# Finding F2 & F3 in a Hook with Given FR & F1

• jessicapearson
In summary, the textbook does not cover this situation where you need to find the resultant, F2 and F3, if you have FR and F1. You can find the resultant by solving the equations for x and y components and then using the pythagoras theorem to get the magnitude of the resultant.

## Homework Statement

I know how to find the resultant or a force if I have been given 1 or 2 or 3 forces etc. Or find a force if I have been given the resultant. However in my textbook there was nothing on a situation where I need to find F2 and F3 if I have been given FR and F1 right?
My question is:
A hook has been subjected to three forces (F1,F2,F3). FR (resultant) = 150kN and its angle from positive x-axis is 60.
F1 = 35kN & angle is 180 from positive x axis.
Calculate magnitude of F2 and F3.
(F2 angle = 135 and F3 angle = 30)

## The Attempt at a Solution

Where I was going with it:
I thought i would write two equations summing the x and y components and then use simultaneous equations to solve..

Sum of x-components:
(35kN)cos(180) + (F2)cos(135) + (F3)cos(30) = (150kN)cos(60)

Sum of y-components:
(35kN)sin(180) + (F2)sin(135) + (F3)sin(30) = (150kN)sin(60)

Then I got to this point and thought, geez, i havn't used simultaneous equations in god knows how long... Didn't really know where to go from here. If anyone can help explain simultaneous equations to this particular problem that would be amazing!
Or, better yet if I went about my initial attempt completely wrong.. then please let me know. Thankyou in advance!

Rearrange one equation to the form F2 = long equation

Then in the other equation replace F2 with that long equation.

Then rearrange the resulting equation to the form F3 = ...

Plug in the numbers to give a value for F3.

look
there are 2 ways
1 : if you have their components you can just add them together * the x and y Or i and j *
if you don't
2 : you can resolve the forces into perpendicular directions
then add the perpendicular components * the x components together and the y components together *
then now you have the components of the resultant
now get the magnitude of the resultant by the pythagoras theorem
square root of X^2 + Y^2 . now you have the magnitude of the vector resultant
the direction of the resultant is basically 1/tan (y/x)