2nd December 2005 - 04:06 AM
Well, I picture it shooting forward then lifting off. But yeah, you are right. And one major difference between the skateboard ex. and the plane ex. is that the belt for the plane doesn't move until the plane starts moving, so you don't even have to worry about it overcoming a large amount of friction. So basically, it's even easier for the plane to move forward relative to the ground then the skateboard.
First, the plane overcomes static friction. Since before it does this the conveyor does nothing, it's no difference than if the plane were on a runway.
Second, since the plane is already moving, (and I suppose this happens instantly, but no matter) the belt starts moving backwards at the same speed of the plane, relative to the ground.
Third, since the belt can not apply a direct backwards force to the plane's body it has to rely on applying a force to the wheels of the plane. So now the wheels are moving extra fast. However, fast moving wheels doesn't really affect the plane too much (a little friction, nothing more.)
So the plane will feel a little resistance to it moving forward from the friction from it's fast moving wheels, but nothing that can come close to overcoming it's heavy duty engines.
"That would be energy expended but no movement of the board. The skate board would stay in place so this makes me think that the plane would stay in place if just enough engine power was applied to keep it there."
Exactly correct if the conveyor is already moving at a set rate. So yes, your thinking is correct. However, all it does is show that the energy required to hold the plane is place against a belt moving backwards at X mph is less than the energy required to move it forward at X mph on solid ground.
So when you are holding the skateboard in place (nice oiled wheels), it's nice and easy to do so even if the conveyor is moving very fast. However, it would be much, much harder to move the skateboard as fast as the conveyor along solid ground.
One last example:
Let's say the conveyor is moving at 100X speed, the exact speed it takes for our skateboard with wings to "take off". The skateboard is standing still on top of the belt, and you are holding it in place.
It might be a little hard to hold the skateboard in place, you might even have to hold it there wtih both hands. But it can be done, exp. if the wheels are well maintained and have as much time and money put into them as plane wheels (I'm sure plane wheels have to be top of the line). So you do have to image a skateboard with super wheels here.
Now, you could push the skateboard forward on the belt with your hands, even when it is moving so fast backwards. Thus, your skatebaord has exceeded 100X IN RELATION TO THE BELT. Not the ground yet, but that's ok.
Now think about moving the skateboard along the ground at 100X with only your hands. It would be impossible, or it would certainly require MUCH more force.
Since the skateboard would leave the conveyor at 100X, that means that if the conveyor behaved the same way as the conveyor with the plane (moving at the same speed the plane moved), then the TOTAL force exerted against the skateboard backwards would not exceed what it felt like when you were holding the skateboard in your hands with the belt moving at 100X. And for most of the process of the skateboard speeding up, the conveyor would be applying LESS friction than it does at 100X, making it even easier.
Back to a conveyor belt behaving the same way as in the plane example.
So if a belt moving at 100X applies 15F force in friction, then as long as the skateboard can overcome that 15F before it reaches a speed of 100X, it will be moving forward relative to the ground. But since you can imagine holding a skateboard in place against 15F not being too tough, then you can imagine that if you attached rocket engines to your skateboard, they would certainly be able to do a better job than your hand, and be able to push the skateboard forward even against the -100X speed of the belt.
So imagine a belt moving at 100X provides 15F force against the plane, and the plane moving along the ground at 100X has both 15F in force against it and 100F in drag(air resistance) against it.
To take off normally, the plane would require 115F in force to get to 100X in speed.
To take off on a belt, since the belt will never exceed applying another 15F in force, then as long as the plane can exceed somewhere around 130F (a little difference sinne I don't think both 15Fs will add together normally) in force if strained, it can take off on the belt.
I hope that helps and I didn't make it too confusing. I also have no idea about my numbers. But I can guarantee that a plane, given a slightly longer runway, could easily overcome a slight increase in resistance on it's takeoff.