Static Equilibrium problem results not well understood. Please help.

[zacc]

Homework Statement

The attached figure shows a weightless bar with several forces applied to it (all in New). The distances are as follow: AB=6m, BC=1m and CD=3m. The question is to calculate DE so there is equilibrium.

Homework Equations

ƩM=0 (Rotational equilibrium) (Counterclockwise moments are +)

The Attempt at a Solution

I have been going around this problem for a while. I tried to apply the equilibrium condition:

ƩM=0 where M are the moments. But I get different answers depending on which point I choose to calculate the moments:

A: 0x2+6x6-8x7+10x12-(10+DE)6=0 This gives DE=6.66
D: 2x10-4x6+8x3-6DE=0 This gives DE=3,33 (the correct answer according to the book)
C: 2x7-6x1+3x12-(3+DE)6=0 This gives DE=4.3

So, I am a little lost here.

The only thing that I can notice is that the system is not at translational equilibrium as:

ƩF ≠ 0 (forces pointing up are +)

In fact, if I make F5=8 N so that ƩF=0 then DE comes to the same answer (2.5) no matter which point I use to calculate the moments. This is what I was expecting before as well.

Could please someone help me to understand these results? Thanks for the help!

 

[Infinitum]

Hi zacc!

The figure seems to be missing?

 

[zacc]

Sorry, for some reason the attachment did not go through the first time. I edited it and it should be there now. Thanks!

 

[Infinitum]

You get different answers because you aren't considering about which point the equilibrium needs to be considered. Strangely, the question doesn't mention this, but from your answers, it turns out to be about D.

Take for example a smaller rod, as in the attachment. Judging from A, it is in rotational equilibrium, but is it from B?

 

[Chestermiller]

Homework Statement

The attached figure shows a weightless bar with several forces applied to it (all in New). The distances are as follow: AB=6m, BC=1m and CD=3m. The question is to calculate DE so there is equilibrium.

Homework Equations

ƩM=0 (Rotational equilibrium) (Counterclockwise moments are +)

The Attempt at a Solution

I have been going around this problem for a while. I tried to apply the equilibrium condition:

ƩM=0 where M are the moments. But I get different answers depending on which point I choose to calculate the moments:

A: 0x2+6x6-8x7+10x12-(10+DE)6=0 This gives DE=6.66
D: 2x10-4x6+8x3-6DE=0 This gives DE=3,33 (the correct answer according to the book)
C: 2x7-6x1+3x12-(3+DE)6=0 This gives DE=4.3

So, I am a little lost here.

The only thing that I can notice is that the system is not at translational equilibrium as:

ƩF ≠ 0 (forces pointing up are +)

In fact, if I make F5=8 N so that ƩF=0 then DE comes to the same answer (2.5) no matter which point I use to calculate the moments. This is what I was expecting before as well.

Could please someone help me to understand these results? Thanks for the help!

Homework Statement

Homework Equations

The Attempt at a Solution

The net upward force is 18, and the net downward force is 16. What does this tell you about the bar being in equilibrium?