Dynamics rigid body cabinet problem

[Pipsqueakalchemist]

Homework Statement

Question and solution below

Relevant Equations

Newton’s 2nd law
Moment equation

So for this question I understand part A but part B is confusing me, when using point B as the centre of the moment, I get different sign for the mad term. If you take clockwise as positive than 100N force and the force at point G are causing a positive moment and gravity is causing an negative moment. But the solutions have different signs as my attempt I don’t understand why. Appreciate it if someone can explain this to me.

 

[Master1022]

Hi there,

Perhaps I am wrong, but from the problem statement, it seems as if the point B is accelerating and thus we are taking moments about an accelerating point. Hence, the $m a d$ term is included. See the derivation below for why this is the case. $G$ is the centre of mass and $A$ is an arbitrary accelerating point.

Hope this is of some help.

 

[Pipsqueakalchemist]

I understand why mad term is included, what I don’t understand is the sign. If you take clockwise direction as positive than the mad term and the 100h should be positive and the weight negative but that’s not the case. If you move the mad term to the left side of the equation the mad term is negative and that’s what I don’t understand.

 

[Master1022]

Sorry I don't quite follow. Can you point me towards which equation you are looking at? I see the equation:

I understand why mad term is included, what I don’t understand is the sign.

What is wrong with the sign in the equation? From the derivation that I posted above, this sign convention seems to agree with that (unless I am missing something...).

If you take clockwise direction as positive than the mad term and the 100h should be positive and the weight negative but that’s not the case. If you move the mad term to the left side of the equation the mad term is negative and that’s what I don’t understand.

The $mad$ term is not on the same side of the equation as the $100h$ term, as shown in the derivation above. I don't believe the horizontal acceleration is being treated as a fictitious force in this instance. By including the $mad$ term on the same side of the equation as the 'actual forces', you are treating it as a fictitious force, which is not what the solutions do. If you are keen on treating it as such (thus allowing you to include it on the left hand side of the moments equation), the fictitious force should actually oppose the direction of the force $F$, which would yield the same moment equation as the solutions show. In short: why would you include the $mad$ term on the same side of the equation as the other moments?

 

[Pipsqueakalchemist]

Oh I see, I think I understand now, well sort of. Good enough to get the right answer.

 

[Master1022]

Oh I see, I think I understand now, well sort of. Good enough to get the right answer.

It just comes down to the moments expression. When we take moments about an accelerating point, we need to include this extra acceleration of the centre of mass in the expression. It is a tricky concept and that is why we often try to take moments about the centre of mass, such that we can ignore this extra term. I would suggest reading up on rigid body dynamics and rotational dynamics for a deeper discussion on the topic.