Everybody is right and everybody is wrong. Here's why. The thing that many people are forgetting or not understanding is that he wheels are free spinning wheels. They are not connected to anything that "drives" the plane. Thrust is generated by the engines. So what does this all mean?
If the plane was stationary (engines off) and the conveyer belt moved 5 mph, the plane would move backwards at 5 mph. It would be a lump of mass on a conveyer belt. However, if I moved the plane slightly forward, the conveyer belt would counter-act that motion and the plane would stand still. However, if I kept adding thrust, eventually at some point the thrust would overcome the inertial energy of the plane and friction of the wheels, so it will eventually begin to move. If the plane can generate enough thrust it will overcome the movement of the conveyer and could potentially take off.
Think of it this way. You are on a bicycle on a people mover conveyer belt, but your feet are off the pedals. Instead you are holding a rope that your buddy on the other end of the people mover is holding. If he pulled on the rope slightly and tried to move you forward, the conveyer belt would move back and you would stay stationary. However, if he pulled on the rope hard and fast enough, he would eventually begin to get you to move forward. This is because at some point, when you can overcome the inertia of you and the bike and the friction in the wheel bearings, all the movement of the conveyer belt will do will spin the wheels and have no affect on your movement. In other words, if you had completely frictionless wheels, the movement of the conveyer would do nothing to affect your movement; a truly frictionless object would exert NO FORCES. Conversely, a 100% friction object would mean that your buddy couldn’t get you to budge (i.e. you are attached to belt). Since real world wheels fall somewhere in between friction and frictionless, there is some point of force/thrust, in which you can overcome the friction and inertial forces holding you back and eventually move (aka plane takes off).
Another way to look at it is, suppose the belt is moving you backwards. You would move backwards at the same speed of the belt. Unless the belt spun back so fast that it overcame your inertial force and the friction of the wheels. In which case, your wheels would just spin and you would stay in place. Think of a table cloth on a table with all the plates and utensils on it. If I pull the cloth slowly, the dishes will move. If I pull it fast enough, the plates don’t move as the cloth is removed. The cloth overcomes the inertial and frictional forces holding the plates down to the table. So going back to the belt moving backwards example. If I hold on to a rope tied to a tree as the belt moves backwards then I would be stationary. No matter how fast the conveyer belt moves, I won’t go anywhere because I’m holding myself stationary. The force exerted by the rope is the frictional and inertial forces of me and the bike. If I start “climbing” the rope, I can actually move forward, even if the conveyer belt was moving at infinite speed.
The reason this question is so debatable and such a brain buster is because given the information, the question is impossible to answer.If the plane can not generate enough thrust to overcome the frictional losses of the wheels, inertial energy of the plane and generate enough speed for proper lift, then the plane can’t take off. If the plane can generate enough thrust to overcome the frictional losses, inertia and speed required for lift, then it will take off. However, we don’t know the frictional losses, weight of the plane or the thrust that the plane can output. Without that information, we don’t have enough raw data to give a proper justifiable answer. If someone tries to make a definitive answer one way or the other, they are wrong. There is simply not enough information to be able to answer the question properly.
(And yes, I am an engineer) :smile:
The whole point of the conundrum is that there is a conveyor belt that spins fast enough to hold a plane in a still position. I don't believe we should read into some sort of trickery on the conundrum or error in the physics of presented scenario.
