Addition of a System of Coplanar Forces

[tophernuts]

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

The resultant force acting is directed along the positive x-axis, determine the magnitudes of F2 and the resultant force

And that F3x=4 and that F3y=3 (its a right angle 3-4-5 triangle)

Homework Equations

F1=F1_x +F1_Y
F2=F2_x +F2_Y
F3=F3_x +F3_Y

The Attempt at a Solution

F1y= 4cos(30) = 3.464
F3y=3

And since the resultant force is along the x-axis, the resultant y force (Fr_y) would therefore have to equal 0.

But when you run the numbers:

Fr_y=F1_Y+F2_Y+F3_Y
Fr_y=(+3.464)N + (-3)N + F2_y
F2_y= -0.464
xsin30=-0.464
x=-0.464/sin30
x=-0.928

But that is impossible because F2 is above the x-axis and therefore couldn't have a negative y value.

This is where I am currently stuck, if it would work out i could figure out the resultant of F2_y and F2_x which would be F2, and the find out the resultant of all three from there on.Thank you in advance,
Chris

 

[cepheid]

Welcome to PF,

1. If the problem statement, all variables and given/known data
And that F3x=4 and that F3y=3 (its a right angle 3-4-5 triangle)

How do you know that F3 is 30 degrees from the x-axis? Your diagram doesn't indicate such.

 

[tophernuts]

I don't, I just know that it is a 3-4-5 triangle.

I know that F2 is 30 degrees away from the x-axis though

 

[tophernuts]

Well, this is embarrassing.
My friend who I was working on it with and I both failed to see the direction of the arrow F1...
As it is pointing downwards, not upwards, this question makes a lot more sense now...

Sorry for your time!

 

[DeeNos]

I would suggest checking your calculations and equations again to ensure accuracy. It is important to double check all variables and equations to avoid any errors. Additionally, it may be helpful to draw a diagram of the forces and use trigonometric functions to solve for the unknown variables. Once the values for F2x and F2y are determined, you can use the Pythagorean theorem to calculate the magnitude of F2 and then find the resultant force by adding all three forces together. It is also important to consider the direction of the forces and use proper vector notation to accurately represent the resultant force. Overall, it is important to approach the problem systematically and carefully to ensure accurate and precise results.