Describe the position of a pulley attached to a sling

[haruspex]

I now have the following equation that seems to be correct:

φ = cos^-1((AC-CD*cos(γ-θ)) / √(AC²+CD²-2*AC*CD*cos(γ-θ))) + 90 - α

I was thinking of something simpler, though it may be equivalent: the sine rule.

 

[haruspex]

But how do I use this to describe the location of D when there is a certain mass hanging at D and there is a certain pulling force in AD?

As I posted, you can use angles θ and φ to write a force balance equation.

 

[Jeroen Staps]

I was thinking of something simpler, though it may be equivalent: the sine rule.

I used the cosine rule twice to come up with this

 

[Jeroen Staps]

As I posted, you can use angles θ and φ to write a force balance equation.

So does my post #45 make sense?

 

[BvU]

Yes, at least for equilibrium. Adding constant acceleration should be easy.

But I wished you wouldn't change notation every time.
And you can easily simplify $\ \sin(\pi/2-\pi/4-\phi)\$ and $\ \cos(\pi/2-\pi/4-\phi)\$ I should hope.

So how many equations with how many unknowns do you now have altogether ?

 

[haruspex]

Adding constant acceleration should be easy.

I believe it is a statics question, how the equilibrium position depends on the applied tension.

 

[Jeroen Staps]

I believe it is a statics question, how the equilibrium position depends on the applied tension.

The question is: What is the position of the pulley when there is a given mass of the load and a given ratio between the force of gravity and the pulling force.

 

[haruspex]

The question is: What is the position of the pulley when there is a given mass of the load and a given ratio between the force of gravity and the pulling force.

Which is the same as I wrote.