<p>An airplane is sitting on an enormous treadmill. As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving. Can the plane take off?</p>
<p>yes, it can</p>
<p>turn the plane around.</p>
<p>if it is a propeller airplane (pulling thrust), yes. If it is a pushing airplane (jet, pusher propeller), no. Need the airflow over the wings.</p>
<p>makes no difference, because the wheels on a plan are free-rolling, the thrust of the plane whether it be from a propeller or a jet engine would push the plane forward until it reached take-off velocity and lifted off.</p>
<p>germans88: I was thinking the same thing but if you look back to the question you’ll see that as the plane moves faster, so does the treadmill. He’s not saying that “If the plane needs to me going 200 mph to liftoff, and the treadmill is going -200mph, will it take off?” - He’s saying that as the plane’s thrust causes the wheels to spin faster, the treadmill also moves faster in the opposite direction. It’s like running on a carpet that someone is pulling in the opposite direction.</p>
<p>if there is airflow over the wing, as there would be with a pulling trust system, it would take off, and then rocket forward once free of the reverse force of the tredmill</p>
<p>germans88 is correct. You need to look at this from an physics/engineering standpoint, not from your every day experience with rugs and treadmills (while the physics doesn’t change for rugs or treadmills, the action of forces within the problem do). </p>
<p>Let’s look at the forces acting on the plane… You have the force of the engines (jet, prop, or whatever) in the direction of flight. Ignoring drag, the only other force (in the longitudinal direction) is the force of the rolling friction, which is based on the aircraft’s weight and the friction coefficient, we can assume this will be a fairly constant force, and much much lower in magnitude than the thrust of the engines. </p>
<p>Therefore, since you have a net thrust in the forward direction, you will accelerate as usual and take off once you reach the minimum speed to produce enough lift to fly.</p>
<p>As a slight correction to my previous posts, I was going to change the answer just slightly to correct for the frictional forces based on the wheel bearings and their respective friction coefficients. That should head off anyone from coming back and tearing my post apart. 
If you had magic wheel bearings with no friction, then the rolling friction of the tires on the ground would be inconsequential. </p>
<p>Even without this correction, the physics of the problem are clear: the forward forces are much much greater in magnitude than any of the forces holding the plane back; therefore, it will accelerate and take off.</p>
<p>I think the original post implied that the magical treadmill would accellerate along with the plane, keeping its relative airspeed zero.</p>
<p>bmanbs2, </p>
<p>Yes, I’m sure thats exactly what the original question implied. However, that doesn’t change the forces acting on the plane very much. The action of the treadmill changes the speed of the wheels, but the force acting on the plane is not terribly dependent on the wheel speed.</p>
<p>Imagine this. Put on a pair of rollerblades and stand on a treadmill. Hold on to the rails, and have someone put the treadmill to 5 mph. You should be able to hold on just fine with very little force trying to throw you off of the treadmill. Your rollerblade wheels will spin at a rate that matches the treadmill. Now, have your friend increase the treadmill speed to 10mph. You should still be able to hold on just fine… Your wheels will spin faster, but I think you would find it quite easy to hold yourself on the treadmill by just using your arms. Imagine if you had a super fast treadmill that could go to 40mph, I would imagine you wouldn’t have much trouble holding yourself up at that speed either. At some point, you would be limited to how fast your bearings could spin, but the force acting on your legs isn’t that different between when the treadmill was 5mph and when it was 40mph.</p>
<p>Interesting. In a frictionless bearing, the treadmill could go infinitly fast, but the airplane wouldn’t move, even without thrust. You are right.</p>
<p>This is why I don’t like physics. It’s only a nessisary evil.</p>
<p>“opposite direction at the same speed the plane is moving”
speed relative to what? the ground or the treadmill? if it is relative to the treadmill, no, the plane will not take off. if it is relative to the ground, the plane takes off with no problem.</p>
<p>can’t have ambiguity in the relative speeds.</p>
<p>for no inertial forces, the bearing needs to be frictionless AND massless (and/or a singularity that applies no torque). the bearing will have orbital and spin angular momentum relative to different surfaces.</p>
<p>I disagree with Sky’s analysis:
Where does that lift come from?</p>
<p>Lift is only generated when the plane has an airspeed relative to the air. In this case, the airspeed is 0, so the plane CANNOT take off.</p>
<p>On the other hand, if you have the airplane running horizontally static on the threadmill and you blow a fan against the airplane, the airplane will be able to take off because now it has an airspeed.</p>
<p>Actually, I think bmanbs nailed it earlier:</p>
<p>
</p>
<p>That is correct because in the case of a pushing airplane, there is no vertical lift because no air is travelling at the wings of the airplane (i.e. no airspeed). But in the case of a propeller plane, it is possible to achieve a lift because the air can flow around the wings, so there is a downward momentum change for the air against the wing.</p>
<p>“An airplane is sitting on an enormous treadmill. As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving. Can the plane take off?”</p>
<p>Wording is essential in riddles. It never says anything about the treadmill speed increasing. The treadmill is moving at the initial speed of the plane (zero). The plane will increase speed and take off.</p>
<p>Guys, please read Sky’s post again; he explains it perfectly.</p>
<p>Think of it with respect to a wheelchair. You’re sitting in a wheelchair on a treadmill. The wheelchair wheels turn w/o friction. I stand behind you and hold you in place. The treadmill starts to move. I just hold you there, and the wheels spin. The treadmill moves faster. I don’t have to hold you with any more force, the wheels just spin faster. Work is done by the treadmill on the wheels, but there is no force whatsoever on the wheelchair from the treadmill. Its only function is to spin the wheels faster. Now say I walk alongside the treadmill and push you along. The speed you move forward is completely independent of the speed with which the treadmill turns.</p>
<p>Remember, as opposed to an automobile, an airplane’s wheels do not relay engine thrust.</p>
<p>
Ohh, right. That’s why i’m not an mech engineer! Then I agree with the explanation above.</p>
<p>I completely agree that this will be the case if the speed of the treadmill increased. I just think the wording of the riddle means that it will be constant.</p>