Collapsible Building: Tall Walls vs Short Walls

[Eagle's Wings]

Homework Statement

which type of building is more likely to collapse, a building with tall walls or short walls.

Homework Equations

not sure,

The Attempt at a Solution

I know that this is a static equilibrium equation and common sense tells me that the taller the walls are, the more likely the building is to collapse but how do I show this using equations?

 

[berkeman]

which type of building is more likely to collapse, a building with tall walls or short walls. i know that this is a static equilibrium equation and common sense tells me that the taller the walls are, the more likely the building is to collapse but how do i show this using equations?

Hint -- write the equations for tipping over equal mass rectangular boxes with different heights (taller box means less surface area on the ground). Does that help?

 

[Eagle's Wings]

is that the center gravity equation?

 

[Eagle's Wings]

okay, that makes sense. thanks so much

 

[rezeew]

There are a few factors that can contribute to the likelihood of a building collapsing, such as the materials used, construction techniques, and external forces. However, in general, taller walls may be more likely to collapse than shorter walls due to the increased weight and height of the building.

One way to show this using equations is by considering the forces acting on the building. In a static equilibrium, the sum of all forces acting on the building must be equal to zero. This can be represented by the equation Fnet = 0, where Fnet is the net force acting on the building.

In the case of a building with tall walls, there may be a greater weight and height of the building, which can increase the force of gravity acting on the building (Fg). This can be represented by the equation Fg = mg, where m is the mass of the building and g is the acceleration due to gravity.

In contrast, a building with shorter walls may have a lower weight and height, resulting in a lower force of gravity acting on the building. This can be represented by Fg = mg, where m is the mass of the building and g is the acceleration due to gravity.

Additionally, taller walls may also experience greater lateral forces, such as wind or seismic forces, due to the increased surface area and height of the building. This can be represented by the equation Fl = ma, where Fl is the lateral force acting on the building, m is the mass of the building, and a is the acceleration due to the lateral force.

In summary, taller walls may experience greater forces, both vertical and lateral, which can increase the likelihood of the building collapsing. However, it is important to note that there are many other factors that can contribute to a building's stability and risk of collapse, and it is not solely determined by the height of the walls.