Finding theta for a torque problem in equilibrium

[boddie]

Homework Statement

A uniform slender beam of mass 10 kg and length 1.2m is resting on a corner which is a knife-edge. The vertical wall on the left is smooth. What is the angle Θ for equilibrium? a=0.5m

Homework Equations

Can someone help me setup the formulas to solve this problem. I looked at it for well over an hour with no clue. I keep coming up with many variables that are no help.

The Attempt at a Solution

i drew a picture of what I was given and attached it. I also filled out additional information that I cae up with but I am not sure if i am going in the right direction.

http://img8.imageshack.us/img8/4807/physicsk.jpg

 

[ThomasMagnus]

The very first thing you should do in every torque problem: Choose a pivot point. Pick a point that will eliminate the "sticky" forces. I would choose where the wall meets the ladder since it eliminates the non-perpendicular force from the wall (usually this is the best choice, but it's up to you)

**Remember
\tau=F_{perpendicular}d

Remember to resolves the torques into their perpendicular components (this is something that I was always stuck on in equilibrium, and also spent days staring at these problems )

 

[ThomasMagnus]

Notice how they have given you a=.5. This is going to help you with finding the torque on the knife and beam.

 

[boddie]

Yah I thought i would have to use the the pivot point as the knife edge that's how i came up with, but I am having problems coming up with component forces cause i seem to have no given values off the bat. just more variables... I am so confused I am about to just rip it up.

 

[ThomasMagnus]

You do have given values. For example, the beam has its center of mass at its mid point (it's uniform) 1.2/2=0.6m and you are given the mass of the beam.

So if you choose where the ladder meets the wall to be the pivot point, the beam will have a torque .6m away from the pivot point--Then you need to find the perpendicular component of the torque (use the force of gravity). Remember that all of the torques must equal zero! (second condition)

 

[ThomasMagnus]

Yah I thought i would have to use the the pivot point as the knife edge that's how i came up with, but I am having problems coming up with component forces cause i seem to have no given values off the bat. just more variables... I am so confused I am about to just rip it up.

You know what, I think that's a better idea, since it will eliminate the torque on the knife.

I'm trying my best but I'm not that advanced in this :)