murf wrote:uncsimes wrote:
(nb - the speed of the planes wheels is the same as the plane itself. As all are attached, they must all be moving at the same speed, assuming bits don't fall off or accelerate away ahead of the airframe)
No!!! Wheel speed can be taken to be the rotational speed of the wheels (not the 'horizontal' speed) and this must be the same as the conveyor belt if the plane stands still.
Under most people's logic: The conveyor body itself is fixed and if the plane is moving forward at 100mph, the top conveyor
belt moves backwards at 100mph meaning the wheels have a rotational speed of 200mph.
All assuming no wheelspin etc.
The 'wheels', as a whole, must move at the same speed as the plane, as they are attached. At 10m/s, after 10 seconds, the plane, its wheels and other components have all travelled 100metres. Unless something has fallen off. Everything will have a displacement of 100m (i.e. travelled 100m in a particular direction, down the runway)
What most people are implying is that the speed of a point on the circumference of the wheels is higher than the speed of the plane. A point on the circ. of the wheel will have travelled a distance of 200m, and will have been travelling at a 'speed' of 20m/s.
If OMHS had said the speed of the tyres, then this is a different problem, and causes the 'impossible solution', i.e. you cannot get a steady state - either the plane stays still and both the tyres and belt travel at , say, 10m/s (in which case there is no force opposing the engines thrust and the whole thing is in contravention of Newtons 1st Law), or the plane moves forward and the belt then has to keep accelerating to match the increasing speed of the tyres (relative to the belt) until both are rotating at an infinite speed (which is silly).
Anyway, the question clearly states that the conveyor matches the speed of the plane. Why bother inventing different questions when some people still aren't convinced by the answer to the original question set?
Anyway - I thought you were in the 'sperical earth, normal laws of physics' camp, not the 'flat earth' one. You now seem to be implying that it is possible for the plane to stand still (and hence not take off). Or have I missed something?? (or am I just being an arse mentioning things which are irrelevant to the fact that the plane takes off
)