The spur gear is subjected to the two forces caused by contact with other gears. Express each force as a Cartesian vector.
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We will first write the components of force F_1. Notice how it lies on the z-y plane, meaning it has no x-component.
(Note how our z-component is negative. This is because the z-component of force F_1 lies along the negative z-axis.)
Thus, we can write force F_1 in Cartesian vector form.
Now, we will look at force F_2.
We can express each component of force F_2 by multiplying the magnitude by each coordinate direction angle shown in the diagram.
Let us now express force F_2 in Cartesian vector form.