Examining Forces in a Symmetric Building

[iamwilson]

Homework Statement

A symmetric building has a roof sloping upward at 34.0 degrees above the horizontal on each side.

A)If each side of the uniform roof weighs 1.10×10^4N , find the horizontal force that this roof exerts at the top of the wall, which tends to push out the walls.

B)Which type of building would be more in danger of collapsing: one with tall walls or one with short walls? Explain

Homework Equations

The Attempt at a Solution

I tried to break the forces into x and y components, x is horizontal so i thought that is the horizontal force.
I also tried use sum of the torque equals zero, but i don't know how to set it up
can someone give me some clues. thanks. It's due tomorrow!

 

[qspeechc]

All I can think of is taller walls having higher centres of mass, therefore would topple more easily.

 

[Moetasim]

I would first commend you for attempting to solve the problem on your own and seeking help when needed. It shows your dedication and critical thinking skills. Now, let's break down the problem and see how we can approach it.

A) The first thing to note is that the roof is symmetric, meaning that it has the same angle and weight on both sides. This means that the horizontal force exerted on each side of the wall will also be the same. To find the horizontal force, we can use the formula F = mg, where F is the force, m is the mass, and g is the acceleration due to gravity. In this case, the mass is given as 1.10x10^4N on each side, and g is a constant of 9.8 m/s^2. Therefore, the horizontal force exerted on each side of the wall is 1.10x10^4N x 9.8 m/s^2 = 1.078x10^5 N.

B) Now, let's consider which type of building would be more in danger of collapsing: one with tall walls or one with short walls. To answer this, we need to understand the forces acting on the building. The walls of a building are designed to withstand both vertical and horizontal forces. In this case, the horizontal force exerted by the roof tends to push out the walls. Therefore, a building with tall walls will be more in danger of collapsing as it will experience a greater horizontal force due to its larger surface area. This is because the force exerted by the roof is directly proportional to the mass of the roof, and a taller wall will have more surface area for the roof to push against. Additionally, taller walls are also more susceptible to wind and other external forces, making them more likely to collapse.

In conclusion, the horizontal force exerted by the roof on each side of the wall is 1.078x10^5 N, and a building with tall walls is more in danger of collapsing due to the larger surface area for the roof to push against. I hope this helps!