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I Birds in a truck riddle (sorry to beat a dead horse)

  1. Jul 9, 2016 #1
    As per the title, apologies for bringing this up again, but all previous threads were closed. Now, I can accept the answer and experimentation done, however as both a pilot and mechanical engineer, I just can't get my head around it. It's been bugging me for years, and created the account just for this : )

    While I can happily agree things fly due to pushing air down and 3rd law, why wouldn't part of all of that energy eventually be dissipated into heat through the fluid's viscosity? To me it appears like a 1st law of thermo thing. Plane does work on air -> Becomes heat + less work on floor.

    Adjacently, to the accepted solution that the air gets pushed to bottom regardless of how high it is, does a propeller forcing air horizontally simply keep on going around the earth forever then?

    The water tank analogy doesn't do it for me either since different mechanisms are at work (buoyancy vs down wash/pressure differential)

    Finally, another way I picture this, is if instead of blowing air molecules down, lets say you had a machine gun which fired pingpong balls. They're fired out at some huge speed and rate, enough that if you're firing downward, its enough force to keep you aloft. By the time they reach the bottom, they will have slowed considerably due to friction, and though the mass flow rate will be the same, the velocity, and subsequent force on the bottom of the box when they hit will be considerably diminished.
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  3. Jul 9, 2016 #2


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    It does. That's why the poor birds have to keep flapping their wings just to maintain a constant height. If they were perched on a rigid support instead of this squishy spready air column, they wouldn't have to keep working - they'd just sit there and let the perch transfer their weight to the floor instead of continuously generating more downwards-moving air to do the weight transfer.
    The propeller makes a small amount of air move very fast. Because it's air and it's a bit viscous over time you end up with more air moving less quickly as the moving air transfers its momentum to the still air around it. Wait long enough and all the air in the system will be moving at a constant speed.

    It's a good exercise to actually do some calculations here. In one second a reasonable aircraft propeller might accelerate 100 cubic meters of air to a speed of 100 meters/second. What is the momentum and kinetic energy of that 100 cubic meters of air? (The density of air, ##p=mv##, and ##E_k=mv^2/2## will get the job done). Now this moving air mixes with all the still air around it (and eventually the entire atmosphere of the earth). That's a much larger volume, and hence mass, of air. Momentum is conserved, so you can calculate the speed that the entire mass of air ends up moving at. Is it noticeable, or is it consistent with your observation that the slipstream from teh propeller does not seem to go on forever? What is its kinetic energy? The difference from the initial kinetic energy is what has been dissipated as heat.
    Friction slows them, but it also speeds up the air around them. This is just Newton's third law at work - the air exerts a frictional force on the balls, so the balls must exert an equal and opposite force on the air. The total downwards momentum is conserved, and in fact this is just the previous propeller example, with the balls from a gun substituted for downwards-moving air molecules from the propeller.
    Last edited: Jul 9, 2016
  4. Jul 9, 2016 #3


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    Imagine an sealed box containing air. The total weight of the system equals the weight of the box and the air inside. The air exerts it's weight on the box via a pressure differential, greater at the bottom, lesser on the top, so that the net downforce exerted by the air on the inside of the box is equal to the weight of the air. Now imaging placing a small remote control helicopter inside the box. Now the weight of the system equals the weight of box, air, and helicopter, regardless if the helicopter is resting on the bottom, or hovering within the box (as long as the center of mass of the system doesn't have a vertical component of acceleration). When hovering, the net effect of the helicopters downforce on the air, increases the pressure gradient and corresponding downforce so that the downforce that the air exerts on the inside of the box equals the weight of the air and the helicopter.
  5. Jul 9, 2016 #4


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    You are confusing momentum and kinetic energy. Macroscopic kinetic energy can be dissipated (converted in to other energy forms). But momentum is conserved.
  6. Jul 13, 2016 #5
    OK, That does make a bit more sense, but I'm still having a hard time visualizing it I guess, while I always grasped conservation of momentum, I guess I never really extended it to the microscopic level, and treated friction as it just 'slows things down' consequence free. I take from this then that kinetic friction is basically a fake, made up force? In reality it's just the undesirable (streamlining) or desirable (braking) transfer of momentum to the air or earth? May as well just be called the momentum transfer efficiency coefficient?

    Secondly, satisfying both conservation of momentum and energy, is it then a consequence that you can never theoretically change 100% of kinetic energy into heat? A car braking rapidly will convert all it's motion into heat (friction) and transfer all its momentum to the earth, but given delta-v^2 of earth being so minuscule, it's approximately 0?
  7. Jul 13, 2016 #6


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    If you are considering a moving object striking a motionless target then yes, no possible collision can convert all of the initial kinetic energy into heat. Conservation of momentum says that the center of mass will always be moving, so the parts will always have some residual kinetic energy. And yes, the delta v2 of an earth that starts at rest is small enough to ignore. [Be careful if you are considering a moving earth -- the delta v2 in that case is non-negligible]

    But would be a huge mistake to trust that result.

    Nothing requires the center of mass to be in motion to start with. If one takes the point of view of a bug sitting still relative to the center of mass then all of the kinetic energy of the two colliding objects can be converted into heat energy with no problem at all. Kinetic energy is not an intrinsic attribute of an object. It is an attribute of an object relative to a frame of reference. When you analyze a situation, you are free to choose any reference frame you like.
  8. Jul 13, 2016 #7


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    And neither is momentum.
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