Equilibrium from the ceiling. Solve using cosines

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In summary, the conversation discusses the location of the center of a rod relative to point B and how to use this information to find the angle the rod makes with the horizontal. The key is to draw a figure with a vertical line from B to the rod center and solve for the triangle's angle located at the center of the rod.
  • #1
tigerwoods99
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thanks
 
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  • #2
Where is the center of the rod located, relative to point B?
 
  • #3
I'm sorry!
 
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  • #4
Yes, I realize that the rod is opposite to angle B. The question was meant to give you a clue about the configuration. So more specifically, what do we know about where the center-of-mass of the hanging rod is located, relative to the point B from which the rod and strings are hung?
 
  • #5
I think the mg of the rod is located directly underneath point B where it is hung from the ceiling
 
  • #6
Yes, exactly. You can use that information to figure out the angle the rod makes with the horizontal.
 
  • #7
Ok. so knowing that does angle B "split" into two halves. I am still not sure where this is taking me.!
 
  • #8
Draw a vertical line from B to the rod center. The triangle is split into two smaller ones. Solve either of the smaller triangles.

Good luck!
 
  • #9
Ok thanks! I think i still need a little more guidance on this though. What will this solve? How will this help find theta?
 
  • #10
The key is to find the triangle's angle located at the center of the rod. If you haven't already, draw a figure including the vertical line between B and the rod center.
 
  • #11
Ok. thanks
 
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1. How do you find the equilibrium position using cosines?

To find the equilibrium position using cosines, you will need to use the law of cosines. This law can be used to solve for an unknown side or angle in a triangle when you know the lengths of two sides and the measure of the included angle.

2. What is the significance of equilibrium in a system?

Equilibrium is a state where there is a balance of forces and no net change in the system. This is an important concept in science as it allows us to predict and understand the behavior of a system. In the case of equilibrium from the ceiling, it refers to the point where the object hanging from the ceiling is not moving and the forces acting on it are in balance.

3. How do you know when a system is in equilibrium?

A system is in equilibrium when the forces acting on it are equal and opposite, resulting in a net force of zero. This means that the system is not accelerating and remains in a state of rest or constant motion. In the case of equilibrium from the ceiling, this can be determined by checking if the object is stationary and if the forces acting on it are balanced.

4. What are the factors that affect equilibrium from the ceiling?

The factors that affect equilibrium from the ceiling include the weight of the object hanging from the ceiling, the angle at which it is suspended, and the strength and direction of the forces acting on it. Other factors such as air resistance and friction may also play a role.

5. Can you use other trigonometric functions to solve for equilibrium from the ceiling?

Yes, you can also use other trigonometric functions such as sine or tangent to solve for equilibrium from the ceiling. However, the use of cosines is preferred as it allows for the calculation of all sides and angles of a triangle, whereas sine and tangent only calculate one side or angle.

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