Originally posted by: Jeff7
Originally posted by: Fenixgoon
Originally posted by: smack Down
Take an dynamics class please.
if you've taken dynamics, you should understand how the tires will be behaving. since you don't understand the tires, you clearly haven't taken dynamics.
self-pwned.
Agreed. I've had a dynamics class. I have presented, twice in this thread, three possible interpretations of the problem.
The treadmill's velocity cannot be a function of the rotational speed of the wheels, as the rotational velocity of the wheels is a function of not only the plane's forward velocity, but also of the linear velocity of the treadmill. The two velocities are functions of each other. As has been said, if you try to increase the velocity of one, it'll affect the other, which will immediately affect the initial component. Result: infinite velocity of both components.
But what the hell, here, again, are the three scenarios:
1) The treadmill/conveyor belt's velocity matches the plane's takeoff speed from an otherwise immobile surface, like a runway. Here, the plane can easily take off, as was just shown on Mythbusters. That scenario is no longer an issue, as it was shown experimentally, twice.
2) The belt's velocity is a function of the wheels' rotational velocity. Here, unless it's an inverse exponential, or fraction of the belt velocity, the velocity of the wheels and belt will quickly approach infinity. Think of a looped relationship in Excel, where one cell's answer winds up referring back to itself. *already discounted as a physically impossible scenario
3) The belt's velocity is carefully set so that it can speed up to any speed, so as to keep the plane stationary, as a result of the rotational inertia of the wheels, as well as bearing/rolling resistance. In theory this is possible, as the rotational inertia and rolling resistance are finite, measurable values. The problem is that the conveyor belt, and thus the plane's wheels, would likely have to move so quickly that the bearings would sustain damage.
If I had some numbers, such as wheel mass, wheel diameter, rolling resistance, engine thrust, and the overall mass of the plane, I think I could solve this problem (that is, determine how fast the wheels would need to rotate) using what was covered in my Dynamics class.
Scenario 3 is the most complex one, as it involves many variables, such as friction, and uses principles from dynamics, such as the rotational inertia of the wheels, and rolling resistance.
In the real world, if you'd put a plane on a conveyor belt, engines off, and started up the belt, the plane would indeed move backward,
and the wheels would begin to rotate, though slowly. The result would be that the plane's backward velocity would be slightly less than that of the treadmill's, due to the motion of the wheels, but this velocity would be a nonzero component.
Given that the wheels have rotational inertia, and given that the bearings have friction, and given a treadmill capable of
any velocity or acceleration, yes, you could increase its speed to produce a force acting against the forward force of the plane's engines. If I had some numbers, such as wheel dimensions and weight, their rolling resistance, plane weight, and engine thrust, I could tell you how fast the treadmill would have to be moving in order to hold the plane stationary.
I have a feeling though that the treadmill would have to move
so fast to hold the plane still, that the wheel bearings on the airplane would overheat and sustain damage, or else the tires would fly apart.