No problem. But I wonder if you could comment on
this post of mine as well.
OK. In that post you wrote:
“I don't believe 9 m/s is the right speed to use here. That's the cart's speed relative to the ground. But the propeller exerts a force on the air, not on the ground. Since the propeller's thrust is moving the propeller through the air at only 2 m/s, only (160 N)(2 m/s) = 320 Watts of power is required.”
If the objective here was to move 72 kg per second of air @ 2.2 m/s, as a fan would, then 320 Watts would definitely be sufficient for that task. But the main objective here is to move the 295 kg cart @ 9 m/s over the ground. To do that requires Work = Force x Distance and in this case that is 160 N x 9 m = 1,440 Joules, or in terms of Power 1,440 J/s (Watts).
That's ok too, of course. We can pick any frame of reference to work in, and we should get the same answer.
OK so as to avoid even the
possibility of ground power, I would prefer to stay in the FOR where the ground is stationary and has no energy.
I don't see why this is true. Why are the relative amounts of kinetic energy at all relevant? See
this post by Michael C for a simple counterexample.
Michael wrote:
"we have a large truck with the brakes off. We give it a push to set it rolling at, say 5 m/s. We throw a tennis ball in the direction of travel, at, say 10 m/s. The tennis ball hits the rear of the truck. We have now increased the kinetic energy of the truck by hitting it with something that has less kinetic energy."
True, but this does not contradict me at all. I said that an object with less kinetic energy can transfer that energy to another object with greater kinetic energy if work is done. Work was done in throwing the tennis ball at the back of the truck. This is also a bad example because it does not reflect the situation we have with the wind moving slower than the cart. If Michael wanted to better simulate that situation, he would have started the truck rolling at 5 m/s then lobbed tennis balls at it at 3 m/s. In fact, let the truck roll through a sea of tennis balls moving at 3 m/s and show how they can transfer any kinetic energy to the truck. I think you will find the truck must cut a path through that sea of tennis balls, pushing them out of its way. The truck will be losing kinetic energy to the tennis balls until it reaches some equilibrium speed either at the same speed the tennis balls are moving, or something even less. There is no way the truck will continue moving at 5 m/s.
It is true that the air is moving slower than the cart, and therefore, the propeller needs to be spinning in order for it to receive energy from the moving air. Some energy is required to spin the propeller, but I see no reason why the amount of energy it subsequently gains from the air can't be more than the energy required to spin it.
This is known as over unity. In Newtonian mechanics, there is no way to use energy such that it creates more energy than what you started with. If there was, we would never need to worry about an energy shortage. There are some weird processes in QM where it is possible to do this, but we don’t need to go there.
I don't think you've shown that. See the post of mine that I referred to above.
I think I have already answered that (also above) but let me know if you would like to discuss it some more.
You can say "the energy is coming from the electric motor", but that doesn't explain in any detail why the electric motor drives the cart forward rather than backward. After all, the tread of the treadmill is moving backward. Why doesn't the cart simply follow the tread backward?
I believe that as you analyze the cart on the treadmill more and more carefully, it will start to seem more and more like the same cart on the ground in a wind. All the relative motions are the same. All the torques and forces are the same. So, why would the cart not behave in the same way?
I assure you I have examined the treadmill in great detail. At first, I was as confused by it as anyone else, but fortunately I do have some experience with mechanical and electrical resonance as well as vibration analysis. That, and the fact that a velocity transform in no way implies any change to the physical system, enabled me to figure out what is happening on the treadmill, and that it has nothing at all to do with wind energy.
You say all the forces and relative motions are the same. Are you very sure about that? Here on the surface of the earth, everything moves along with that surface, even as the earth is spinning very rapidly on its axis. We move along with it because of our inertia, as well as the effect of the gravitational force on us and friction with the surface. If you jump in the air, you continue moving with the surface, it doesn’t move under you, because you cannot escape from the inertia and the earth’s gravitational force on you.
On a treadmill,
once you start to move backwards with the tread, you also have inertia and if you jump up the tread does not move under you either, so it seems the same as the surface of the earth, but it isn’t! What if you don’t start the treadmill, but jump in the air and then switch the treadmill on while you are in the air? In that case, the tread will move under you. Now, instead of landing full on the tread, just very quickly and lightly bounce up and down. If you do it right, you can hold your position relative to the ground, while the tread moves under you. If you have a treadmill, try it! I will bet you any amount of money you cannot bounce straight up and down on any level road that is on the surface of the earth, and get it to move under you! (without any external force, such as wind force)So there must be something different! That something is simply
not allowing the inertia of the treadmill to have an effect on you, by never allowing yourself to be dragged back with it in the first place.
Why do you think the cart must be held in place while the tread runs under it, to get it started? Two reasons, both equally important 1) to prevent the tread from building up any inertia in the cart 2) to get the wheels spinning and the propeller thrust going so the cart will no longer need to be held by hand. Now you have a cart in what is called a latched state, running on the treadmill with no inertia from the tread.
It will slide and bounce around in a way that you will never see a cart on any road do. The treadmill is NOTHING like a cart on a road! Just forget about it unless you want to make little toys to amuse the kiddies.
Once you throw away the so-called treadmill equivalency, and you examine the NALSA data carefully, you will find there is NOTHING to support the claim of DDWFTTW, certainly no mathematics! It is a farce and it is time it was totally exposed as such.