Uniform ladder against wall held by rope at angle theta

[xduckksx]

Homework Statement

A uniform ladder AB, of weight W and length 2.5m rests against a smooth vertical wall OA with its foot on smooth horizontal ground OB. The ladder is in a vertical plane perpendicular to the wall. It is kept in position with OA=2m and OB=1.5m by a light rope OC joining O to a point C on the ladder such that angle COB=theta. Show that the tension T in the rope is given by

T=(3W)/(8cos(theta)-6sin(theta))

Homework Equations

This is just a moments question.

The Attempt at a Solution

I've tried taking moments about B, but don't seem to get why there are two terms in theta in that equation.

 

[SammyS]

Show what you have tried, and where you are stuck, so we can help you.

 

[xduckksx]

I'm really not sure how to proceed. If I take moments about B, there seem to be two forces I need to include: the tension in the rope, and the weight force. Am I correct?

 

[SammyS]

Use the moment about A.

 

[xduckksx]

When I try moment about A,
Clockwise moment is due to the tension, with value moment=2Tcostheta. as well as weight.
Anticlockwise moment is due to the normal force at B (which is twice the weight force), hence moment here is 0.75W.
Then solving I get T=3W/(8costheta). So where does the -6sintheta come from?

 

[SammyS]

Does the problem state anything about the location of point C? (I doubt that it does.)

 

[xduckksx]

Nope, C can vary.

 

[SammyS]

When I try moment about A,
Clockwise moment is due to the tension, with value moment=2Tcostheta. as well as weight.
Anticlockwise moment is due to the normal force at B (which is twice the weight force), hence moment here is 0.75W.
Then solving I get T=3W/(8costheta). So where does the -6sintheta come from?

Why do you say that the normal force is twice the weight force?

 

[xduckksx]

I'm not sure. Should it be the same?

And can you explain where that -6sin theta comes from?

 

[SammyS]

A component of T is vertical. The normal force at B must cancel both the force of gravity and the vertical component of T.

 

[xduckksx]

Isn't this accounted for in calculating the clockwise moment of the overall tension?

Oh, I see. The normal force at B also takes into account this vertical component. FML.