2014-02-16, 04:13 PM
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.
The bolded part is likely your problem. I'm not sure what the "head to tail" method is, but if one method of rearranging triangles is a right triangle (you use Pythagorean theorem) and one isn't, they aren't the same triangles and you will get different magnitudes and directions.