At point of contact of wheel and belt, both the belt and wheel circumference are moving in the same direction. Therefore, the cart should go with the belt.
An external force will prevent this, allowing the wheel axle to remain stationary, and so inhibit the motion. This force is low, being total friction to the belt, so a light touch of the finger, or drag from a propeller, will easily hold it in place. The prop does not move the cart relative to the belt, but simply prevents is from moving back with the belt.
Completely backwards again. Ignoring for a moment the mass of the wheels, a cart, just on wheels without any extra gubbinses, would not "go with the belt", except for an external force to overcome inertia. It would stay still, as Newton's First Law dictates, allowing its wheels to rotate under it. THE FRICTIONAL FORCES are what would cause it to go with the belt, clearly demonstrated by making them infinite. The fact that in the real world a cart with just wheels does not have zero friction means that if it was left on a very long treadmill, it would be accelerated down-belt until it reached terminal velocity due to drag from the wind, probably just actual belt-speed depending on its aerodynamic features and amount of friction, rolling resistance, etc.. Once you get that bit right, you see that the mechanism of the cart with its prop has to not just go a little bit forward (even so, pretty darn miraculous), but has to overcome the constant forces pushing it backwards. In other words, it has to reach windspeed before it can just outpace it a bit. Ynot's videos are useful for two things in particular: you can start the cart from "standstill in still air" and increase the windspeed to where it is sufficient to make the cart outpace the wind; and you can see by how much it outpaces it, continually, steady state. This should dispel any remaining doubts about where the cart achieves its natural speed relative to the wind, for those who understand relative motion, frames of reference, etc.
The wheel and so the propellor can not move at any other velocity than directly determined by the belt, unless the wheels can rotate slower than the belt. Faster is not possible, as no matter what the grearing, the propellor cannot drive the wheel faster than the wheel that drives it.
Wrong. Not only demonstrated as wrong, but physically naive. If we replaced all elements in the system with toothed gears - belt-wheel-prop-air-belt - then you'd have a point, but the prop-air and the air-belt interfaces are flexible.
It is not possible for a cart to move at say 2m/s slower than a 4m/s belt, while 'traveling up the belt', because then the wheels must spin at half the velocity of the belt.
Well, a plane can taxi along an aircraft carrier in the direction of the stern making its velocity w.r.t. sea half that of the ship. What the cart demonstrates is that not only do you not need a separate engine to do that in air that is stationary w.r.t. the sea, but the cart will go directly down ship faster than the ship, reversing its direction w.r.t. the sea from that of the ship it is on.
Somebody really ought to do that, film it, and post in on youtube, by the way. ETA: Unfortunately, ships of sufficient length to demonstrate DDWFTTW from a standing start might not be capable of sufficient speed, nor is it easy to demonstrate that the air movement is solely due to the passage of the ship (i.e. that it's a completely still day). Thank goodness for treadmills and equivalent frames!
The cart is brought to speed by operator influence, so that it may balance in place.
No, it is brought to speed by operator influence because the treadmill is only a few feet long.
The treadmill has nothing to do with a cart in wind.
You're like a creationist taken to see a cliff face full of fossils.
The belt and wheel do not go at different speeds. The only other option is for the wheel to completely slip on the belt, and so go slower then the belt, but that means motion down the belt.
You've changed the sense, now. Going slower than the belt was going up-belt a couple of paragraphs ago. Not only that, but "slipping" was what you suggested made the cart go up-belt in the videos.
You were saying?:...
You contradict yourself, and do not notice that in your case, both the axle and tyre move relative to the road.
I've never denied it. I've assumed it was fairly obvious. Parts of the tyre move at
different velocities relative to the road.
There are other errors. The wheels on the front and rear of a car are often at different angular velocities.
Mostly untrue or negligible difference, but irrelevant anyway.
The average diameter of the driven wheel is actually smaller than an undriven wheel. That is how thrust develops. On a tire, this causes the tread to 'slip' to make up the difference.
NOMINATED (not that almost everything above also shouldn't be, but that really is the dog's nadgers).
ETA: That'll be why dragsters don't develop any thrust I suppose. They should have the small wheels at the back!...or are they front-wheel drive?
Actually, someone ought to take humber's version of how wheels work and email Dunlop or some vehicle dynamics labs. We could post the replies here. Perhaps have a conversation with NASA on gravity, freefall, etc. and do the same.
