I'm having a bit of a mental block, and would appreciate some physics help here. I feel like I should know this, but am missing something obvious. If I want to levitate a 70-kg person off the ground, the amount of Force required to lift them is easy to calculate: 70kg * 9.8 m/s^2 = 686N. So far so good. Now, to calculate the amount of Energy needed to move the person upwards by 1m is 686N * 1m = 686J. Ok, now we've got him floating a meter above the ground. Except that he's not just going to float there indefinitely unless 686N of force is applied to him, to counteract the force of gravity. How do I figure out how much Power (i.e. constant input of Energy) is required to keep him floating there? Power (thrust) is defined in terms of velocity or distance displaced, and since he's just sitting levitating, not moving, I'm not sure how to calculate that. Someone please help me out. For someone rather well versed in science, this is both frustrating and slightly embarrassing not to be able to figure this out.
Im not sure about this. But shouldnt it just be as much power as the gravity is pulling him down? I dont know how much power that is but lets say its 100 then shouldnt 100 from the other direction(?) keep him floating? Just a thought im not sure
The problem is that gravity is a Force (acting on a mass) not a Power. So you would need 686N of Force to counteract the Force of gravity. The problem with translating this into Energy is that you would have to multiply it by the distance the Force is being applied over, which, since he is floating, is 0. But it can't take no Energy to keep him afloat in the absence of other forces (like magnetism) or a surface for him to rest on.
You just did. 0d = 0 work = 0 power. How much work does a table exert over the objects "levitating" on it? At which rate is that work being performed?
I think you mistake the meaning of power. For example. Calculate how much work is doing an engine that tries to hold an object up but fails, countering just half of the gravity.
Well, think of it this way: if he had a rocket attached to his butt, how much thrust would it need to exert for him to hover? The answer isn't 0, because it needs to hold him up against gravity. Or take a helicopter; for it to hover, its rotor needs to exert a certain amount of thrust downward. (In these two cases, it's thrust output, not the energy expended, I'm interested in, because for my initial question, I'm interested in the answer with close to perfect efficiency.)
Thrust is force, not power. The amount of thrust you'd need depends exclusively on the mass and the acceleration you wish to exert on the aforementioned butt. You want a thrust of buttmass * 9.81 m/s2.
Oh, duh. I apparently can't read Wikipedia or think objectively at 2AM. I think my problem is that I'm trying to keep him levitated in the air directly *just* by injecting force into the system, which isn't quite the right approach. And since there's no direct conversion between thrust and power/energy, I would have to figure out the physical mechanism for levitating him (creating a virtual thruster by moving air towards or away from him at relatively high speeds), and calculate the power required for that. *sigh* Why do things always have to get so complicated. So, I could "pop" him in the air with a fairly direct application of energy. Does it make sense to repeatedly pop him slightly, just enough to keep him aloft, and sort of.... integrate the pops across time to find the energy required? I'm still a little groggy, so that might not make sense to you, or to me after I've had some coffee.
I think you got the mistake with the previous vision but I don't know how to help you without more information of what you're looking for. You can indeed hold something in the air by direct application of force. Essentially, every kinetic effect will be a direct application of force if you find the correct point of view, so what are you trying to find that can't be solved by defining how much force you can apply? I should wait for your extra info but I'll add another suggestion just as a guess: Is your problem solved by using "force by time" (instead of force by space)?
No, I'm not trying to calculate this in terms of force required, that's easy (686N), I'm trying to do it in terms of energy required, which now seems silly to my caffeinated self, because this can't be accomplished through direct energy expenditure -- there has to be a machanism to convert the energy into force (like a strong wind pushing him up). My real goal was to calculate equivalent amounts of energy for, say, boiling a lake, in terms of something easier to wrap my mind around, like lifting an object. I'm going to try this again, except make it something much simpler, like sliding a large block on a frictionless surface (this is easy enough to envision from experience).
Have you tried thinking of alternate solutions for your problem? You're trying to calculate the energy needed to levitate an object. An object like a helium filled balloon doesn't use energy to keep it afloat. The hellium is lighter than the air so it floats on the air. I mention it because I saw your comment on boiling a lake. There are actually two ways to boil water: The most common and easiest way is to heat the water until it reaches the boiling point. The second way is to lower the atmosphere around the water, which lowers the boiling point. This way actually allows you to make cold water boil.
Fun topic. You already got pretty good responses. Let me try to give an example which may better correspond to what you are looking for. Say you have a hovering helicopter. It's not doing physical work by hovering, but it is consuming fuel. Is that what you want, basically, the fuel consumption rate for a hovering helicopter, except that in your case you are dealing with presumably a more exotic form of levitation?
I didn't see the second page, and though my post was the latest. Moving my edit to a new post here: After running some calculations, evaporating an olympic size swimming pool would require 8,000 each to perform as much work as dragging a one-ton steel block over a mile on a steel surface. Accomplishing this in 4 hours would require the energy output of 1.7 million people riding stationary bikes for that period of time. And these are both assuming perfect efficiency. I'm going to say that this is *far* beyond the bounds of feasability to accomplish even for a large, organized group. And in response to Ellipse: it would be interesting to lower the atmospheric pressure, but if it was outside, it would be next to impossible to sustain an environment with pressure that low, as air would rush in to equalize the pressure, and in my magic system, there's not really a good way of magicians creating a barrier, unless you can think of a way to do that. It seems wildly unfeasible to me to be able to evaporate large amounts of water by any method, based on my research. I think I'll have to find another sinister way to exploit my magic system (I apparently can't think evilly enough). And Porcupine: Right, except now that I'm thinking straight, I realize that it's completely dependent on the method of levitation. Within my magical system, direct levitation is impossible, so it would need to be accomplished in a more indirect way, which would require figuring out an efficient method of producing thrust by manipulating energy; shooting air downwards and essentially creating a bubble of air is one possible way, but the calculations required are non-trivial. This will still likely appear in my story as an exotic, innovative use of magic (which will likely require the user to have some understanding of engineering to accomplish properly), but it's not going to server the current purpose I wanted it to.
F= d(mv)/dt or v.(dm/dt)+m.(dv/dt) Only when dm/dt=0 (usual with rigid bodies) it becomes m.(dv/dt) = m.a That's why a rocket can move against gravity: because dm/dt is not zero. Maybe you can have your floating body have a dm/dt that compensates the m.g ? Floating bodies otherwise means a net force of 0, i.e., a force indeed working against the m.g. HTH
It is extremely easy to evaporate the amount of water needed to fill an Olympic sized swimming pool. It just depends on how the water is distributed. Since evaporation rate scales with surface area, if you increase the surface area you get more evaporation. Cooling towers work on this principle. On a darker note... throwing a few uranium fuel rods into your pool will also evaporate the pool quite fast, as everybody has been learning these last few days.
Isn't (one of) the point of magic to get around realistic explanations? Do you imagine your audience will demand to be reassured of the scientific feasibility of magical levitation? If not, it probably doesn't matter. Idk tho. Seems plenty interesting. Makes me want to brush up on my physics
No, the point of magic is to enable things outside of the laws of physics and our own rules of possibility; a good magic system has its own set of realistic expectations based in its mechanics. Magic systems without a set of rules to follow often become a crutch and a source of deus ex machina resolutions to sticky situations ("Oh, we're in mortal danger, but, don't worry, I've never told anyone before, and we'll likely never speak of it again, but I can teleport us away!" or "Even though all magic before this point has required hand motions, and my arms are tied up, I, for some reason never explained before, have the unique ability to cast spells without the hand motions."). I could easily extend the rules of the system to include levitation for my own convenience as an author, but if I do that, my magic system will become inconsistent (the way my magic system works doesn't have room for levitation, so it would be anamolous at best).
I guess I should have underlined my keywords or something. When I said realistic, I was referring to this reality - getting around the explanatory constraints of the phenomena of this reality. Yes, I know that magic & other phlebotinum are bound by suspension of disbelief like anything else & deus ex' are bad. I didn't mean that the presence of magic automatically negates the necessity for relative realism. Rather, that using something as mysterious & paranormal as magic (in that it's not explained enough to be called science) generally seems to require a higher level of suspension of disbelief & contentment with not fully understanding the intricacies & nuances of the spell, power, ect. Fantasy/magical subject material seem to prime readers to not expect to have everything explained to them, basically, & the degree of scientific meticulosity in your post appeared extraneous, potentially. At least insofar as the actually telling the story. Anyhow, just an off the cuff bit of sardonicism. Didn't mean much by it or read much into it. Didn't mean for ya to misunderstand meh, lol. I'm pretty tired, I guess I should have worded that better. Unfortunately I have nothing constructive to contribute to your inquiry so I'll leave your thread in peace. Good luck
Well, basically, I was just explaining why I couldn't just add levitation to my magic system. That's not the answer for me, so, since it's not feasible to do, I'll find something else.
Work is force times distance. To keep an object suspended requires a force, but no work is done. Power is work multipled by time. Again, because there is nor work performed, there is no power expenditure. If that seems counterintuitive, consiser a table supporting an object. The table e3xerts a force upward on the object, and the object exerts an equal force downward on the table. Work eventually manifests as heat, but the table does not give off heat in order to support the object, nor is any other form of energy generation manifested. This is Physics 101. It was drilled into us in 8.01, which was indeed the freshman level physics course.
Right, my late-night problem was forgetting that converting work to force requires some mechanism. You can't just pump energy into an object and make it levitate -- you need something to convert that energy to force (like that energy moving air, or a rocket thruster or propeller). The table happens to be a mechanism that provides the force (normal force, in this case) without requiring the input of energy. (I went to an engineering school, this stuff is all fairly easy to me, though I sometimes need my memory to be jogged a little.) Levitation *is* possible in my system, but it's more indirect -- it requires me to come up with a mechanism, making the calculations nontrivial.
