A 50-story building is being planned. It is to be 200.0 high with a base 48.0 by 66.0 . Its total mass will be about 2.5×107 , and its weight therefore about 2.5×108 . Suppose a 200 wind exerts a force of 860 over the 66.0 wide face .
Part A
Calculate the magnitude of the torque about the potential pivot point, the rear edge of the building (where acts in the figure). 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.
To calculate the magnitude of the torque, we need to first understand the concept of torque and how it is calculated.
Torque is the measure of the turning force around an axis or pivot point. It is calculated as the product of the force applied and the perpendicular distance from the axis of rotation to the line of action of the force.
In this case, the wind is exerting a force of 860 N over the 66.0 m wide face of the building. We assume that the wind force acts at the midpoint of the face.
To calculate the torque, we need to determine the perpendicular distance between the pivot point and the line of action of the force. Since the pivot point is the rear edge of the building, which has a width of 48.0 m, the distance between the pivot and the midpoint of the face is half of the width, i.e., 24.0 m.
Now, we can calculate the torque using the formula:
Torque = Force × Distance
Torque = 860 N × 24.0 m
Torque = 20640 N⋅m
Therefore, the magnitude of the torque about the potential pivot point, the rear edge of the building, is 20640 N⋅m.