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Energy dependence on observer framework

by hokhani
Tags: dependence, energy, framework, observer
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hokhani
#1
Jun13-14, 12:33 PM
P: 270
Does mechanical energy of a system depend on the framework of an observer (neglecting a constant)?
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Nugatory
#2
Jun13-14, 01:28 PM
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Quote Quote by hokhani View Post
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.
HallsofIvy
#3
Jun13-14, 02:37 PM
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I agree with Nugatory but I can't help but wonder what you mean by "neglecting a constant".

hokhani
#4
Jun15-14, 02:57 AM
P: 270
Energy dependence on observer framework

Quote Quote by HallsofIvy View Post
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?
mattt
#5
Jun15-14, 05:29 AM
P: 125
Quote Quote by hokhani View Post
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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