03 Nov 06
And that is your problem.
There have been some good clear examples/analogies provided and many people have attempted to explain this to you yet you still insist on pushing your ignorant interpretation.
I have tried the toy car on a plank scenario that you seemed to ridicule, and i suggest you try it too.
To make it more rigorous get a second person to push the car while you move the plank, i used a plank about 10ft long resting on a horizontal workbench.
I got my friend to push the toy at a constant velocity relative to the motionless workbench.
I then pulled the plank back quickly, simulating the conveyor belt. He reported no detectable change in the force required to maintain the speed of the toy on the plank. The toy continued to move forward at the same velocity relative to the workbench. The ONLY thing that changed was that the little wheels rolled a little faster. The extra friction from faster rolling wheels was not enough to slow the car any detectable amount.
I strongly suggest you try this for yourself. If you aren't convinced after trying it then i doubt anything will convince you and you'll likely remain ignorant for the rest of your life.
06 Nov 06
Originally posted by MarsanI've had it with this.
And that is your problem.
There have been some good clear examples/analogies provided and many people have attempted to explain this to you yet you still insist on pushing your ignorant interpretation.
I have tried the toy car on a plank scenario that you seemed to ridicule, and i suggest you try it too.
To make it more rigorous get a second person t ...[text shortened]... doubt anything will convince you and you'll likely remain ignorant for the rest of your life.
For the last time, read the bloody question:
A plane is standing on a runway that can move (some sort of treadmill). The plane moves in one direction, while the conveyer moves at the same speed but in the opposite direction. Can the plane take off?"
THEY ARE MOVING AT THE SAME SPEED.
This can only mean relative to each other.
The plane cannot, therefore move at a higher speed than the belt BY DEFINITION IN THE PROBLEM.
Good grief.
06 Nov 06
Originally posted by sugiezdOK, one more try.
I've had it with this.
For the last time, read the bloody question:
A plane is standing on a runway that can move (some sort of treadmill). The plane moves in one direction, while the conveyer moves at the same speed but in the opposite direction. Can the plane take off?"
THEY ARE MOVING AT THE SAME SPEED.
This can only mean relative to each oth ...[text shortened]... t, therefore move at a higher speed than the belt BY DEFINITION IN THE PROBLEM.
Good grief.
Velocity of plane wrt belt = u(t)
Velocity of plane wrt ground = v(t)
Velocity of belt wrt ground = -w(t)
Therefore v(t) = u(t) - w(t)
You have interpreted the question to mean the speed of the belt is the same as the speed of the plane with respect to the belt, w(t) = u(t). This would mean that v(t) is zero, as you keep claiming. However, this is dynamically impossible (as is shown below).
An interpretation that is actually feasible is that the speed of the belt is the same as the speed of the plane with respect to the ground:
w(t) = v(t).
Using F = ma:
Thrust - Friction due to wheel - Air resistance = Mass dv/dt,
Thrust >> Friction, because the wheels are freely rotating.
If v(t) starts at zero, air resistance initially is zero
Therefore dv/dt > 0
Therefore v(t) increases
We can only have v(t) for all time (your scenario) if the friction in
the wheel completely counteracts the thrust of the plane. Which really isn't plausible (planes would never be able to take off if there was that much friction!)
Or, to put it one final way. If there is no friction in the wheels it does not matter how fast the belt is travelling, as it makes no difference whatsoever.
06 Nov 06
Originally posted by mtthwPlease define "t".
OK, one more try.
Velocity of plane wrt belt = u(t)
Velocity of plane wrt ground = v(t)
Velocity of belt wrt ground = -w(t)
Therefore v(t) = u(t) - w(t)
You have interpreted the question to mean the speed of the belt is the same as the speed of the plane with respect to the belt, w(t) = u(t). This would mean that v(t) is zero, as you keep claimi ...[text shortened]... i]it does not matter how fast the belt is travelling, as it makes no difference whatsoever.[/i]
Are you saying that it is impossible for a plane on a belt to be stationary with respect to the ground - "However, this is dynamically impossible" ?
Whilst not accepting that this is true, if so the problem is impossible as stated.
You can't have it both ways.
06 Nov 06
Originally posted by sugiezdt is time - so v(t) is a function of time
Please define "t".
Are you saying that it is impossible for a plane on a belt to be stationary with respect to the ground - "However, this is dynamically impossible" ?
Whilst not accepting that this is true, if so the problem is impossible as stated.
You can't have it both ways.
I'm saying that a plane without brakes on with its engines producing thrust cannot be stationary with respect to the ground on the belt, unless something else is preventing it moving (i.e. some other force is applied).
There are different ways of interpreting the problem stated. It refers to "speed", but not what that speed is with respect to. You could argue that the question is poorly stated, but you could also argue that there is only one interpretation that is possible, and so recognising that is part of solving the problem.
06 Nov 06
Originally posted by mtthwI'd guessed that but if you define a variable as a velocity, the (t) is spurious.
t is time - so v(t) is a function of time
I'm saying that a plane without brakes on with its engines producing thrust cannot be stationary with respect to the ground on the belt, unless something else is preventing it moving (i.e. some other force is applied).
There are different ways of interpreting the problem stated. It refers to "speed", but not wha ...[text shortened]... one interpretation that is possible, and so recognising that is part of solving the problem.
I'm not disputing Newton's second law and I agree that the plane will accelerate with repect to the belt and that is all that you have managed to prove.
If the belt accelerates at the same rate then.....
06 Nov 06
When I first came across this puzzler I came to the conclusion that the plane would not fly if the belt speed was exactly equal to the plane speed in the opposite direction.
After further thought I decided I was wrong.
I was thinking in terms of the plane pushing itself forward on the ground or belt. A plane does not work that way. It pushes or pulls itself forward through the air, and it will do that regardless of what the ground or belt is doing.
06 Nov 06
1 edit
Originally posted by sugiezd...it still doesn't apply sufficient force to the plane to stop it accelerating. The plane will accelerate unless the friction equals the forward thrust. This just isn't going to happen.
I'd guessed that but if you define a variable as a velocity, the (t) is spurious.
I'm not disputing Newton's second law and I agree that the plane will accelerate with repect to the belt and that is all that you have managed to prove.
If the belt accelerates at the same rate then.....
The proof applies to v, defined as the velocity with respect to the ground.
06 Nov 06
Originally posted by MarsanI presume that this was a carefully controlled laboratory experiment?
And that is your problem.
There have been some good clear examples/analogies provided and many people have attempted to explain this to you yet you still insist on pushing your ignorant interpretation.
I have tried the toy car on a plank scenario that you seemed to ridicule, and i suggest you try it too.
To make it more rigorous get a second person t ...[text shortened]... doubt anything will convince you and you'll likely remain ignorant for the rest of your life.
No... I thought not.
06 Nov 06
Originally posted by mtthwWhy do presume that the plane and belt cannot be in equilibrium?
...it still doesn't apply sufficient force to the plane to stop it accelerating. The plane will accelerate unless the friction equals the forward thrust. This just isn't going to happen.
The proof applies to v, defined as the velocity with respect to the ground.
If the plane is not accelerating, motor at constant rpm then it will have a constant velocity with respect to the ground if it has the same speed on the belt as the belt has in relation to the gound (Newton's first law).
This is the condition defined in the problem.
06 Nov 06
Originally posted by sugiezdExplain the forces! The engine is switched on, providing thrust.
Why do presume that the plane and belt cannot be in equilibrium?
If the plane is not accelerating, motor at constant rpm then it will have a constant velocity with respect to the ground if it has the same speed on the belt as the belt has in relation to the gound (Newton's first law).
This is the condition defined in the problem.
Where is the force stopping it accelerating? The wheels turn freely, they can't apply enough friction.
06 Nov 06
Originally posted by mtthwMotor off - which way does the plane move - backwards (stationary on belt, belt moving backwards).
Explain the forces! The engine is switched on, providing thrust.
Where is the force stopping it accelerating? The wheels turn freely, they can't apply enough friction.
Agreed?
Motor on tick-over, brakes on - still moving backwards (still stationary on belt, belt moving backwards). .
Agreed?
Partial release of brake, plane moves forward on belt, brakes used to maintain constant speed relative to belt. If both are moving at 5 kph, what happens to the plane relative to a fixed point outside the belt?