What else?
Yes, but you said the only solution. The one you give is is relative to the boat at waterspeed, but that would mean the drag is zero at waterspeed. That's impossible. However, there is also a solution when u=0, where the object is still in still water. That has zero drag, but no u, either.
No, it gives you two solutions at the limit, Sol. You seem to have made the mistake of not realizing that one is impossible.
Same as above.
An algebraic solution will do. Try a Laplace transform.
The force available to drive the object falls as the force against it rises. While the object is accelerating, thos forces are not in balance. One is square law, so it starts off relatively benignly, being lower than the driving force, but then increases rapidly to swamp it. It cannot reach waterspeed. Not even if the driving force is constant with velocity.
A confession of ignorance.
Cast iron.
I guess I should tell humber not to take it the wrong way either - because I mean it exactly like it sounds.
I haven't read anything from humber in a while, and I have to confess I haven't read past the first sentence of this post. But I guarantee you're wrong. Please don't take that the wrong way SZ.
I guess I should tell humber not to take it the wrong way either - because I mean it exactly like it sounds.
I don't see how that follows, Mender. The boat will slow when the power is cut, but not be at a standstill wrt the water? If you mean that if it is going slower than the water, and then the engine is cut, it would be driven forward by its momentum until it slows to the speed it would have for the same boat, but without the engine's power.
If its going faster than downstream, yes, but that takes motor power. A powered vehicle is not what is being considered, but objects driven by the medium. They cannot reach waterspeed, the 'at rest' condition
I think that I would like to see that he really understood what you asked.
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If that's the question, then the boat will stop when its kinetic energy is dissipated by the drag of the boat.
I think you dropped a comma after the word "energy", but in any case I need to clarify that point. The value of the kinetic energy associated with some particular object in one frame is not necessarily the same in another frame (because the velocity may also be measured as being different). However, if we're looking at an isolated system then total energy is conserved. Is that what you meant? Force, mass, and acceleration are identical in two inertial reference frames (and friction also).
I don't understand why you say the treadmill "fails quite obviously for all intermediate values". I was a bit lax in only talking about a cart on the treadmill while also at rest w.r.t. treadmill body/ground. We can also have the cart moving backwards at the same speed as the belt (as if it was at rest on "real ground" with a tailwind blowing past) and at any other speed also. Of course, we might need to have a longer treadmill in that case to ensure we have enough time to observe its behaviour before it possibly runs off one end of the belt or the other. But (hypothetically) we can make that treadmill longer and longer, in fact let's save some time and let it go all the way around the world. (At this point I'll refer you back my post #2744 in the original thread which I understand you are still working on replying to!)
the treadmill with belt moving at say, 10 mph, and with the mass of surrounding air at rest w.r.t to the treadmill body is equivalent to a "real wind" of 10 mph flowing over a patch of ground (let's say also covered with treadmill belt material). You can now add the cart at whatever speed you wish (relative to the belt/ground) and the two systems are still equivalent.I don't understand what you mean by "freeze it at standstill"? Can you elaborate please. Nor do I understand what "dynamic properties" are missing. Of course we do need to have the surface characteristics of the "real ground" and those of "treadmill" to be at least reasonably similar for the two to be more correctly interchangeable, but that also doesn't seem to be a major sticking point (no pun intended!)
Perhaps you can define "wind" or "real wind" for me so I know what you mean and why you say treadmill wind is not like a real wind. Sorry if I've missed this in some earlier post(s), but I still have no idea what you are getting at by making that distinction. I would have thought "wind" could reasonably well understood as air (usually) moving past the observer or some object (or some frame of reference) in a reasonably smooth and continuous flow? Here I mean "moving" as a relative thing, including the possibility of there being no relative motion (no wind). What makes one wind more "real" than another?
I look forward to hearing more (although "today" in your preferred frame may be "tomorrow" in mine!)
. The humber universe never ceases to amaze me. humber a boat achieving the speed of the river it is drifting in is equivalent to a boat that is powered slowing down to nothing once the power is turned off.