The beam is subjected to the two forces shown. Express each force in Cartesian vector form and determine the magnitude and coordinate direction angles of the resultant force.
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Using the diagram, we can express each component corresponding to it’s force.
We will first look at force F_1. Note how it lies on the z-y plane, therefore, it does not have a x-component.
(note how our z-component is negative. This is because the force is going downwards. In other words, the z-component lies in the negative z-axis.)
We can now express force F_1 in Cartesian form as follows:
Now, we will look at force F_2. Each component can be found by multiplying the magnitude of the force by the corresponding coordinate direction angles.
Let us now express force F_2 in Cartesian form.
We can find the resultant force by adding the two forces together.
The magnitude of the resultant force is:
The coordinate direction angles can be found by taking the cosine inverse of each component of the resultant force divided by it’s magnitude.
magnitude of F_R\,=\,496 lb