Energy dependence on observer framework

In summary, the mechanical energy of a system does depend on the framework of an observer, but only when considering the kinetic energy of a moving object. In inertial frames, the energy formalism is valid and can be used to solve problems. However, in non-inertial frames, inertial forces must be taken into account in order for the energy formalism to be valid.
  • #1
hokhani
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Does mechanical energy of a system depend on the framework of an observer (neglecting a constant)?
 
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  • #2
hokhani said:
Does mechanical energy of a system depend on the framework of an observer (neglecting a constant)?

Yes. The kinetic energy of a bullet is zero in the frame of an observer who is at rest relative to the bullet, non-zero for an observer who is at rest relative to the target of the bullet.
 
  • #3
I agree with Nugatory but I can't help but wonder what you mean by "neglecting a constant".
 
  • #4
HallsofIvy said:
I agree with Nugatory but I can't help but wonder what you mean by "neglecting a constant".

Ok, Right. The statement "neglecting a constant" is my mistake.
I clarify my purpose of the question:
Newton's laws are only valid in inertial framework. I like to know whether energy formalism is valid in non-inertial framework or not? In other words, can one solve the problems exactly, using conservation of energy in non-inertial framework?
 
  • #5
hokhani said:
Ok, Right. The statement "neglecting a constant" is my mistake.
I clarify my purpose of the question:
Newton's laws are only valid in inertial framework. I like to know whether energy formalism is valid in non-inertial framework or not? In other words, can one solve the problems exactly, using conservation of energy in non-inertial framework?


[itex]\int_{t_0}^{t_1}\vec{F}(t)\cdot\vec{v}(t)dt = \frac{1}{2}m v^2(t_1) - \frac{1}{2}m v^2(t_0)[/itex] is valid in frames where [itex]\vec{F}(t) = m \frac{d\vec{v}(t)}{dt}[/itex]

That is, in inertial frames.

You still can use it in non-inertial frames IF you add "inertial forces".


[itex]\int_{t_0}^{t_1}\vec{F}(t)\cdot\vec{v}(t)dt = U(x(t_0),y(t_0),z(t_0))- U(x(t_1),y(t_1),z(t_1))[/itex] is valid in any frame where [itex]\vec{F}(x,y,z) = -\nabla U(x,y,z)[/itex]

where [itex]U(x,y,z)[/itex] does not vary with time in this frame.
 
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1. What is the concept of "energy dependence on observer framework"?

The concept of "energy dependence on observer framework" refers to the idea that the measurement of energy in a physical system is dependent on the frame of reference of the observer. This means that the energy value can vary depending on the relative motion of the observer in relation to the system being measured.

2. How does the observer's frame of reference affect energy measurements?

The observer's frame of reference affects energy measurements because energy is a relative quantity and is dependent on the observer's point of view. For example, an object moving at a certain speed may have a different kinetic energy value for an observer who is stationary compared to an observer who is moving at the same speed as the object.

3. What is the role of relativity in the concept of energy dependence on observer framework?

The concept of energy dependence on observer framework is closely related to the theory of relativity, specifically the theory of special relativity. This theory states that the laws of physics are the same for all observers in uniform motion and that the relative motion between an observer and a system can affect the measurement of energy.

4. Are there any real-world applications of the concept of energy dependence on observer framework?

Yes, there are several real-world applications of this concept. For example, in particle accelerators, the energy of particles is measured by colliding them with a stationary target, and the energy measurement is dependent on the frame of reference of the observer. This concept is also important in understanding the behavior of light and other electromagnetic radiation.

5. How can we account for energy dependence on observer framework in our measurements?

To account for energy dependence on observer framework in our measurements, we need to take into consideration the relative motion between the observer and the system being measured. This can be done by using equations and formulas that incorporate the concept of relativity, such as the Lorentz transformation equations. It is important to carefully consider the frame of reference of the observer in order to accurately measure energy in a physical system.

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