# Statics: Magnitude of vectors HELP

#### mrpburke

Statics: Magnitude of vectors HELP!!

Could someone just tell me how to start this problem. I cant seem to think of anything right now.

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#### mrpburke

Anybody???

I found the answer...68.2kN but I have no idea how to get that.

#### jtbell

Mentor
Call the vector sum of the three forces ${\vec F}_{net}$, so you have the vector equation

$${\vec F}_{net} = {\vec F}_A + {\vec F}_B + {\vec F}_C$$

Write down the corresponding x- and y- component equations, using the magnitudes and angles of the forces. For example, the x-component of ${\vec F}_A$ is $|{\vec F}_A} | \cos \theta_A$. You're given that the three forces have the same magnitude, so use $|{\vec F}_A} |$ for all of them, but of course the angles are different. And ${\vec F}_{net}$ has its own magnitude (which you're given) and angle (which is unknown).

Once you have those two equations, you should have enough information to solve for $|{\vec F}_A} |$.

#### FluxCapacitator

As with all vector problems, I'd start by finding the components. To find the components, use basic geometry to find the angles.

Then you could write one equation saying 200= the sum of all the components
and a few equations equating the magnitudes.

If that didn't help you, say so, and I'll try to explain it more explicitly.

#### jtbell

Mentor
jtbell said:
Write down the corresponding x- and y- component equations, using the magnitudes and angles of the forces.
I'd better point out that whenever you have a problem involving magnitudes and angles of forces (or any other vectors, for that matter), this is usually a good way to start.

#### mrpburke

Could someone work that out a bit more. I'm just not seeing it:(

#### FredGarvin

Each force, A B and C can be broken down into their x and y components...You are given the triangle for each vector. Can you get that far to describe each of the three vectos?

#### mrpburke

I have A, B, and C broken down to x and y components. Now what?

#### mrpburke

I keep getting 47.09kN for the magnitude of Fa. I think the answer in the book is wrong.

#### jtbell

Mentor
Well, I don't think anybody here has psychic "remote vision," so we can't tell you where your mistake is unless you show us your work!

My calculation agrees with the book's answer of 68.2 kN, by the way.

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#### mrpburke

How are you getting that answer?

#### jtbell

Mentor
I did it the way I described earlier. The x- and y- equations gave me two equations in two unknowns: the magnitude of the individual forces, $| {\vec F}_A |$, and the direction (angle) of the net force.

#### mrpburke

I'm workin on it.

#### mrpburke

So set up into 2 equations is it...

200cos@ = |Fa|1.88
200sin@ = |Fa|2.45
????

when that's worked out it comes to 64.7 which isnt quite right.

#### mrpburke

I got 67.4kN. I'll scan it and post up the work tomorrow morning so someone can tell me what I did wrong.

#### mrpburke

Here's what I have. Somebody PLEASE show me what I'm doing wrong!

#### jtbell

Mentor
When calculating components, always measure the angle from the x-axis (in which case the x-component uses the cosine and the y-component uses the sine) or from the y-axis (in which case you switch the sine and cosine). It looks like your angles are the interior angles of those triangles in the diagram, which is OK for one of them but not for the other two.

#### mrpburke

Holy crap!!! I could of swore I've done this before but I think I finally got it right.

Lemme work it out neatly and post it up!!!

#### jtbell

Mentor
Yeah, just fixing those two angles should do it.

#### mrpburke

I think that's gonna be it!!!

Thanks!

#### mrpburke

jtbell said:
Yeah, just fixing those two angles should do it.
I've been all over that just never did it quite like that. I dont know why I didnt even think of that.

gahh....I hate it when it's something simple like that

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