why are taller towers of blocks easier to topple?



I was building blocks with my daughter, and as the tower got higher, it became much more volatile. Why does this happen?

In: Physics

As you add more and more layers of blocks, minor misalignments stack up until the center of mass is unsupported, causing the blocks to fall down.

For something to tip over, its center of gravity needs to be moved over its footprint. Basically you need to apply a force to it to tip it a certain number of degrees.

As it gets taller, the principles of torque means that it is easier to push (less force required) and the principles of trigonometry mean that the number of degrees needed before its center of gravity is over its footprint is reduced.

It’s to do with the principle of moments and leverage.

If you imagine the entire tower being a lever, with the pivot point (centre of rotation) of the tower being the very bottom edge, the greater the perpendicular distance from the line of the action of the force on the tower to the pivot, the weaker the force of the pivot needed for the centre of mass to pass over the pivot. (Moment = Fd, F=force d=perpendicular distance from pivot to force).

Essentially in order to have the same moment, you can have a lot of force on a short lever, or a long lever with little force; which is how wrenches work.

Once the centre of mass is beyond the pivot, i.e. there is no supporting force on the centre of mass, gravity does the rest in the collapse.