How Can You Start Proving the Connection in a Conservation of Energy Problem?

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SUMMARY

The discussion focuses on proving the connection in a conservation of energy problem involving tension (T), weight (W), mass (m), velocity (v), and length (L). The key equations presented include T - W = (mv^2)/L and mgL(1 - cos(θ)) = (mv^2)/2. The relationship T = W(3 - 2cos(θ)) is also established. The solution approach involves using vector notation to express T in terms of W and gravitational force, leading to a comprehensive understanding of the energy conservation principles at play.

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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?
 
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blayman5 said:

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:

[tex]\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)[/tex]. I'll leave the conclusion up to you to resolve.
 

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