Physics force tension question?

Question

ok i ama bit confused when you have an object hangng from two cables... i know you do F1 F2 F3 and you come up with two variables and solve for eachother. say you have a lamp hanging that weighs 150N and the angles are 35 degrees and 15 degrees how would i solve that?

Answer 1

First of all, you have a situation where your lamp is in static equilibrium, which means the net force on your object is zero. This is very important to the solution of this problem. We will want to find the verticle components of the forces felt on the lamp first. Clearly it has some weight (150 N) directed in the negative y-direction. It also can be thought of as having two forces, one due to the tension in each cable. I will assume that the angles given are from the horizontal. I will define Fy1 and Fy2 as my tensions from the two cables in the y-direction.

W+Fy1+Fy2=0 (no net force on the object in the verticle direction)

-150 N + F1sin(15) + F2 sin(35) = 0 ,which is one of our two equations.

The other equation comes out of the fact that there must be no net force in the horizontal direction as well.

F1x+F2x=0

F1cos(15)+F2cos(35)=0 since one of these force components is negative (they are in opposite directions) I will solve this as:

F1cos(15)=F2cos(35)

So I get the series of equations

-150 N +F1sin(15)+F2sin(35)=0
F1cos(15) = F2cos(35)

where F1 is the force due to tension on one cable and F2 is the force due to tension on the other cable. It should be quite clear how to algebraically solve this problem from here.

Problems like this one are essentially a basic use on Newton's second and third law. I would review them and think about the implications of those two laws. I specifically do not state Newton's first law as Newton's first law is implied from Newton's second law.