Dynamics homework — Does this cabinet sliding on the floor tip over?

[Pipsqueakalchemist]

Homework Statement

I have the solutions and questions below

Relevant Equations

Sum of moment = (Moment of inertia)*(angular velocity)

So for this question, 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.

 

[Pipsqueakalchemist]

I understand part A just not part B

 

[Lnewqban]

About the pivot point B, you have the positive moment of 100 N times maximum h plus the negative moment of 0.3 m times weight.
Both moments should be in balance just before the cabinet starts to tip over.

 

[Pipsqueakalchemist]

What I’m confused about is the sign of the mad term. The solution has it such that the mad causes a negative moment when you move the mad term to the left side of the equation. Shouldn’t it the mad term cause a positive moment about point B?

 

[Lnewqban]

I may be wrong, but I believe that there should not be a mad term in that equation.
The horizontal net force (100 N - friction force) is the cause, while acceleration a is the effect.
Remove the 100 N force, and acceleration inmediately becomes negative (for the case of μ=0.25) or zero (for the case μ=0).

There is horizontal acceleration, but there is no angular acceleration while height h has not reached its critical value to make the cabinet tip over.

As the point of application of the 100 N force gets higher, the value of the horizontal net force that induces the horizontal acceleration remains the same.
Nevertheless, the positive moment induced by the 100 N force gradually increases until reaching the value of the negative moment induced by the weight of the cabinet which until that moment had kept some force on legs A because it had been greater than the positive moment.

Please, see:
http://mechanicsmap.psu.edu/websites/6_friction/slipping_vs_tipping/pdf/TippingVsSlipping_WorkedExample2.pdf

At the impending tipping moment, there is no more force on legs A while each leg B supports half of the cabinet's weight, and both moments about B cancel each other.

 

[Master1022]

Hi,

I have responded on the other/new post of this question. Is this question different from the new thread? (seems like the same one, but maybe I am missing something)

 

[Pipsqueakalchemist]

It’s the same one, I just reposted it