Proving T-W=(mv²)/L from conservation of energy

[blayman5]

Homework Statement

I have to prove in a conservation of energy question

T-W =(mv^2)/L

mgL(1-cosO)=(mv^2)/2

mg=W

T=W(3-2Cos0)

How could I go about starting this?

 

[asleight]

Homework Statement

I have to prove in a conservation of energy question

T-W =(mv^2)/L

mgL(1-cosO)=(mv^2)/2

mg=W

T=W(3-2Cos0)

How could I go about starting this?

Well, you can do this:

$$\vec{T} = \vec{W} + m\vec{v}^2/\vec{L} = m\vec{g} + m\vec{g}\vec{L}(1-\cos\theta) = \vec{W}\vec{L}(1-\cos\theta)$$. I'll leave the conclusion up to you to resolve.