Recent content by Jeroen Staps

Is it now possible to extract theta from ##\cos(\arctan(\dfrac{AB-CD \sin(\theta)} {BC-CD\cos(\theta)})) ## I know that ##\cos(\arctan(x)) =\dfrac{1}{\sqrt{x^2+1}}##

I understand the derivation, Thanks!

The coordinates are for example as is the length of CD. The goal is to express φ in terms of θ or the other way around. And all the other parameters in the expression have to be known.

Yes, CD is fixed and AD is not. And the length of CD is known

The problem is that I keep getting a inverse cosine inside a cosine or a sine and when I get this there is no possibility to get θ out of the inverse cosine right?

Then I get this: And φ still contains θ in it

Homework Statement I need to solve a system of two equations for T and θ algebraic and with all the other parameters known. φ is equal to: Homework Equations The relevant equations are the two equations left of * in the image below The Attempt at a Solution I tried Gauss elimination but I...

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.

So does my post #45 make sense?

I used the cosine rule twice to come up with this

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?

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

And I have that: BD2=AB2+AD2-2*AB*AD*cos(α2) when you substitute AD from the earlier post in this equation then you have an equation to solve α2 with θ as unknown and α2 is equal to α-(180-90-φ). So I can express θ in φ

Need more?

Does this make sense?