Math behind tipping/toppling a column or vertical structure

[ewap98]

I want to know where to look for information relating to toppling. I have looked at stability of equilibrium but the real question is:

If say for arguments sake, there is a column 2m high and 1/4m wide - it would be easy, if we knew the weight of the column, to establish the force required from the left to push the column about its rotationary point on the right. However, If I were to place a support on the right of the column (perhaps 1/4m high and extended out to the ground) - what would be the minimum length the support would need to be in order that the column could not be toppled?

This may be a simple question I don't know!

Thank you for any help

 

[TVP45]

It could still be tipped over, just not as easily.

 

[ewap98]

surely eventually if the support projected far enough you wouldn't be able to tip it? But how far is "far enough"?

 

[Doc Al]

Adding a support (some kind of extension to the object, I presume) effectively widens the base of the object. If you know how to figure the force needed to topple the object without the added support, use the same method to figure the force needed with the support. (Assuming the object doesn't slide, you just need to overcome the torque due to its weight.)

But if you push hard enough, it's going topple, slide, or break. The best you can do is make it harder to topple.

 

[Andy Resnick]

You already have an idea, based on the way you worded the problem- you said you are pushing *relative to a rotation point*. That's the key- when you add a support, you are changing the moment arm that you apply. One answer to your question is that you are unable to topple the column when the moment arm you apply goes to zero.

As for the specifics, I don't know a simple formula. I imagine a decent statics textbook (or online resource) would have something. Look up "flagpole problem" for ideas.