1. ## Resolving forces question

In the picture I have attached, you have to resolve the two forces (T, equal value) as the red R down the middle, but I was always taught to resolve forces by connecting them up as shown by the green R at the bottom.

Am I getting confused between resolving forces and equilibria? What's going on? Should I just never use that method/what method should I use?

Usually that method (with the green R) seems to work if you arrange the forces to make a triangle

2. ## Re: Resolving forces question

Originally Posted by Mukilab
In the picture I have attached, you have to resolve the two forces (T, equal value) as the red R down the middle, but I was always taught to resolve forces by connecting them up as shown by the green R at the bottom.

Am I getting confused between resolving forces and equilibria? What's going on? Should I just never use that method/what method should I use?

Usually that method (with the green R) seems to work if you arrange the forces to make a triangle
Remember that vectors can always be moved around. What you need to do is to, say, start with the T at an angle, add (vectorally) that to the T that is vertical, and that will determine the resultant (your green R.) That will give you the triangle you are interested in. The problem with this approach (and any other approach) is that we have no angles to put into the formulas. All we have is a value for T, but we can't resolve the T's into components without an angle.

Resolving forces is breaking them down into vector components. Equilibrium problems are set up by noting there is no net force in the problem, meaning that all the forces add up to be 0. In your case we have $\bf{T} + \bf{T} + \bf{R} = 0$ (This means that the direction of the green R is incorrect. It should be pointing "up" and to the right.)

-Dan