# Energy capacity to do work (frames of references)

## Main Question or Discussion Point

I have a problem understanding how we can say that an object has energy of x joules because energy depends on the frame of reference right ? I mean let say a bird is moving with velocity of 5 m/s if I were a stationary man I would observe that it has a kinetic energy but if I were moving with 5 m/s then it would have zero energy, so how can energy be a meassure of the capacity of an object to do work and why is it considered to be the same thing as mass as being a property of the object itself if it depends on the frame of reference?

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jtbell
Mentor
If you and the bird are both moving at 5 m/s with respect to the ground, in the same direction, how can the bird do any work on you?

rcgldr
Homework Helper
If you take into account all the objects affected by a change in energy, then the total energy for that closed system remains constant, regardless of the (inertial) frame of reference. Ignoring losses to heat, potential energy (electrical, chemical, gravitational) can be converted into kinetic energy. Momentum of the system will also be conserved (the center of mass remains moving at constant velocity or zero).

For example, imagine a rocket in outer space. The chemical energy of the fuel is used to accelerate the rocket and the exhaust fuel. The total increase in kinetic energy of rocket and fuel are equal to the chemical energy of the fuel converted (ignoring losses to heat), and are the same regardless of the frame of reference.

A similar analogy could be made for a car accelerating on the earth, as long as you consider the car and the earth as the closed system where both car and earth experience an energy change when the car's engine performs work (chemical to kinetic energy convertion).

well it can't so what I am asking is that whether energy like mass is a property of the object itself rather than affected by the one who measures it or does it mean the capacity to do work on a certain object and changes by the change of the motion of the object? if so then how could it be equated to mass?
also is it insufficient to say an object has kinetic energy of some value without saying with which references it was taken from? I mean the bird had different kinetic energies in the two scenarios which one is to be considered?

Doc Al
Mentor
well it can't so what I am asking is that whether energy like mass is a property of the object itself rather than affected by the one who measures it or does it mean the capacity to do work on a certain object and changes by the change of the motion of the object?
Kinetic energy depends on the frame of reference; it's not an intrinsic property of an object.
if so then how could it be equated to mass?
It isn't.
also is it insufficient to say an object has kinetic energy of some value without saying with which references it was taken from?
Right. To say an object has a certain KE is meaningless if the frame of reference is not specified. (Of course, often it's clear from the context what the frame of reference is.)
I mean the bird had different kinetic energies in the two scenarios which one is to be considered?
You choose the frame of reference most useful for your purpose. The physics doesn't change.

Kinetic energy isn't equated to mass? KE = 1/2mv^2 seems to equate to mass by 1/2 the relative velocity squared is how to me...It is equated to mass by accounting for the velocity, at the same relative velocity two equal masses have equal kinetic energy...thus (mass = KE*X) mass is always proportional to KE, the variable proportionality(X) being (the relative velocity squared) to (2)....I would say

Doc Al
Mentor
Kinetic energy isn't equated to mass? KE = 1/2mv^2 seems to equate to mass by 1/2 the relative velocity squared is how to me...
KE doesn't 'equate' to mass, but to 1/2mv^2. Big difference! Obviously it depends on the reference frame.

Definition of EQUATE
transitive verb
1
a : to make equal : equalize b : to make such an allowance or correction in as will reduce to a common standard or obtain a correct result
2
: to treat, represent, or regard as equal, equivalent, or comparable <equates disagreement with disloyalty>
It is made equal, equalized, by a variable proportionality we can correct KE to give the result of mass by dividing it by 1/2v^2.. to use an example, At the same relative speed, we have the same mass and the same KE, if you have relative velocity compared to me, and I don't know your mass, but I could measure you KE, I could equate that to you mass by allowing for your velocity

To be equatable just means to be proportional...imho

Doc Al
Mentor
It is made equal, equalized, by a variable proportionality we can correct KE to give the result of mass by dividing it by 1/2v^2.. to use an example, At the same relative speed, we have the same mass and the same KE, if you have relative velocity compared to me, and I don't know your mass, but I could measure you KE, I could equate that to you mass by allowing for your velocity
Did you read the thread to see what the OP might have meant by his statement?

To be equatable just means to be proportional...imho
Reread the definition that you quoted.

well it can't so what I am asking is that whether energy like mass is a property of the object itself rather than affected by the one who measures it or does it mean the capacity to do work on a certain object and changes by the change of the motion of the object? if so then how could it be equated to mass?
also is it insufficient to say an object has kinetic energy of some value without saying with which references it was taken from? I mean the bird had different kinetic energies in the two scenarios which one is to be considered?

Seems to me he is asking How can in be equated to mass if it is relative to your frame of reference... And the answer is it can be because it is dependant on only two quantities, mass and velocity, since velocity is relative to the reference frame, KE will be proportionately relative. i.e. the relative KE and the relative v change at the same rate if you were to compare in two different reference frames. that being the case, the mass will be the same if you divide relative KE by 1/2relative velocity^2 even though they are both relative to the frame of reference

change at the same rate is a bad wording, they change at a porportional rate...hah

but it probably is my vocabulary that is lacking...it maybe cannot be equated, but it can be related?