The helicopter in the drawing is moving horizontally to the right at a constant velocity. The weight of the helicopter is W = 59000 N. The lift force vector L generated by the rotating blade makes an angle of 21.0° with respect to the vertical.
L=W/cos21
R=Wsin21
To find the magnitude of the lift force, we can use the weight of the helicopter and the given angle. The lift force and weight are balancing each other vertically in order to keep the helicopter in the air.
First, we can find the vertical component of the lift force (Ly) using trigonometry. Since the angle between the lift force vector and the vertical is given as 21.0°, we can use the sine function:
Ly = L * sin(angle)
where L represents the magnitude of the lift force.
In this case, we are given the weight (W) of the helicopter, but we need to make sure it is expressed in terms of its vertical component. The weight vector is always vertical, so we can write it as:
W = W * cos(90°)
Next, we can equate the vertical component of the lift force to the weight:
Ly = W * cos(90°)
or, substituting the values:
L * sin(angle) = W * cos(90°)
Now, we can solve for L:
L = (W * cos(90°)) / sin(angle)
Substituting the given values:
L = (59000 N * cos(90°)) / sin(21.0°)
Calculating this expression will give you the magnitude of the lift force (L).