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?
I found a) to be 58163.17315N
(b) Determine the magnitude of the air resistance R that opposes the motion.
To determine the magnitude of the air resistance (R) that opposes the motion of the helicopter, we need to assess the horizontal component of the lift force. Since the helicopter is moving horizontally to the right at a constant velocity, the vertical component of the lift force is balanced by the weight of the helicopter (W).
To get the magnitude of the lift force (L), we can use trigonometry. Since we know the angle (21.0°) between the lift force and the vertical, we can find the vertical component of the lift force using the equation:
L_vertical = L * sin(θ)
where L_vertical is the vertical component of the lift force and θ is the angle with respect to the vertical.
In this case, since we are given the weight of the helicopter (W = 54300 N), we can assume that the vertical component of the lift force equals the weight, meaning:
L_vertical = W
Now let's substitute this value into the equation we derived earlier:
W = L * sin(θ)
Rearranging the equation to solve for L:
L = W / sin(θ)
Now we can substitute the known values:
L = 54300 N / sin(21.0°)
Evaluating this mathematically, we find:
L = 58163.17315 N
So the magnitude of the lift force is 58163.17315 N.
Now, for part (b) of the question, the magnitude of the air resistance (R) is equal to the horizontal component of the lift force. To calculate this, we can use another trigonometric function:
R = L * cos(θ)
Substituting the known values:
R = 58163.17315 N * cos(21.0°)
Evaluating this mathematically, we find:
R ≈ 54518.88886 N
Therefore, the magnitude of the air resistance (R) that opposes the motion of the helicopter is approximately 54518.88886 N.