Statics and friction equations for a rope system

[chrisyuen]

Homework Statement

Homework Equations

F = uR

The Attempt at a Solution

I don't understand the followings:

For equilibrium at A, the equation should be F₁ = T sin $$\theta$$. Am I right?

While for the one at B, the equation should be F₂ = T sin $$\theta$$. Am I right?

In addition, how can I get cos $$\theta$$ = (au² + 1)^-0.5 at the last answer?

Thank you very much!

 

[chrisyuen]

Homework Statement

Homework Equations

F = uR

The Attempt at a Solution

I don't understand the followings:

For equilibrium at A, the equation should be F₁ = T sin $$\theta$$. Am I right?

While for the one at B, the equation should be F₂ = T sin $$\theta$$. Am I right?

In addition, how can I get cos $$\theta$$ = (au² + 1)^-0.5 at the last answer?

Thank you very much!

I tried some methods and found the followings finally:

tan $$\theta$$ = 3u = 3u / 1

Put the above result to a right-angled triangle with adjacent side = 1 and opposite side = 3u,

we can get cos $$\theta$$ = (9u² + 1)^-0.5.

I guessed that the "a" is actually a "9" which is a typo instead. Am I right?

 

[Shooting Star]

I tried some methods and found the followings finally:

tan $$\theta$$ = 3u = 3u / 1

Put the above result to a right-angled triangle with adjacent side = 1 and opposite side = 3u,

we can get cos $$\theta$$ = (9u² + 1)^-0.5.

I guessed that the "a" is actually a "9" which is a typo instead. Am I right?

You seem to be quite right.