A basic Engineering Physics (vectors/forces) problem

[Declaimed]

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.

[VerrKol]

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.

[Marksman Bryan]

On my phone and I briefly skimmed the problem -

with vectors, split them into horizontal and vertical components and add those individually to get the horizontal/vertical components of your resultant. Use trig and Pythag theorem to find the magnitude and angle of your resultant.

I am reading something about adding 90 to an angle - BAD. DONT DO THIS. If you get a negative that's a-ok. Vectors are a magnitude and direction (think of despicable me); sign typically indicates direction.

[Dudewitbow]

i'm assuming it looks similar to:

f1=2.452N
m1 = .25kg
theta1 = 30 deg(from the 0)

f2= 3.433N
m2= .25kg
theta 2 = 50 deg(reversed from the 180)

X component:(minus as the 2 forces are working against each other in the x direction I think)
f1cos(30)-f2cos(50)= resultant force in x direction
2.123-2.206= 0.083

Y component:(+ since they are working in the same y direction)
f1sin(30)+f2sin(50) = resultant force in y direction
1.226+2.630=3.856

so the final vector has an x component of 0.083, and a y component of 3.856

use Pythagorean theorem to find F of the hypotenuse(the actual resultant force amount)

making a triangle, that would be quadrant 1 where tan(thetaresultant) = 3.856/.083
or theta(r) ~= 88.77 degrees

finding |r| should be easy point on


didn't do any numberchecking(in bed atm in the dark), but that's how I would have approached the problem