Skip to main content
Ch. 12 - Static Equilibrium; Elasticity and Fracture
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 12 - Static Equilibrium; Elasticity and FractureProblem 62
Chapter 12, Problem 62

A 50-story building is being planned. It is to be 180.0 m high with a base 46.0 m by 76.0 m. Its total mass will be about 1.8 x 10⁷ kg, and its weight therefore about 1.8 x 10⁸ N. Suppose a 200-km/h wind exerts a force of 950N/m² over the 76.0-m-wide face (Fig. 12–86). Calculate the torque about the potential pivot point, the rear edge of the building (where FE→\(\overrightarrow{F_{E}\)} acts in Fig. 12–86), 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. [Hint: FE→\(\overrightarrow{F_{E}\)} in Fig. 12–86 represents the force that the Earth would exert on the building in the case where the building would just begin to tip.]
Diagram of a 50-story building showing forces acting on it, including weight, wind force, and center of gravity.

Verified step by step guidance
1
Determine the force exerted by the wind on the building. The force is given by the pressure exerted by the wind multiplied by the area of the face of the building. Use the formula: F=pA, where p is the pressure (950 N/m²) and A is the area of the face (76.0 m × 180.0 m).
Calculate the torque due to the wind force about the rear edge of the building. The torque is given by the formula: τ=Fd, where F is the total force exerted by the wind and d is the perpendicular distance from the pivot point to the line of action of the force. Since the force acts at the midpoint of the face, d is half the height of the building (180.0 m / 2).
Determine the torque due to the building's weight about the rear edge. The weight acts at the center of mass of the building, which is at the geometric center of the base. The perpendicular distance from the pivot point to the line of action of the weight is half the width of the base (46.0 m / 2). Use the formula: τ=Wd, where W is the weight of the building (1.8 × 10⁸ N).
Compare the torques. If the torque due to the wind force is greater than the torque due to the building's weight, the building will topple. Otherwise, it will remain stable. Use the inequality: τwind>τweight to determine the stability.
Conclude whether the building will topple or remain stable based on the comparison of the torques. If the building is stable, explain that the torque due to the weight provides sufficient counterbalance to the torque due to the wind force. If it topples, explain that the wind force creates a torque that exceeds the stabilizing torque from the building's weight.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
6m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Torque

Torque is a measure of the rotational force applied to an object, calculated as the product of the force and the distance from the pivot point to the line of action of the force. In this scenario, the torque generated by the wind force acting on the building's face will determine whether the building will rotate about its rear edge. The formula for torque (τ) is τ = r × F, where r is the distance from the pivot to the point of force application, and F is the force applied.
Recommended video:
Guided course
08:55
Net Torque & Sign of Torque

Center of Mass

The center of mass of an object is the point at which its mass is evenly distributed in all directions. For a building, the center of mass is crucial in determining stability; if the center of mass is above the pivot point when a torque is applied, the building may topple. In this case, the wind force acts at the midpoint of the building's face, which is essential for calculating the torque and assessing the risk of toppling.
Recommended video:
Guided course
06:30
Intro to Center of Mass

Equilibrium and Stability

Equilibrium refers to a state where the sum of forces and torques acting on an object is zero, meaning the object is in a stable position. For the building to remain upright, the torque due to the wind must not exceed the torque due to the weight of the building acting through its center of mass. Analyzing the conditions for equilibrium helps determine whether the building will remain stable or topple under the influence of external forces like wind.
Recommended video:
Guided course
10:13
Torque & Equilibrium
Related Practice
Textbook Question

A pole projects horizontally from the front wall of a shop. A 6.1-kg sign hangs from the pole at a point 2.2 m from the wall (Fig. 12–88). If the pole is not to fall off, there must be another torque exerted to balance it. What exerts this torque? Use a diagram to show how this torque must act.

10
views
Textbook Question

A steel cable is to support an elevator whose total (loaded) mass is not to exceed 3100 kg. If the maximum acceleration of the elevator is 1.8 m/s² , calculate the diameter of cable required. Assume a safety factor of 8.0.

Textbook Question

The subterranean tension ring that surrounds the dome in Fig. 12–39 exerts the balancing horizontal force on the abutments for the dome and is 36-sided, so each segment makes a 10° angle with the adjacent one (Fig. 12–83). Calculate the tension F that must exist in each segment so that the required force of 4.2 x 10⁵ N can be exerted at each corner (Example 12–14).

1
views
Textbook Question

A heavy load Mg = 62.0 kN hangs at point E of the single cantilever truss shown in Fig. 12–81. Use a torque equation for the truss as a whole to determine the tension FT in the support cable, and then determine the force FA→\(\overrightarrow{F_{A}\)} on the truss at pin A. Neglect the weight of the trusses, which is small compared to the load.

Textbook Question

A pole projects horizontally from the front wall of a shop. A 6.1-kg sign hangs from the pole at a point 2.2 m from the wall (Fig. 12–88). Discuss whether compression, tension, and/or shear play a role in part (b).

1
views
Textbook Question

A pole projects horizontally from the front wall of a shop. A 6.1-kg sign hangs from the pole at a point 2.2 m from the wall (Fig. 12–88). What is the torque due to this sign calculated about the point where the pole meets the wall?

1
views