Statics Tension, Spring, and, DownWard Force

1 reply · 2K views · last reply
Boba Fet
Messages
4
Reaction score
0

Homework Statement



Diagram of a vertical force P pulling down on point A, where a 2-ft cord AB runs up-left to a wall and a spring AC runs up-right to a wall, with each horizontal span marked 2 ft; labeled Probs. 3-22/23.

Homework Equations


I am Stuck getting Theta out of the last step of equation. I have found that theta is 35 by trial and error.( i wrote an excel program)[/B]

The Attempt at a Solution


Handwritten statics derivation on graph paper with force diagrams, equilibrium equations for tension and spring forces, and a highlighted final expression P/2K = 2cos(theta) times a ratio of square-root terms.
 
My final equation is similar to yours, but not exactly the same:

$$\frac{P}{k}=\tan{\theta}\frac{(4-\cos{\theta})[\sqrt{5-4\cos{\theta}}-1]}{\sqrt{5-4\cos{\theta}}}$$

I didn't check my algebra, so I'm not sure of this.