Declaimed Wrote:Woo, alright. So, I'll throw this out there right off the bat: I'm taking a college level Physics course, but I've had no experience with anything Physics prior. So forgive me if I seem like I don't know what I'm doing (because I probably don't). I have a lab that I'm working on involving forces, and using vectors to graphically depict/analytically calculate said forces. Here is my dilemma:

Given two forces, F1 and F2:

F1 =
Force: 2.452 N
Mass: .25 kg
Direction: 30 degrees

F2 =
Force: 3.433 N
Mass: .35 kg
Direction: 130 degrees

[As cos 130 yields a negative value, I added 90 to it to get my angle measure back into Q1 for a positive value and used that for my calculations]

, I am to find the resultant |R| (its magnitude and direction).


Using the head-to-tail method of moving vectors, I moved F2 on the graph without rotating it to the tail of F1, and constructed |R| by drawing a straight line from the tail of F2 to the head of F1. This forms a triangle (not a right triangle, just a triangle). The first part of this exercise asks me to graphically depict and measure the resultant force. Measuring things out with a ruler and protractor, I come to the result:

|R|:
Force(N) = 3.813 N
Direction: 93.5 degrees.



The next step is to calculate the resultant analytically. The formula below is given to accomplish this:

Rx = ([F1]x+[F2]x) = [F1]cos(angle[F1]) + [F2]cos(angle[F2])
Ry = ([F1]y+[F2]y) = [F1]sin(angle[F1]) + [F2]sin(angle[F2])
|R| = sqrt([Rx]^2+[Ry]^2)

Plugging in my values I get:

Rx = ([F1]x+[F2]x) = [2.452]cos(30) + [3.433]cos(40)
Ry = ([F1]y+[F2]y) = [2.452]sin(30) + [3.433]sin(40)

Rx = 4.7533
Ry = 3.4327
Rx^2 = 22.594
Ry^2 = 11.783

|R| = sqrt([Rx]^2+[Ry]^2)

|R| = sqrt(22.594+11.783)
|R| = sqrt(34.377)
|R| = 5.8632


So, analytically:
|R|:
Force(N) = 5.863 N
Direction: 72.2 degrees.
Mass: 0.60 kg



My analytical and graphical results are extremely different. I can't figure out where I'm going wrong.