# Vector resolution and vector addition

1. Oct 29, 2009

### pooker

1. The problem statement, all variables and given/known data

We were given six homework assignments for lab. We were required to find the force and angle through three given experiments.

1. Experimental using a force table
2. Graphically using head to tail, etc
3. Analytical using basic means to find the answers

2. Relevant equations

I have two problems

1st problem
Vector resolution
F1 = (.1)gN theta = 30
F2 (.2)gN theta = 90
F3 (.3)gN theta = 225

2nd Problem
Vector resolution
F = (.3)gN theta = 60

Find fx and Fy

3. The attempt at a solution

1st Problem attempt at solution

Using the force table I got F = (.130)gN Theta = 150
Using Graphical I got F = (.131)gN theta = 162

Now my problem is with analytical

I used these equations

Rx = Rcostheta
Ry = Rsintheta
r = sqrt(rx^2 + ry^2)
theta = arctan rx/ry

rx = .1cos30 + .2cos90 + .3cos225 = -.1255
ry = .1sin30 + .2sin90 + .3sin225 = .038

R = sqrt( -.1255^2 + .038^2) = .131

Theta = arctan .038/-.1255
Theta = 343.2 ???? It seems grossly off. I feel like I am forgetting something, but our book does not even really cover three vectors. I had to look online for how to do it.

2nd problem attempt

Using force table
Fx = .140gN
Fy = .245 gN

Using graphical (I plotted this like a 90 degree triangle
Fx = .16gN
Fy = .25gN

Using analytical

I know c^2 = a^2 + b^2 so .9 = a^2 + b^2

b / sintheta = R / sin Y

sin theta is the angle R casts onto A which equals 60
Sin Y is the angle sides B and A make

b / sin60 = .3/sin90

b / .866 = .3

b = .866(.3) = .2598

so Fy = .2598

.9 = .2598^2 + a^2
.9 = .0675 + a^2
.8325 = a^2 = .91

so Fx = .91 ??? Why is it so low as compared to the graphical and experimental? I feel something is off. All of my other calculations were pretty dead on .