If FB = 550 N and FC = 750 N , determine the magnitude and coordinate direction angles of the resultant force acting on the flag pole. Determine coordinate direction angle α of the resultant force acting on the flag pole. Determine coordinate direction angle β of the resultant force acting on the flag pole. Determine coordinate direction angle γ of the resultant force acting on the flag pole.
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You have all the points involved. The vector from (0,0,z) to (x,y,0) is just
<x,y,-z>. The angle from the x-y plane to the point on the pole is
tanθ = z/√(x^2+y^2)
To determine the magnitude and coordinate direction angles of the resultant force acting on the flag pole, we can use vector addition.
The magnitude of the resultant force can be calculated using the Pythagorean theorem:
Magnitude of Resultant Force = √(FB^2 + FC^2)
= √(550^2 + 750^2)
= √(302500 + 562500)
= √(865000)
≈ 930.589 N
Now, let's determine the coordinate direction angles.
The coordinate direction angles are the angles made by the resultant force with the positive x, y, and z axes. In this case, we will assume that the positive x-axis is in the horizontal direction, the positive y-axis is upward, and the positive z-axis is perpendicular to the x-y plane.
To determine the angle α, we need to find the angle between the horizontal x-axis and the projection of the resultant force onto the x-y plane.
Angle α = arctan(FC/FB)
= arctan(750/550)
= arctan(1.36)
≈ 52.07 degrees
To determine the angle β, we need to find the angle between the vertical y-axis and the resultant force.
Angle β = arctan(FC/FB)
= arctan(750/550)
= arctan(1.36)
≈ 52.07 degrees
Note that α and β will have the same value in this case because the resultant force is in the x-y plane.
To determine the angle γ, we need to find the angle between the resultant force and the z-axis.
Angle γ = arctan(√(FB^2 + FC^2)/FD)
= arctan(√(550^2 + 750^2)/FD)
= arctan(√(302500 + 562500)/FD)
= arctan(√(865000)/FD)
≈ arctan(930.589/FD)
Unfortunately, the given value of FD is missing, so we cannot determine the angle γ without knowing that value.
In summary:
- The magnitude of the resultant force is approximately 930.589 N.
- The coordinate direction angle α is approximately 52.07 degrees.
- The coordinate direction angle β is also approximately 52.07 degrees.
- The coordinate direction angle γ cannot be determined without knowing the value of FD.