Statics and equilibrium - asking for some guidance

In summary: I find an expression for one of the missing values, and put this in the other formula.What do you mean by "put this in the other formula"?
  • #1
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Hi,

I'm not used to communicate physics in English, so my language may be a bit off.

This task is fairly simplistic. It's a figure which is held up in points A and B (both having an x and y force exerted on them), and the figure has a joint C. It is depicted in attached files.

The answers are supposed to be F_A = 13,00 kN, F_B = 7,85 kN, F_C = 9,88 kN.

My results are erroneous.

Can anyone please give me some guidance?

Here's my process:

I separate A-C from B-C and get C with internal forces with equally large opposing forces.

Figure A-C:

Sigma M_A (clockwise is +) = 0

5*2 + 10*2 - 4*C_Ay + 4*C_Ax = 0

=> 30 - 4C_Ay + 4C_Ax = 0, this is (1)

Figure B-C:

Sigma M_B (clockwise is +) = 0

(- cos(arctan(3/4)) * 12 * 2,5) - (sin(arctan(3/4)) * 12 * (tan(arctan(3/4)) * 2,5)) - C_Bx * 3 - C_By *4 = 0

- 37,5 - 3C_Bx - 4 C_By = 0, this is (2)I find an expression for one of the missing values, and put this in the other formula.

And my result is wrong. Always wrong for these tasks. I must do some fundamental error. Any help will be appriciated.
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  • #2
Finn J said:
Sigma M_B (clockwise is +) = 0

- 37,5 - 3C_Bx - 4 C_By = 0, this is (2)

Why are you using negative signs in front of C_Bx and C_By?

Isn't the positive x-direction to the right and the positive y-direction upward?
 
  • #3
Because C has internal forces and I assumed direction. Both of which work against momentum. On the other figure there's opposite forces in C. Or am I wrong?
 
  • #4
Finn J said:
Because C has internal forces and I assumed direction. Both of which work against momentum. On the other figure there's opposite forces in C. Or am I wrong?
There are various ways to treat signs. If your mathematics is completely consistent then a variable representing an unknown force can be given the "wrong" sign and when you obtain it's value, it will be a negative number. The simplest way to be consistent is to give forces pointing in the positive x or y direction a "+" sign.

I find an expression for one of the missing values, and put this in the other formula.
How are you doing that? Are you setting C_Ax = C_Bx or are you setting C_Ax = - C_Bx ?
 

1. What is the definition of statics and equilibrium?

Statics is the branch of mechanics that deals with the study of objects at rest or in a state of constant motion. Equilibrium refers to a state in which all forces acting on an object are balanced, resulting in no change in the object's motion.

2. What are the main principles of statics and equilibrium?

The main principles of statics and equilibrium are the laws of motion, specifically Newton's First Law, which states that an object at rest will remain at rest and an object in motion will remain in motion unless acted upon by an unbalanced force. Another important principle is the concept of torque, which is the rotational equivalent of force and is used to analyze rotational equilibrium.

3. How are forces represented in statics and equilibrium?

Forces are represented using vectors in statics and equilibrium. Vectors have both magnitude and direction, and are used to show the direction and amount of force acting on an object. They are typically represented by arrows, with the length of the arrow representing the magnitude of the force and the direction of the arrow indicating the direction of the force.

4. What is the difference between a static and a dynamic equilibrium?

A static equilibrium refers to a state in which an object is at rest or moving at a constant speed with no acceleration. A dynamic equilibrium, on the other hand, refers to a state in which an object is in motion with a constant velocity, meaning that the object is moving at a constant speed and in a straight line.

5. How is the concept of equilibrium applied in real-life situations?

The concept of equilibrium is applied in various real-life situations, such as designing structures like buildings and bridges, analyzing the stability of objects like vehicles and aircraft, and understanding the balance of forces in the human body. It is also used in fields such as engineering, physics, and biomechanics to solve problems related to statics and equilibrium.

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