1. ## vectors

an object P is acted upon by 3 coplanar forces one force is a hundred pounds due south another is 150 pointing due east and the third is 200 lbs 30 degrees north of east. What is the force needed to prevent P from moving

Do you know how to write vectors and add vectors?

An object $\displaystyle P$ is acted upon by 3 coplanar forces.
One force is 100 pounds due south,
another is 150 pounds due east
and the third is 200 pounds 30° north of east.
What is the force needed to prevent $\displaystyle P$ from moving?
Code:
                          w
*
200   *
*
P   * 30°
o - - - - - - * v
|     150
100 |
|
*
u

We have: .$\displaystyle \begin{array}{ccc} \vec u &=& \langle 0,\:\text{-}100\rangle \\ \vec v &=& \langle 150,\:0\rangle \\ \vec w &=& \langle 100\sqrt{3},\:100\rangle \end{array}$

The resultant vector is: .$\displaystyle \vec u + \vec v + \vec w \;=\;\langle 250\sqrt{3},\:0\rangle$

$\displaystyle P$ is moving directly east with a force of $\displaystyle 250\sqrt{3}$ pounds

To prevent movement, $\displaystyle 250\sqrt{3}$ pounds of force must be applied directly west.
. . The applied vector would be: .$\displaystyle \langle \text{-}250\sqrt{3},\:0\rangle$

3. Shouldn't this:
Originally Posted by Soroban

The resultant vector is: .$\displaystyle \vec u + \vec v + \vec w \;=\;\langle 250\sqrt{3},\:0\rangle$
Be this?
$\displaystyle \vec u + \vec v + \vec w \;=\;\langle 150+100\sqrt{3},\:0\rangle$

4. the answer in the book is 323 lbs due west not equivalent to either of the answers u two gave. what is wrong

5. I edited my previous post. Check the answer now, it should be correct.

6. ok i get that but how do u know the force must be applied due west to stop the object