Physics Question

[ordinaryjoe]

Ah, the confusing bit is in the phrasing of the question, the two answers provided make you immediately think the plane is turning. So will it just move in a diagonal then like previously posted?

If you look at the diagram on the bottom left, it shows that the plane is not turning.

And for all you saying that the plane would drop in altitude, it would not necessarily. If it turned 3 degrees, it would still have 99.9% of the upwards force, which could easily have been compensated before the question started by flying slightly faster. However, over 5% of the magnitude of the lift would be accelerating it sideways (so an acceleration of about half a metre per second, which over a few minutes is very significant)

 

[Barbie]

If we put it on a treadmill, will it yaw to the right?

 

[DireEmblem]

I agree this is an overly simplified question.

The plane is not increasing/decreasing in altitude

Hence out of the two, the answer is least likely to be #1

The wings are the same and the lift is constant on both wings

Given such statement, the plane must remain banked at the same angle, hence if it is turning, it will get to a point where the change in flight path becomes constant, again if we assume there is no change in altitude.

 

[Lightnix]

If we put it on a treadmill, will it yaw to the right?

Yes the wheel will come off and everybody will die. However, it will all be a plot by the American government who will say that the middle East is what done it so that they can steal all of their oil and become rich tycoon quintillionaires.

 

[Dj_Jestar]

I agree this is an overly simplified question.


Hence out of the two, the answer is least likely to be #1


Given such statement, the plane must remain banked at the same angle, hence if it is turning, it will get to a point where the change in flight path becomes constant, again if we assume there is no change in altitude.

There is no rotation.. for the umpteenth time.

 

[trentlad]

Come on then OP, what's the answer and justification from your Physics teacher?

 

[Angleboy]

Im going to put this in terms that most on here should understand..

The plane ends up straffing (whilst still moving forwards)

The correct answer is fig 1.

/thread

 

[ordinaryjoe]

Come on then OP, what's the answer and justification from your Physics teacher?

I eventually managed to convince my physics teacher that answer 1 was correct. I explained in the 2nd page:

Path 1 because:
mavity and the upwards verticle component of the lift cancel (No change in altitude)
The horizontal component of the lift provides an acceleration (to the right in this diagram)
The plane can not twist, as all forces act through the centre of mass (mavity always does, and the lift would have to to counter mavity), so there is nothing to change the direction which the plane faces, and therefore, the horizontal component is always in the same direction.

This would give a parabolic curve (mine isn't an exact diagram, but shows the point) because if we call forward the y axis and sideways the x axis:
y is proportional to t
x is proportional to t squared so t is proportional to root x
Therefore, y is proportional to root x giving the parabolic curve

I then talked about how silly my physics teacher was and how difficult it was to explain something which seemed obvious to me to a friend who I thought was good at physics, only for him to take my teachers original view, saying the force to the right was a centripetal force, which is wrong, as the force would have to consistently be going towards the centre of the circle. Bah he's wrong and I'm right

 

["andy"]

path 1 but its a silly question and i would be questioning why you are being tested on it when so many deciding factors/variables are removed

 

[Pug]

i'd have guessed a diagonal sort path starting from the first point in fig 1. finishing at the end point in fig1 via a straight line

I'm not sure why the rate of "turn" on that route should increase when the effects on the plane, and its condition (speed, altitude roll angle) are constant. But i'm no physicist, i haven't read the thread and its late!

 

[bam0]

And for those of you mentioning asymptotes, I don't think that is right, as parabolas don't have asymptotes. Asymptotes are lines which the curve will approach, but never ever reach. e.g. The curve, y=1/x would have an asymptote of y=0, as no real value of x would give y a value of 0. There is however, no asymptote for the curve y=x^(1/2)

Of course, the rate of forward motion is consistent so as you say there is no value it would never reach, doh.

 

[Sin_Chase]

Can someone explain why it would move on a parabolic curve and not a straight line?

 

[1pudding1]

Stupid question, its pointless calling it an aeroplane. Its totalled limited to 2 dimensions and if its fixed in orientation with no air resistance and drag applied at all, so that the lateral velocity doesnt rotate it so it 'flys' in a circle you may as well call it a point mass moving with constant velocity forwards with a lateral force applied, in which case the answer is a little more obvious.

 

[SpeedFreak]

path 1 but I'd argue that the diagram is a little off.

 

[JonJ678]

Even for GCSE physics this is ridiculous. Surely the OP has forgotten parts of the question between discussing it and posting here?

The plane will accelerate in the direction of the resultant of the (apparently two) forces acting.

No air resistance => no drag. I'm taking this to mean the resultant force is in the plane perpendicular to direction of motion, and that velocity is constant. After all, if there's no drag, and no thrust, we're stuck with constant velocity.

No change in altitude => vertical force is zero

This leaves the resultant force acting horizontally, perpendicular to the motion of the plane. A body with an initial velocity, acceleration acting perpendicular to the velocity, moves in a circle.

It's unfortunate that assuming there is no thrust means you cannot maintain level flight. If gliding, with no air resistance, you have weight = lift. You then bank, directing a component of lift inwards, weight is now > lift, and it'll accelerate downwards. As such its more reasonable to believe it loses altitude, so viewed from above its path would be a circle, but viewed from the side you see it falling from the sky.

Which brings me back to my belief that the question is badly paraphrased.

 

[Efour]

only way we will ever know is to recover the black box and listen to the pilots recordings

 

[ThePirateHulk]

Personally, I think the plane would drop like a stone.

 

[Jokester]

Can someone explain why it would move on a parabolic curve and not a straight line?

Because there is a constant acceleration parallel to the x axis that doesn't change. This means you have a fixed speed going up the y axis, but the speed along the x axis is continually increasing, which when you combine the two components you end up with a velocity that tends to act in the x direction as opposed to the y direction that it starts in.

A body with an initial velocity, acceleration acting perpendicular to the velocity, moves in a circle.

The acceleration is not perpendicular to the velocity, it acts only in one direction, parallel to the x axis.

 

[Sin_Chase]

Why would the speed along the x axis be increasing?

 

[Dj_Jestar]

Even for GCSE physics this is ridiculous. Surely the OP has forgotten parts of the question between discussing it and posting here?

The plane will accelerate in the direction of the resultant of the (apparently two) forces acting.

No air resistance => no drag. I'm taking this to mean the resultant force is in the plane perpendicular to direction of motion, and that velocity is constant. After all, if there's no drag, and no thrust, we're stuck with constant velocity.

No change in altitude => vertical force is zero

This leaves the resultant force acting horizontally, perpendicular to the motion of the plane. A body with an initial velocity, acceleration acting perpendicular to the velocity, moves in a circle.

It's unfortunate that assuming there is no thrust means you cannot maintain level flight. If gliding, with no air resistance, you have weight = lift. You then bank, directing a component of lift inwards, weight is now > lift, and it'll accelerate downwards. As such its more reasonable to believe it loses altitude, so viewed from above its path would be a circle, but viewed from the side you see it falling from the sky.

Which brings me back to my belief that the question is badly paraphrased.

Dude, there is no rotation/yaw. The aircraft always points in the same direction.

Kind of ironic for you to come swanning in and complain it's ridiculous, only to get it completely wrong, eh?