Conceptual Question about reference frames

AI Thread Summary
Kinetic energy is not the same in all inertial reference frames, as it varies based on the observer's frame of reference. For example, an object may have kinetic energy in one frame while appearing at rest in another, resulting in zero kinetic energy. However, energy is conserved across all inertial reference frames, adhering to the same physical laws regardless of the observer's motion. This principle holds true in both Classical and Special Relativity. Thus, while kinetic energy is frame-dependent, energy conservation remains consistent across different inertial frames.
kikko
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Homework Statement



Do objects same kinetic energy in all inertial reference frames?
For objects interacting, is energy conserved in all inertial reference frames?


Homework Equations



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The Attempt at a Solution



I think the answers are No for the first one, and Yes for the second one. Am I right?
 
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what is your logic or thought experiment for getting these answers?

Some people think in terms of billiard balls and consider what happens when they collide.
 
My logic is that since depending on what reference frame you are in, you view different objects at rest, so they'd have different amounts of kinetic energy.

My logic for the 2nd is that intertial reference frames obey the same laws of physics, so energy will be conserved. Am I correct with both responses?
 
kikko said:
My logic is that since depending on what reference frame you are in, you view different objects at rest, so they'd have different amounts of kinetic energy.

My logic for the 2nd is that intertial reference frames obey the same laws of physics, so energy will be conserved. Am I correct with both responses?
I think your answers are correct. Here's my logic for the first one:

I'm standing by the road and a car whizzes by at 60mph so its energy is 1/2 m v^2
Next I'm in a car going 60 mph along side the other car so to me his velocity is 0mph hence 0 energy

so I conclude the kinetic energy of an object is relative to my frame of reference

I'll let you consider a thought experiment for the second one.
 
Observations of speed, and therefore, kinetic energy, can differ depending on which inertial frame of reference one is considering. This applies in both Galilean (Classical) and Special Relativity.

Energy, momentum, etc. are conserved in all inertial frames of reference. This is also true in both Classical and Special Relativity.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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