Originally posted by: sao123
Originally posted by: ducci
Alright, you sound smart. I am not disagreeing with you. I just have a question, and it's really all that bothers me about this scenario:
If the wheels are spinning, and the treadmill is going, all while the engines are pushing the plane forward - wouldn't this cause the wheels to "slide" on the surface of the treadmill?
For example, if I'm on rollerblades on a treadmill and I'm holding a rope attached to a pole in front of me, and I pull forward, the wheels would undoubtedly slide. How is that any different in this case?
I was under the impression the question declared that there was no sliding of the wheels, so I'm just wondering what the explanation for that would be. Thanks man.
:beer:
The wheels will not slide.... the wheels simply turn faster.
They do not have a theoretical maximal velocity cap.
Originally posted by: smack Down
Suppose we have an identical plane, on an identical conveyor-runway but the plane has no engines. I think at this point we have established the fact that the thrust comes from the engines and not the wheels. If you turn on the conveyor given the connection interfaces described above, the wheels WILL SPIN equal and opposite to the motion of the conveyor, this rotation is caused by a force applied to a location away from the center of mass of the object. In order to prevent translational motion, a rotating body requires a force couple. In this example the inertial mass of the plane is so many orders of magnitude above the effective x force acting on the plane, that secondary order effects such as air resistance will negate any already negligible movement. This completes the couple.
If I read this right you are saying the force for the wheels is so small it can be ignored. I'm not sure you are correct in ignoring such a force unless you can show it is bounded. If the force isn't bounded then it is infinite because the treadmill will make it so.
This number is bounded.
the maximal amount of force capable of being transferred through the rotational axel is equal to the frictional force of that same system.
Since the frictional equation is
F = u * N
u is the coefficient of friction = approximately .05 (for lubricated steel bearings)
N is the perpendicular force = mass of the plane * 9.8M/s^2
regardless of these values, this number is constant, and does not change with repesct to any velocity of the plane, treadmill, or other.