Slab resting on two supports: Maximum weight added without tipping?

[tjosan]

Homework Statement

A slab is placed on two supports. At one edge, a weight is added. How large can the weight be before the slab tips over? The slab weighs 300 kg, and the density is constant. See image for attempted solution and a drawing of the slab.

Relevant Equations

F_1*d_1=F_2*d_2

Hi,

My attempted solution is in the image:

I choose the edge on the left side, but the solution should be similar on both sides (just substitute C for A).

(I missed to multiply by "g" in F_2.)

Is this the correct way of thinking? I'm not sure about the distance "D".

 

[BvU]

Hello,

I can't follow what you do on the left side:
On the right side you calculate a moment (not a force, so the use of the symbol F is misleading) W_B * g * B/2

If I work out your expression for F₁ I get W_A * g * A + W₁ * g * A/2
and it should be the other way around...

 

[tjosan]

Hello,

I can't follow what you do on the left side:
On the right side you calculate a moment (not a force, so the use of the symbol F is misleading) W_B * g * B/2

If I work out your expression for F₁ I get W_A * g * A + W₁ * g * A/2
and it should be the other way around...

Thank you.

Yeah, made a mistake and wrote it as a force.

Are you saying it should be:
W_A * g * A/2 + W₁ * g * A ?

What I did on the left side, or what I tried to do, was to add the extra lever distance resulting from the weight W1, by calcuting the ratio of W1 to W1+WA and adding it to A/2 - if this makes any sense?

 

[BvU]

I suppose it makes sense but was processed erroneously.

Anyway, you should work with the sum of moments without having to fall back to shifting lever distances ! Much less error-prone

 

[tjosan]

Would it requie more or less weight if W1 was placed on the corner of the slab? Is it dependent on the width?

 

[BvU]

For the direction we did the analysis in it makes no difference. For a direction into the paper we have no information