Finding theta for a torque problem in equilibrium

In summary, the problem involves a uniform beam with a mass of 10 kg and a length of 1.2m resting on a knife-edge on a smooth vertical wall. The goal is to find the angle Θ for equilibrium. The first step is to choose a pivot point, which should eliminate any non-perpendicular forces. The pivot point can be chosen at the intersection of the wall and the beam. The next step is to find the perpendicular component of the torque, which can be done by using the force of gravity. All torques must equal zero for equilibrium to be achieved.
  • #1
boddie
8
0

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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  • #2
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
[tex]\tau[/tex]=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:)
 
  • #3
Notice how they have given you a=.5. This is going to help you with finding the torque on the knife and beam.
 
  • #4
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.
 
  • #5
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)
 
  • #6
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 :)
 

1. What is meant by "theta" in a torque problem?

In a torque problem, "theta" refers to the angle at which a force is applied to an object. It is measured in radians or degrees and determines the direction of the torque.

2. How is theta related to torque and equilibrium in a problem?

In a torque problem, theta is a crucial factor in determining the magnitude and direction of the torque on an object. In order for an object to be in equilibrium, the sum of all torques acting on it must be equal to zero. Theta helps to determine the direction of the torque and whether it is contributing to or counteracting the other forces.

3. How can theta be calculated for a torque problem in equilibrium?

Theta can be calculated using the formula: theta = tan^-1 (r x F / r x Fperpendicular) where r is the distance from the pivot point to the point where the force is applied, F is the magnitude of the force, and Fperpendicular is the component of the force that is perpendicular to the lever arm.

4. Can theta be negative in a torque problem?

Yes, theta can be either positive or negative in a torque problem, depending on the direction of the force and the direction of rotation. If the force is applied in the opposite direction of the rotation, theta will be negative. If the force is applied in the same direction as the rotation, theta will be positive.

5. How does changing theta affect the torque in a problem?

Changing theta will affect the magnitude and/or direction of the torque in a problem. As theta increases, the torque will also increase. Additionally, changing the direction of theta will change the direction of the torque. In order to achieve equilibrium, theta must be carefully considered in relation to the other forces acting on the object.

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