• Support PF! Buy your school textbooks, materials and every day products Here!

Vector problem

  • #1

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 text book 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)

Homework Equations





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!
 

Answers and Replies

  • #2
CWatters
Science Advisor
Homework Helper
Gold Member
10,529
2,295
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.
 
  • #3
178
4
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 dont
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)
 

Related Threads on Vector problem

  • Last Post
Replies
4
Views
506
  • Last Post
Replies
8
Views
814
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
3
Views
817
  • Last Post
Replies
14
Views
668
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
771
  • Last Post
Replies
1
Views
835
  • Last Post
Replies
3
Views
1K
Top