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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 triangleAttachment 28331

Re: Resolving forces question

Quote:

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

Attachment 28331

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 $\displaystyle \bf{T} + \bf{T} + \bf{R} = 0$ (This means that the direction of the green R is incorrect. It should be pointing "up" and to the right.)

-Dan

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Re: Resolving forces question

Thank you for your reply, for your first paragraph do you mean drawn like this: Attachment 28335 ?

I did it again and I seem to have done the cosine wrong. That image is what I did originally but I scrapped it because I thought it was wrong. Thank you for the clarity!

How would I draw that image if I wanted to resolve? Would I have to make sure the arrows go round in a circle? As in they point in a cyclical thing so you can follow the arrows around forever, unlike in resolving forces where two arrowheads bump into each other... if that makes sense.

EDIT::: The problem is this new picture I put up works with the equations and for the answers but it isn't it exactly the same as the former picture since both times arrowheads are 'bumping'? All I've done in the other one is slightly moved the forces around. I mean, it makes sense intuitively but I'm not sure how to justify it solidly. Exams on Monday though, so I'll probably go with gut instinct!

EDIT2:: Maybe because in the first arrows are coming from a point whilst in the second they are leading into one another? Again, intuitive and not solid