Finding theta for a torque problem in equilibrium

AI Thread Summary
To solve the torque problem involving a uniform slender beam in equilibrium, it is essential to select an appropriate pivot point, such as where the wall meets the beam, to simplify calculations by eliminating non-perpendicular forces. The beam's center of mass is located at its midpoint, which is crucial for determining the torque due to gravity. The torque must be resolved into its perpendicular components, and all torques acting on the system must sum to zero for equilibrium. Given the beam's mass and dimensions, these values can be used to establish the necessary equations. Properly applying these principles will lead to finding the angle Θ for equilibrium.
boddie
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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
 
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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=Fperpendiculard

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

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