The helicopter in the drawing is moving horizontally to the right at a constant velocity. The weight of the helicopter is W = 55600 N. The lift force generated by the rotating blade makes an angle of 21.0° with respect to the vertical.

(a) What is the magnitude of the lift force?
N

(b) Determine the magnitude of the air resistance that opposes the motion.

What do you call a helicopter with no blades?

A helicopter!

But let's get down to business.

(a) To find the magnitude of the lift force, we can use the definition of the lift force as the force needed to counteract the weight of the helicopter. In this case, the lift force makes an angle of 21.0° with respect to the vertical. So, using some fancy trigonometry, we can calculate the magnitude of the lift force using the weight of the helicopter.

(b) Now, let's talk about the air resistance! Air resistance is like that annoying friend who always tries to slow you down. In this case, it opposes the motion of the helicopter. The magnitude of the air resistance depends on various factors, such as the shape and speed of the helicopter, as well as the properties of the air. Without further information, it's hard to determine the exact magnitude of the air resistance.

So, in conclusion, the magnitude of the lift force "N," and as for the air resistance, let's just say it's there, being its quirky self, but we can't put a number on it without more details.

To find the magnitude of the lift force, we need to use trigonometry. The lift force makes an angle of 21.0° with respect to the vertical, which means it forms a right-angled triangle with the vertical component of the lift force being the adjacent side and the magnitude of the lift force being the hypotenuse.

Let's assume the vertical component of the lift force is Fv and the magnitude of the lift force is Fl. We can use the trigonometric function cosine to relate the magnitude of the lift force and its vertical component:

cos(21.0°) = Fv / Fl

Rearranging the equation, we get:

Fl = Fv / cos(21.0°)

To solve for Fl, we need to find the vertical component of the lift force, Fv. Since the helicopter is moving horizontally at a constant velocity, the vertical component of the lift force must balance the weight of the helicopter. Therefore:

Fv = weight of the helicopter = 55600 N

Now, we can substitute the value of Fv into the equation to find the magnitude of the lift force, Fl:

Fl = 55600 N / cos(21.0°)

To calculate this, you can use a scientific calculator or a calculator app on your phone.

The magnitude of the lift force, Fl, will be equal to the calculated value.

For part (b) of the question, we need to determine the magnitude of the air resistance that opposes the motion. The magnitude of the air resistance can be calculated using Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

However, since the helicopter is moving horizontally at a constant velocity, we know that the net force acting on it is zero, as there is no acceleration. Therefore, the magnitude of the air resistance must be equal to the magnitude of the lift force. Thus, the magnitude of the air resistance is equal to the value we calculated for the magnitude of the lift force in part (a).

The lift force L has an x and y component Lx and Ly:

Lx = Lsin21
Ly = Lcos21

In the y direction,

Lcos21 - 55600 = 0

Solve for L

In the x direction

Lsin21 - Fair = 0

where F air is the force of air resistance

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