A problem in rigid bodies equillibrium

[ehabmozart]

Homework Statement

The platform assembly has weight W1 and center of gravity at G1. If it is intended to support a
maximum load W2 placed at point G2,,determine the smallest counterweight W that should be
placed at B in order to prevent the platform from tipping over.

Homework Equations

Equilibrium of rigid bodies

The Attempt at a Solution

Well, the steps are quite easy only if the FBD is drawn correctly... First of all, in the solution given in the second thumbnail, the counterweight points downwards.. Why is it so?? Isn't it COUNTER weight so it points upwards... Anyway, I let it go... Secondly and most importantly, in the solution's approach they equated the moment about D to be 0... As far as I know the 'correct' equation should be

-W₂.f + W₁.c + W_B.(b+c) +N_c.(a+b+c)= 0 ... However, in the book they omit the last part on the left side which is ignoring the normal at C as if it doesn't create any moment about D... Can someone explain this??

Thanks to whoever gives me a kind hand!

 

[SteamKing]

The problem with your image is it's only a thumbnail. Do you have a larger version which can actually be seen?

 

[ehabmozart]

The problem with your image is it's only a thumbnail. Do you have a larger version which can actually be seen?

I have uploaded a larger and better picture.. Thanks for noting!

 

[SteamKing]

Well, the steps are quite easy only if the FBD is drawn correctly... First of all, in the solution given in the second thumbnail, the counterweight points downwards.. Why is it so?? Isn't it COUNTER weight so it points upwards...

It's called a 'counter weight' not because it defies the law of gravity, but because it serves to counter the tipping action which the platform would undergo if this weight were not present. It's a weight (it has mass) just like the weight of the platform, so its direction is pointing toward the center of the earth.

Anyway, I let it go... Secondly and most importantly, in the solution's approach they equated the moment about D to be 0...

Since the platform is in equilibrium, the moment about D (or any other point) must be zero.
Similarly, the sum of all the forces acting on the platform must be zero as well.

As far as I know the 'correct' equation should be

-W₂.f + W₁.c + W_B.(b+c) +N_c.(a+b+c)= 0 ... However, in the book they omit the last part on the left side which is ignoring the normal at C as if it doesn't create any moment about D... Can someone explain this??

The problem is asking you to find the minimum amount of weight to put at point B which would keep the platform from tipping over. Clearly, if there is insufficient weight at point B, then the reaction force at point C must be directed downward to keep the platform in equilibrium, in order to counteract the moment caused by the man in the bucket wanting to tip over the platform. By calculating the value of the counterweight at B which gives a zero reaction at point C, then the minimum value of the weight has been determined. If more than this amount of weight is placed at point B, then a positive reaction at point C would develop in order to keep the platform in equilibrium.