# Force System

1. Dec 17, 2007

### america8371

1. The problem statement, all variables and given/known data
Determine the resultant of the three forces shown, given that P1= 50kN, P2=80kN, and P3=120kN and the dimension a is 4m.

2. Relevant equations
I think im supposed to use
R=$$\Sigma$$F=F1 + F2 + F3 + ....

3. The attempt at a solution
P1=50$$\lambda$$=50(4i+aj / $$\sqrt{a^{2}+16}$$)
P2=80$$\lambda$$=120(2i+aj+3k / $$\sqrt{a^{2}+13}$$)
P3=120$$\lambda$$=80(4i+aj+3k / $$\sqrt{a^{2}+25}$$)

R=(40,000i+2,500a^{2}j / a^{2}+16)
+ (57,600i+14,400a^{2}j+129,600k / a^{2}+13)
+(102,400i+6,400a^{2}j+57,600k / a^{2}+25)

I'm not too sure if I started the problem correctly, let me know what yall think, thanks in advance.

Last edited: Dec 18, 2007
2. Dec 17, 2007

### rl.bhat

In the problem P2=80kN, and P3=120kN .But in the attempted solution the are different. And why you have taken j vector negative?

3. Dec 18, 2007

### america8371

Because I'm an idiot.
Just kidding, when I redrew the graph on my paper I drew the start of the vectors on the origin, I really don't know why I did that, lol.
I also made the corrections on the j vector.
Thank you so much for pointing those out.

If my work is correct im not sure what to do next.
Any help would be appreciated.

4. Dec 18, 2007

### rl.bhat

Because I'm an idiot. No..No..You are right. You have calculated P1, P2 and P3 by using the position vectors. So keep j -ve. Put the value of a. Calculate (50/sqrt32) and so on. Then add the vectors. For the resultant you cannot square the vectors and add them.