Your analysis is correct. You have not made a mistake. The change in kinetic energy is indeed different in different reference frames.etotheipi said:surely the change in kinetic energy should be the same in different frames of reference? I was wondering what mistake or misconception I have made
Dale said:Your analysis is correct. You have not made a mistake. The change in kinetic energy is indeed different in different reference frames.
You may be concerned about conservation of energy. Conservation is a separate issue. KE is frame variant, but energy is still conserved
Consider the work done by the rocket on the exhaust stream.etotheipi said:The situations are identical, so it appears that the amount of work done by the rockets should also be the same.
If you count all the participating bodies, energy dissipation does not depend on the choice of reference frame. It is an invariant. It is only if one restricts attention to a single object (e.g. the rocket) that a net effect is seen.VVS2000 said:I too actually posted a similar question regarding friction and energy loss. Yeah even I don't know how changing your frame of referece will affect the energy dissipation
As @jbriggs444 alluded to in post 4, the key is to consider the KE of the exhaust. I would go so far as to say that all confusions about energy conservation in rockets is due to a failure to consider the energy of the exhaust.etotheipi said:Furthermore, what value of energy would we quote if trying to figure out e.g. how much fuel to use?
The concept of "difference in energy not the same in different reference frames" refers to the idea that the amount of energy observed in a system can vary depending on the reference frame from which it is measured. This is due to the fact that energy is a relative quantity and can be affected by factors such as motion and gravitational forces.
Considering different reference frames is important because it allows us to accurately measure and understand the energy of a system. Energy is not an absolute quantity and can appear differently depending on the observer's frame of reference. By taking into account different reference frames, we can avoid making incorrect assumptions about the energy of a system.
The theory of relativity, specifically the special theory of relativity, explains the relationship between energy and reference frames. It states that energy and mass are equivalent and that the observed energy of a system can vary depending on the observer's frame of reference. This is known as the principle of relativity and is a key concept in understanding the differences in energy in different reference frames.
One example is the Doppler effect, which is the change in frequency or wavelength of a wave as observed by an observer in a different frame of reference. This can be seen in the difference in pitch of a siren as a vehicle approaches and passes by an observer. The energy of the sound waves appears different to the observer depending on their frame of reference.
Accounting for different reference frames is crucial in maintaining the principle of energy conservation. In a closed system, the total energy remains constant, but it may appear differently to different observers depending on their frame of reference. By considering all reference frames, we can accurately track and account for the energy in a system and ensure that it is conserved.