# Math Help - Forces as a Vectors

1. ## Forces as a Vectors

Find the horizontal and vertical components of each of the forces:

f) 36N acting vertically

${\overrightarrow {r} } = (0, 36sin \theta)$

How do I find the $y$ value for the component if I cannot solve for $36sin \theta$?

Find the resultant of each pair of forces acting on an object.

d) forces of 7N east and 12N north

$\sqrt {|{\overrightarrow {r} }|^2}$ = $\sqrt{7^2 + 12^2}$
$|{\overrightarrow {r} }| = 13.9$

$tan \theta = \frac {12}{7}$
$\theta = 60$°

Therefore, 13.9N, _____________ (How do I find the direction of this force? Can you please show me how using a diagram?)

e) forces of 6N southwest and 8N northwest

g) forces of 6N southeast and 8N northwest

2. Originally Posted by Macleef
Find the horizontal and vertical components of each of the forces:

f) 36N acting vertically

${\overrightarrow {r} } = (0, 36sin \theta)$

How do I find the $y$ value for the component if I cannot solve for $36sin \theta$?
You are over-thinking it. The vector is vertical, hence it is acting entirely in the y direction. So the vector is (0, 36). (If you want, $\theta = 90^o$.)

-Dan

3. Originally Posted by Macleef
Find the resultant of each pair of forces acting on an object.

d) forces of 7N east and 12N north

$\sqrt {|{\overrightarrow {r} }|^2}$ = $\sqrt{7^2 + 12^2}$
$|{\overrightarrow {r} }| = 13.9$

$tan \theta = \frac {12}{7}$
$\theta = 60$°

Therefore, 13.9N, _____________ (How do I find the direction of this force? Can you please show me how using a diagram?)
You pretty much have it.

So the magnitude is $r = \sqrt{7^2 + 12^2} = 13.892443989$ and the angle (in the first quadrant, since the x and y components are both positive) will be 59.743562836 degrees. (Or 60. degrees N of E.)