- #1

rudransh verma

Gold Member

- 1,067

- 95

- Homework Statement
- Three forces causes a net acceleration of ##3 \frac {m}{sec^2}## . Two of the forces ##F_1## and ##F_2## are 10N and 20N. Find the ##F_3## in unit vector notation?

Mass of the body is 2 kg.

- Relevant Equations
- ##\vec F= m\vec a##

##\vec{F_1} +\vec{F_2}+\vec{F_3} = m \vec a##

**x component of ##F_3##**

##F_{3x}= m a_x- F_{1x}-F_{2x}##

= ##ma\cos 50-F_1\cos(-150)-F_2\cos90##

**y component of ##F_3##**

##F_{3y}= m a_y-F_{1y}-F_{2y}##

=##ma\sin50-F_1\sin(-150)-F_2\sin90##

And so on…

My question how we can represent it in diagram ##F_1\sin(-150)##. I suppose what is ##\sin(-150)## : ##\sin(-30)## and -30 is measured from position X axis. So what is the component now . Is it now in Forth Quadrant from 3rd.

I can understand the component ##F_1\sin30## or ##F_1\cos30## in diagram but the above component, I don’t.

I could have done it via reference angle taking a right triangle in each quadrant and taking acute angles and put a sign accordingly to each component after calculating magnitude of each component. But I choose to do it more systematically by textbook way.

I was told you can do it by unit circle convention. That’s what I am aiming for, for doing all the vector questions. Taking all the angles from + direction of x-axis and straight away putting in ##\cos and \sin##. In this way I don’t have to worry about the signs. It is dealt automatically.

#### Attachments

Last edited: