Answer to Question #104300 in Classical Mechanics for Cielo Joseph

Question

1. Airplanes usually use their wings to turn: When the plane is tilted at an angle θ, the lift (L) from the wings provides a vertical component and a horizontal component. The direction of the lift is in the plane of symmetry of the plane (up from the wings). Suppose that the plane is tilted at an angle θ = 29.0∘ and that it is making an exactly horizontal, circular path at a uniform speed of 455 kph. Take g = 9.80 m.s^-2 for three significant figures (the value at Sydney).

What is the radius of its turn? _____ km.

2. During this turn of the airplane, suppose that a passenger puts a nearly full glass of water on the tray table in front of her. What happens to the water? The plane is turning right for the passenger.

a) It spills out of the glass to the left
b) It spills out of the glass to the right
c) It stays in the glass, with its surface parallel to the tray table.
d) None of these.

Answer 1

Angle of lift of the plane $\theta =29.0^\circ$

Speed of the circular path =455Kph=126.39 m/sec

gravitational acceleration $=9.8 m/sec^2$

Let the L is the lift force of the flight.

The $L\cos \theta=\dfrac{mv^2}{R}------(i)$

and $L\sin\theta=mg-----(ii)$

from the equation (i) and (ii)

$\tan\theta=\dfrac{Rg}{v^2}$

$\tan (29^\circ)=\dfrac{R\times 9.80}{126.4\times 126.4}$

$R=\dfrac{126.39\times 126.39 \times \tan(29^\circ)}{9.8}$

$R=903.54$ m

2)

Water in the glass will not spill out because the due to the rotation of the plane, the water inside the cup will become parallel to the surface of the tray.

It is happening because of the centripetal force gained by the plane, due to which water inside the cup will also gain the sufficient centripetal force, hence it will not spills out.

So, option C is the correct answer.