I attached the problem.In the solutions my professor posted, he

[pyroknife]

I attached the problem.
In the solutions my professor posted, he stated that acceleration is 0 in all directions. thus he can use the equation
ar=r''-r*(θ')^2 to find r''=4.62.
where ar is the the acceleration in the direction of the dotted line r.

I don't understand how the acceleration can be 0. What about gravity? Isn't that acting in the r direction??

 

[cepheid]

The acceleration has to be constant in all directions, because the plane is traveling in a straight line at a constant speed.

Gravity is directly canceled by lift.

 

[pyroknife]

The acceleration has to be constant in all directions, because the plane is traveling in a straight line at a constant speed.

Gravity is directly canceled by lift.

What does do you mean by "cancelled by lift?"

I remember doing other problems (2D motion mainly) where something like a plane is flying in a horizontally at a constant speed which means that the acceleration in the x is 0, but we would always assume that the acceleration in the y is gravity.

 

[cepheid]

What does do you mean by "cancelled by lift?"

I remember doing other problems (2D motion mainly) where something like a plane is flying in a horizontally at a constant speed which means that the acceleration in the x is 0, but we would always assume that the acceleration in the y is gravity.

No, the acceleration in the y direction is 0. Otherwise it would start moving vertically.

Lift is the force that keeps planes in the air. It's the force that counteracts their weight. Without it, the planes would fall out of the sky.

You may have been remembered that you always assumed that the weight was mg. That's certainly true. It's just not the only vertical force that is acting here.

 

[pyroknife]

No, the acceleration in the y direction is 0. Otherwise it would start moving vertically.

Lift is the force that keeps planes in the air. It's the force that counteracts their weight. Without it, the planes would fall out of the sky.

You may have been remembered that you always assumed that the weight was mg. That's certainly true. It's just not the only vertical force that is acting here.

Oh I didn't know that, so lift is like analogous to the normal force for an object resting on the surface of the earth?

Thanks.

 

[cepheid]

Oh I didn't know that, so lift is like analogous to the normal force for an object resting on the surface of the earth?

Thanks.

Yeah sort of. Again, to emphasize: if the vertical acceleration of the plane was just g, then it would start to accelerate downward just like any object in free fall. Since it doesn't do that, there must be some force counteracting the weight.

I think the way lift is generated, to put it simply, is that when air runs over a wing, the wing exerts a downward force on the air. (How/why, I do not know). By Newton's 3rd law, the air must exert a corresponding upward force on the wing of equal magnitude. We call this upward force "lift." The faster the plane goes, the more lift you get.

The issue of "what makes a plane fly" is somewhat controversial, because an incorrect explanation is given in many school textbooks. The statement is that the upper surface of a wing is curved, and that the air flow splits and goes over the top surface and bottom surface in equal time. Therefore, the air must flow over the top surface faster (since it has more distance to cover due to the curve), and the Bernoulli equation says that the pressure on the top is therefore lower (due to the faster flow). The difference in pressure between the top and bottom is cited as the cause of the lift. I want to emphasize that this explanation involving the Bernoulli equation is totally wrong as far as I can see. There is no reason why the air should flow over the top and bottom surface in the same amount of time. Furthermore, this does not explain why a plane can fly perfectly well upside down. Yet, somehow, this explanation of lift continues to be taught.

What I said before is the correct explanation: a wing applies a downforce to the air somehow. I fully admit that I do not know how it does so.

 

[cepheid]

Looking at wikipedia, it looks like the overall flow is just *deflected* downward by the wing as the air flows past it.