# Toppling force calculation

by BertSmurf
Tags: calculation, force, toppling
 P: 8 I am attempting to design a base to support a post that will be pulled horizontally at its top. A 2D image of the post will be a simple inverted "T" The top of the post will be pulled horizontally by a force of approximatly 900N What I need to do is design a suitable base for this post that will prevent it from toppling (suitable weight and dimension) I am a little confused on the mathematics that govern the force required to topple something like this. A moment balance about the point around which the post will topple (the edge of the base) seems to imply that the problem is independent of the COG (since the prependicular distance wont change as COG is in the middle) and this cant be right. Can some one please shed some light on this?
HW Helper
Thanks
P: 26,148
Hi BertSmurf! Welcome to PF!
 Quote by BertSmurf A moment balance about the point around which the post will topple (the edge of the base) seems to imply that the problem is independent of the COG (since the prependicular distance wont change as COG is in the middle) and this cant be right.
No, it is right …

for a fixed mass, the height of the centre of mass will not affect the force needed to start it toppling.

(but obviously, once it moves, the higher the centre of mass, the easier it becomes )
 Sci Advisor HW Helper PF Gold P: 6,050 The line of action of the posts weight thru its com is perpendicular to the pivot at the edge of the base. The wider the base, the harder it is to topple.
 P: 8 Toppling force calculation Thanks for the help guys. Now that I look at it, it seems obvious enough! :)
 P: 8 Ok, I seem to have stumbled upon a bit of a contradiction here. I took moments the centre of the base as the post was just about to tip over (so the line of action was directly above the point over which the whole post assembley would rotate). The forces acting on the post are the weight of the post (W) acting down at the centre of gravity (a distance HCOG from the base) and a horizontal force (F) is acting at the top of the post (a height Hpost from the base). The post is at an angle λ to the ground. (my assumed x and y planes are at this same inclination for simlicity of calculations) The inclined x component of the Weight of the Post is Wsinλ*HCOG The inclined x component of the applied force is Fcosλ*Hpost Summing these moments gives the equation Wsinλ*HCOG+Fcosλ*Hpost=0 Resolving for F gives: F=-Wsinλ*HCOG/Fcosλ*Hpost Looking at this equation means that as the COG is higher, the required force increases and vice versa. This is surely wrong.... Can someone please point me in the right direction, I am making a wrong assumtion somewhere but cant figure it out.