Is my forces diagram correct? (static equilibrium problem)

[Femme_physics]

(static equilibrium problem)

Homework Statement

Calculate the force R that acts on the axis of the crane (O), if the crane lifts in a constant speed a mass of 500 kg. The incline angle of the cable to the horizontal line is 45 degrees. Do not consider pulley friction.

The answers are:

R = 9063.23 [N]
Beta = 67.5 degrees

[PLAIN]http://img130.imageshack.us/img130/2276/forcesquest.jpg

The Attempt at a Solution

I've only made a force diagram to ask you guys whether it's correct.

[PLAIN]http://img339.imageshack.us/img339/7528/forces.jpg


*sighs* Truth is playing with triangles, law of Sines, and sum of all forces on X and Y is getting me nowhere -- but is this the way to solve it? I think that if my force diagram is correct it should be easy...just too many unknowns...

 

[PhanthomJay]

You are doing more work than necessary...the OP just wants the force applied at O, so draw a FBD of the pulley, note the tension in the rope, and use Newton 1 in the x and y directions to solve for Rx and Ry...and Pythagorus to solve for R. The direction of R must be along the bisector of the angle between the ropes.

 

[Femme_physics]

Well, I've taken your advice and I'm inching close to the answer in terms of the numerical result but still a bit off... it seems to make since though... (angle is a piece of cake once I have the correct Rx and Ry...clear I don't yet)

I attached the file of my new diagram and method to solve it...do you mind taking a look?

 

[PhanthomJay]

Well, I've taken your advice and I'm inching close to the answer in terms of the numerical result but still a bit off... it seems to make since though... (angle is a piece of cake once I have the correct Rx and Ry...clear I don't yet)

I attached the file of my new diagram and method to solve it...do you mind taking a look?

Again your equations are good but your math is lousy . Add up mg and Tsin45 again...

 

[Femme_physics]

Ah...it's that stupid calculator *embarrassed grin*...thanks a lot phantom :D What'd I do without you!

 

[PhanthomJay]

Ah...it's that stupid calculator *embarrassed grin*...thanks a lot phantom :D What'd I do without you!

Well,without me, you can always count on nvn or tiny-tim...and a host of others...

 

[Femme_physics]

Hehe... I love this forum. Best stuff on the internet!