The chisel exerts a force of 20 lb on the wood dowel rod which is turning in a lathe. Resolve this force into components acting (a) along the n and t axes and (b) along the x and y axes.

#### Solution:

We will first draw the components of the 20 lb force along the n and t axes.

Using the sine and cosine functions, we can figure out the values F_n and F_t. Remember that sine is opposite over hypotneuse, while cosine is adjacent over hypotneuse.

F_n\,=\,-14.1 lb

(Note how the value is negative, this is because force F_n is heading towards the negative n-axis)

\sin45^0\,=\,\dfrac{F_t}{20}

F_t\,=\,14.1 lb

Now, we can focus on part (b) of the question. This time, we will draw our vector components along the x and y axes.

(Notice how we extended the 20 lb force. This visual representation makes it easier for us to calculate the values required)

*The 15^0 angle can be found by realizing that if we extend the x-axis as shown in our diagram, it creates a semi-circle, which has an angle of 180^0. Our force therefore must be applied at an angle of 15^0 because (45+60+30+60)-180^0=15^0. *

As before, we can use sine and cosine functions to figure out the components along the x and y-axes.

F_x\,=\,19.3 lb

\sin15^0\,=\,\dfrac{F_y}{20}

F_y\,=\,5.18 lb

#### Final Answers:

**a)**

F_n\,=\,-14.1 lb

F_t\,=\,14.1 lb

**b)**

F_x\,=\,19.3 lb

F_y\,=\,5.18 lb

good