Calculate the torque about the potential pivot point

[MAins]

"A 50 story building is being planned. It is to be 200 m high with a base of 40 m by 70 m. Its total mass will be about 1.8^7 kg, and its weight therefore 1.8 x 10^8 N. Suppose a 200 km/h wind exerts a force of 950 N/m^2 over the 70 m wide face. Calculate the torque about the potential pivot point, the rear edge of the building (where F_E acts in) and determine whether the building will topple. Assume the total force of the wind acts at the midpoint of the building's face, and that the building is not anchored in bedrock."

Apparently the answer is
∑τ = F_A(1000 m) - mg(20 m) = -2.2x10^9 mN

but I have no idea how to derive this. Please explain!

 

[PhanthomJay]

"A 50 story building is being planned. It is to be 200 m high with a base of 40 m by 70 m. Its total mass will be about 1.8^7 kg, and its weight therefore 1.8 x 10^8 N. Suppose a 200 km/h wind exerts a force of 950 N/m^2 over the 70 m wide face. Calculate the torque about the potential pivot point, the rear edge of the building (where F_E acts in) and determine whether the building will topple. Assume the total force of the wind acts at the midpoint of the building's face, and that the building is not anchored in bedrock."

Apparently the answer is
∑τ = F_A(1000 m) do you mean F_A(100m)? - mg(20 m) = -2.2x10^9 mN

but I have no idea how to derive this. Please explain!

See above in red. If so, calculate the force of the wind (F_A) over the 200m X 70m face of ther building. What is the torque caused by the wind force about the rear edge of the 40 foot wide building? What is the torque of the building's weight about that edge? Which is greater? What does that imply?

 

[Moetasim]

As a scientist, it is important to first understand the given information and the physical principles involved before attempting to derive the solution. Let's break down the given information:

1. A 50 story building is being planned with a height of 200 m and a base of 40 m by 70 m. This means that the building is a rectangular prism with a height of 200 m, a length of 40 m, and a width of 70 m.

2. The total mass of the building is 1.8 x 10^7 kg, and its weight is therefore 1.8 x 10^8 N. This means that the building has a weight of 1.8 x 10^8 N acting downwards due to gravity.

3. A 200 km/h wind exerts a force of 950 N/m^2 over the 70 m wide face of the building. This means that the wind exerts a force of 950 N per square meter of the building's face.

4. The total force of the wind acts at the midpoint of the building's face. This means that the force of the wind is evenly distributed over the entire 70 m width of the building's face.

5. The building is not anchored in bedrock. This means that there is no external force acting to keep the building in place.

Now, let's use the principle of torque to calculate the torque about the potential pivot point, which is the rear edge of the building. Torque is defined as the product of a force and its lever arm, or the perpendicular distance from the pivot point to the line of action of the force. In this case, the pivot point is the rear edge of the building, the force is the wind force, and the lever arm is the distance from the pivot point to the midpoint of the building's face.

We can calculate the torque about the potential pivot point as follows:

∑τ = F x r

Where:
∑τ = total torque
F = force
r = lever arm

In this case, the force (F) is the wind force, which is 950 N/m^2. The lever arm (r) is half of the width of the building's face, or 35 m.

∑τ = (950 N/m^2) x (35 m) = 33,250 Nm

However, this calculation only gives us the torque about the midpoint of