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If an aeroplane is flying horizontally at an altitude of H , and with a constant velocity of V (no air resistance) horizontally .

Is there a relationship between the potential energy of the aeroplane due to its vertical height and its kinetic energy due to its horizontal velocity?

Is it correct that $E_p + E_k$ is equal to the Total Mechanical Energy?

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  • $\begingroup$ No. A plane at one altitude can fly at any speed it wants to. $\endgroup$ – user1936752 Aug 22 '15 at 13:50
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Just to clarify the comment above a little.

You can treat the velocity of your plane, neglecting air resistance, as completely independent of it's height, if you have studied vectors you may know how this can be drawn out on a graph.

The plane has a potential energy, mgh (mass by g by height) and this potential energy does not depend in any way on how fast it is flying in a horizontal direction.

It's kinetic energy, at a constant velocity, is the same at every height it flies at, again ignoring the air resistance, so it's kinetic energy is independent of it's height.

Kinetic energy is (1/2)mv$^2$ and potential energy is mgh. The total energy of the plane is the sum of those two sources of energy.

Have a look at this link Total Mechanical Energy and scroll down to the last section of the page to their definition of Total Mechanical Energy (TME) and their example.

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    $\begingroup$ thanks. Correct me if im wrong, but is the kinetic energy then mv^2/2 and the potential energy mgh, and the total mechanical energy the sum of those? or is the total mechanical energy = mgh, since the vertical speed = 0 at height h? $\endgroup$ – Carefullcars Aug 22 '15 at 14:36
  • $\begingroup$ updated the answer with a link about your question. $\endgroup$ – user81619 Aug 22 '15 at 15:15
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    $\begingroup$ Thanks, i was under the impression that the sum of Ek and Ep always was a constant, but according to the website you linked: "There are conditions under which the total mechanical energy will be a constant value and conditions under which it will be a changing value.", it doesnt have to be constant. So if an airplane is going 300m/s horizontally at a heigh of 3000m, its total mechanical energy = m * 300^2/2 + mgh. $\endgroup$ – Carefullcars Aug 22 '15 at 16:45
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    $\begingroup$ I thought you might be confused a little about this and I was going to say it earlier. Say you hold a stone at rest in your hand 10 metres above the ground. PE = mgh and KE = 0. Now let it drop and it ends up, just before it hits the ground, it's PE is 0 (as h is 0) but all of its PE has been converted into KE. So in this case the sum is a constant, but in the plane case you start with different conditions. Hope this makes sense to you. $\endgroup$ – user81619 Aug 22 '15 at 16:54

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