idea.
lets say robot and engine, i want to calculate the efficiency of the engine.
it will be different in both F.O.R, but according to Einstein all "inertial" frames are...
So how would You solve the problem?
EDIT:
And I am still not sure what work was done looking from my F.O.R(non inertial) on a body.
btw a familiar problem is a body on a slope, where the solution is that the normal force does negative force in a certian frame that was described.

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## 1. What is energy in different frames of reference?

Energy in different frames of reference refers to the concept that the amount of energy an object possesses can vary depending on the observer's perspective or frame of reference.

## 2. How does energy change in different frames of reference?

According to the principle of relativity, energy is conserved in all frames of reference, meaning that the total amount of energy in a closed system remains constant. However, the distribution of energy between different forms, such as kinetic and potential energy, may vary depending on the frame of reference.

## 3. Can the total energy in a system change in different frames of reference?

No, the total energy in a closed system will always remain constant regardless of the observer's frame of reference. This is known as the law of conservation of energy.

## 4. How does the concept of energy in different frames of reference relate to the theory of relativity?

The theory of relativity states that the laws of physics are the same for all observers, regardless of their relative motion. This means that the total energy in a system will be the same for all observers, but the distribution of energy between different forms may vary.

## 5. Can energy be transferred between different frames of reference?

Yes, energy can be transferred between different frames of reference through various processes such as work or heat transfer. However, the total amount of energy will remain constant in all frames of reference.