The spur gear is subjected to the two forces caused by contact with other gears. Express each force as a Cartesian vector.

#### Solution:

Show me the final answerâ†“

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.

F_{1z}\,=\,50\left(\dfrac{24}{25}\right)\,=\,-48 lb

(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.

F_{2y}=180\cos135^0=-127 lb

F_{2z}=180\cos60^0=90 lb

Let us now express force F_2 in Cartesian vector form.

#### Final Answers:

F_2\,=\,\left\{90i-127j+90k\right\} lb

i love you thankuuuuuuuuu