# Statics Table Homework: Equilibrium & Free Body Diagrams Explained

• javik
In summary, the conversation discusses using free body diagrams, moments, and equilibrium to determine the stability of a table under a load of 300N at a certain distance from the origin. The process involves calculating the forces at different points on the table and considering the reaction at Leg B as the load moves away from the center. The key to determining if the table will flip over or fail is finding the point where the reaction at Leg B disappears. Additionally, the position of the applied load must be equal to the centroid of the reaction forces.
javik

## Homework Equations

Free Body Diagrams, Moments, Equilibrium

## The Attempt at a Solution

Started off by giving x,y,z coordinates to the 4 points (A,B,C,E). E is the centre of the table and I used that as my origin.

A=(-1.034, 0, -0.6) [Leg to the Left)
B=(1.034, 0, 0.6) [Furthest Leg]
C=(0,0,1.2) (Leg Closest)
E=(0,0,0)

From there, I knew that the table was exerting a force of 147.15 N (15 x 9.81) downwards over it's whole area. So to find the force it exerted at it's centre of gravity, I then multiplied this value by the surface. (Is this correct Methodology?)

So at Point E their was a downwards force of 166.423 N.

From there, I did a free body diagram and calculated Vertical Force Equilibrium of the System. So I got 166.423 = Av, Bv, and Cv.

I then went on to calculate moment equilibrium but got stuck as i pondered the next question:

what constitutes as the table flipping over or failing?. My first approach was to look for the point at which their is an imbalance in the system. But this would constitute any force acting upon the system. Not the 300N load at 0.447m from the origin as stipulated in the answer!

How do i approach this question? I seem to have something fundamentally wrong

Cheers

Look at the reaction in Leg B as P moves further away from the center of the table. Is there a distance x from the center where P is applied at which the reaction at B vanishes?

Another helpful principle is that the position of the applied load must be equal and opposite to the centroid of the reaction forces.

## 1. What is equilibrium?

Equilibrium refers to a state in which all forces acting on an object are balanced, resulting in a constant velocity or no motion at all.

## 2. What is a free body diagram?

A free body diagram is a visual representation of an object or system, showing all the forces acting on it, without considering the effects of its surroundings.

## 3. How do you solve problems involving equilibrium and free body diagrams?

To solve these problems, you must first identify all the forces acting on the object and their directions. Then, you must use the principles of equilibrium to set up equations and solve for the unknown forces.

## 4. What are the key principles of equilibrium?

The key principles of equilibrium are Newton's First Law, which states that an object in equilibrium will remain at rest or in constant motion unless acted upon by an unbalanced force, and the fact that the sum of all forces in the x and y directions must be equal to zero.

## 5. What are some common types of forces that can appear in equilibrium problems?

Some common types of forces are tension, compression, friction, normal force, and weight. It is important to carefully consider all forces acting on an object in order to accurately solve equilibrium problems.

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