00:01
Our question says that pancake collapse of a tall building happens in sections shown in figure 9 -71a.
00:08
The infrastructure of any given floor k must be supported by weight w of all higher floors.
00:14
Normally, the infrastructure is constructed with safety factor s so that it can be standing, withstanding this even greater downward force of sw.
00:24
If, however, the support columns between k and l suddenly collapse and allow the higher floors to free fall together, the force in the collapse can be exerted sw and after a brief pause caused k to collapse on the floor j, which will collapse on the floor i and so on until the ground is reached.
00:40
Assuming that the floors are separated by a distance of d equal 4 .0 meters and have the same mass, also assume that the floor is k free fall onto k, and the collision lasts 1 .5 milliseconds under these simplified conditions.
00:56
What value must the safety factor s exceed to prevent the pancake collapse of the okay, so we're going to solve for that.
01:04
But we're going to let m be the mass of the higher floors.
01:07
So by conservation of energy, the speed of the higher floors just before the impact can be given from the following.
01:14
So we have the mass times gravity times the distance is equal to one half mv squared.
01:26
The m is cancel.
01:27
Solve for v...