Statics Table Homework: Equilibrium & Free Body Diagrams Explained

[javik]

Homework Statement

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

 

[SteamKing]

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?

 

[pongo38]

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