Rocky 701 asked in Science & MathematicsPhysics · 7 years ago

# Does a jet airplane flying through the air above TOronto have kinetic energy, potential energy, or both?

I think it's both but idk why, help!!

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• E
Lv 7
7 years ago

The airplane only has kinetic energy. Potential energy is a property of systems, not objects. (It's an energy of arrangement, and you can't re-arrange one thing.) So, while the Earth/airplane system may have potential energy, the airplane itself can't.

(Yes, an object such a spring may have potential energy, but that is really the result of re-arranging the individual atoms of the spring, so the spring is actually being treated as a system of atoms in that case, not as an object.)

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Edit: None N makes a good point. There must, indeed, be a reference frame for the plane to have kinetic energy. But that doesn't invalidate what I've said. After choosing a reference frame, the plane itself still has the kinetic energy--it is the object in motion. But the plane itself will never have potential energy. Potential energy is often misidentified as an energy of "position", for which a single object and a reference frame would be sufficient. But it is really an energy of *arrangement*, which requires that there be a second object in the system. You can move one thing (position), but even with a reference frame, you can't re-arrange one thing.

Potential energy is a result of conservative forces acting between objects within a system, and since these interaction forces always act on both objects (Newton's Third Law), the potential energy cannot be attributed to individual objects. It is a property of the system as a whole. Contrary to None N's claim, the Earth, orbiting the Sun, does not have potential energy. There is, however, potential energy in the Earth/Sun system.

Consider this: If you think the airplane has potential energy, when you try to figure out how fast it's going when it hits the ground, why don't you consider the work done on it by the gravitational force?

Finally, None N has made another good point. If someone else asked you this question, there's an excellent chance they want the answer "both". This is an extremely common misunderstanding that is perpetuated by poorly-written textbooks. So the question for you is, do you actually want to learn some physics, or do you just want to tell someone what they want to hear?

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Edit: Sorry, None N, that wasn't as clear as I'd have liked, because the whole "reference frame" issue wasn't the point I was trying to make. Yes, your choice of reference frame will determine the amount of kinetic energy the airplane has, and that amount may be zero. But "the airplane" can never have potential energy. Not because a particular choice of reference frame gives it zero potential energy, but because the concept of potential energy doesn't even apply to it.

If you choose the plane alone to be your system, then yes, the increase in the plane's kinetic energy (which is the energy of the system) as it falls is due to the work done on the system by the external force of gravity.

But if you choose the plane and Earth together to be your system, the gravitational force cannot change the energy of the system, because it is an internal force. In that case, the kinetic energy of the plane (part of the system) increases as the potential energy of the system decreases (energy is conserved in this system).

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None N: You say that the plane's kinetic energy increases as it falls, due to gravity doing work on it. OK, but if you think the plane itself has potential energy, what do you think happens to it as the plane falls? If you think gravity does work, AND the "plane's potential energy" decreases, you will end up with an invalid expression for the plane's kinetic energy. The way to fix the problem is to define your system carefully, and to realize that potential energy is a property of a system with internal conservative forces.

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I agree, None N, that a reference frame is necessary for the plane to have non-zero kinetic energy.

No, the issue is not that the question doesn't state "with respect to the Earth". The issue is that the concept of potential energy only applies to systems with conservative internal forces. The plane itself is not such a system, so the concept doesn't even apply. Note that this is different from the issue with kinetic energy. The concept of kinetic energy applies to the plane regardless of reference frame--although there are frames in which the kinetic energy is zero. But no choice of reference frame will give the plane potential energy, not even zero potential energy—the concept doesn’t even apply.

Your final sentence, “Energy is conserved” is not meaningful until a system is defined.

(Sorry, insufficient characters to address your last point. I even had to delete an earlier point to make room for this last reply.)

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Sloppy definitions are pervasive for this topic, even in textbooks. Will cont. in comments.

• None N
Lv 4
7 years ago

E's answer is interesting and is what I'll use to launch into a only tangentially related point but I believe he's made a mistake in somehow assuming that a airplane can have kinetic energy without being in a system too. An object can't even have a velocity without some reference frame.

Consider this, right now if you're sitting at your desk, you certainly don't seem to be moving, ie. no kinetic energy, nor would you see to have much potential energy, considering how you aren't falling.

But you're on the earth, which is hurtling around the sun at 67,062 miles per hour and which is constantly falling into the sun giving it potential energy.

Perhaps more relevantly, consider the example of the plane again. To a person on the ground looking up at the plane, it should be obvious that the airplane has both kinetic, it's flying, and potential, once again, it's flying, energy. But to a person ON the airplane, the plane does not appear to be moving, nor does the seem like the plane could fall from the sky. RATHER it appear that the earth is moving and that the earth could rapidly rise into the plane.

All of these energies are relative and based on what your reference points are.

That being said, the answer your problem is asking for is probably that is has both. It's moving relative to the surface of the earth, and it could certainly into the earth.

EDIT:

E, how can a plane have kinetic energy if you can't tell it's moving? If you choose the reference frame as a person on the plane for instance, the plane appears to have zero velocity. Rather the Earth appears to be moving. Your call that the plane has kinetic energy regardless of choice of reference frame is strange, all objects are moving relative to some reference frame, motion is relative. I don't understand the distinction you're making between potential and kinetic energy.

Furthermore the change in kinetic energy due to the plane falling is work done by the gravitational force, so I have no idea what you're trying to say there.

EDIT:

E,

Ok, so I think I understand what you're trying to say here. Correct if I'm wrong but basically since potential energy is defined by a system, and the question does not explicitly ask for the gravitational potential energy of the plane with respect to the Earth you'd like to say that the plane has no potential energy?

While I see your point about careful definition of a system being important, then likewise, definition of your reference frame should be important so I don't see why the plane can be said to have kinetic energy.

I still don't see anything wrong with gravity doing work. It increases the kinetic energy and causes the decrease the gravitational potential energy via the work it does. Energy is still conserved.

EDIT:

OK I THINK I REALLY TRULY UNDERSTAND YOUR POINT NOW.

In the airplane example, consider gravity as an external force doing work on the airplane, after all without a system you can't say why there's gravity, only that there's some external force. Then from all appearances and maths the airplane only gains kinetic energy, there is no potential energy term; you can't say an airplane by itself has potential energy, only the Earth, airplane system.

The simple fact I don't really believe in your definition here; I don't see why an object's relationships with other objects can't be said to be part of the properties of an object. Furthermore all the definitions of potential energy I find says things like

"the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors." From Google, see sources. All other sources I have found, abit with minimal searching say much the same.

While I see your point about it is necessary to have a system of objects to have potential energy, I believe the definition of potential energy does not preclude talking about the potential energy of single objects within a system.

Since it appears you're out of space I suppose we'll not have much more discussion, I much enjoyed it.

• Anonymous
7 years ago

You're right, it certainly has both!

Kinetic Energy is defined as the energy related to motion. The plane is flying, therefore moving, giving it kinetic energy.

The formula is KE=(mv^2)/2, where m is the mass, and v is the velocity of the plane. Since both of those exist, Kinetic Energy is present.

Also, the plane has potential energy, because it is elevated off of the ground. Potential energy is essentially energy of position. When something is elevated, gravity pulls it down. I try to remember it as it being the potential to have kinetic energy, i.e. the plane beginning to fall, giving it vertical kinetic energy. Also, you could imagine an arrow pulled about to be shot out of a bow. When the arrow is pulled back, it has the potential to move. A professor may not be to kind with that definition, but it may help you remember it!

Potential Energy is mathematically defined as(when related to height, as with the plane),

PE=mgh, where m is mass, g is the acceleration of gravity, and h is the height. The plane has a mass, it hopefully has a height(unless we crashed somewhere), and gravity is present for everything. Therefore, since m, g, and h are all present, Potential energy is present also.

Hope this helps.

• 7 years ago

I'm guessing both, it's obviously moving, so kinetic energy is present, and as it's in the air, is has a ton of potential energy, as it could fall, at which point that would be turned into kinetic energy. Cheers!