The helicopter in the drawing is moving horizontally to the right at a constant velocity. The weight of the helicopter is W=54300 N. The lift force L 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? (b) Determine the magnitude of the air resistance R that opposes the motion.
To solve this problem, we need to break down the forces acting on the helicopter:
(a) Magnitude of Lift Force (L):
The lift force (L) can be determined using trigonometry. We can decompose the lift force along two perpendicular axes: the vertical axis and the horizontal axis.
Considering the given angle of 21.0° with respect to the vertical, the vertical component of the lift force (L_vertical) can be found using the sine function:
L_vertical = L * sin(theta)
L_vertical = W
Solving for L, we have:
L = W / sin(theta)
L = 54300 N / sin(21.0°)
L ≈ 157933.5 N
Therefore, the magnitude of the lift force is approximately 157933.5 N.
(b) Magnitude of Air Resistance (R):
Since the helicopter is moving horizontally to the right at a constant velocity, and there is no acceleration mentioned, we know that the net force in the horizontal direction is zero. Thus, the air resistance (R) is equal in magnitude to the applied force.
Therefore, the magnitude of the air resistance (R) is equal to the weight of the helicopter:
R = W = 54300 N.
Hence, the magnitude of the air resistance is 54300 N.