Question

(Fsub1)1.077i - (Fsub3)sin(theta)i +
(Fsub1)0.533j - (Fsub3)cos(theta)j

http://www.williamdoney.com/students/ENGG%20201/hwk%20solutions%20-%2012th%20edition/12e%20chap%2002.pdf#page=41

Answer 1

When equating i & j, how could they be split up like that?
Is the problem finished by inverse tan?

Answer 2

What part you stuck on? 0_o
I'm a little confused by your original post

Answer 3

We're looking at problem 2-46?

Answer 4

yes

Answer 5

So what you wrote above is the two resultant equations added together?

Answer 6

Oh oh that's where your question is, where they split them up I guess

Answer 7

I didn't really do much of anything; and yes. I don't get how the answer comes about from the i's and j's...

Answer 8

\[\Large\rm \vec F_R=\vec F_1+\vec F_2+\vec F_3\]\[\Large\rm \vec 0=(1.774\vec F_1-\vec F_3 \sin \theta)\hat i+(0.533\vec F_1-\vec F_3\cos\theta)\hat j\]It's a little misleading since we see a zero on the left side.
But that really is the zero vector.
You can think of it like this,

Answer 9

\[\Large\rm 0\hat i+0\hat j=(1.774\vec F_1-\vec F_3 \sin \theta)\hat i+(0.533\vec F_1-\vec F_3\cos\theta)\hat j\]

Answer 10

And then you equate the i's with the i's,
j's with the j's

Answer 11

oh, all right...I'm getting the idea...
let me see...

Answer 12

wait, so I set the equations equal to each other?

Answer 13

\[\large\rm \color{orangered}{0}\hat i+0\hat j=(\color{orangered}{1.774\vec F_1-\vec F_3 \sin \theta})\hat i+(0.533\vec F_1-\vec F_3\cos\theta)\hat j\]Match up the i's with the i's, that gives us our first equation,\[\Large\rm 0=1.774\vec F_1-\vec F_3 \sin \theta\]Then do the same with the j's, matching them up.

Answer 14

But this will leave you with a system of `2 equations` and `3 unknowns`. I can't seem to figure out how they solved for F3 and theta.... We don't have enough equations.
Maybe I'm missing something.

Answer 15

haaa, that's what I was confused about

Answer 16

@dan815 @SithsAndGiggles
Hmm I'm confused >.<

Answer 17

something with pythagorean's theorem or inverse tan maybe

Answer 18

lets draw the picture

Answer 19

There aren't 3 unknowns, because you don't need to find F_1, only f_3 in terms of F_1.

Hint for solving these simultaneous equations:
\[ \displaystyle \begin{cases} ax = by \\ cx = dy \end{cases} \Rightarrow \frac{a}{c} = \frac{b}{d} \]
(ignoring cases where any are 0)