Figure 12.1  A single force F acts on a rigid object at the point P. Fig. 12.1, p.363

Figure 12.2  Two forces of equal magnitude are applied at equal distances from the center of mass of a rigid object. Fig. 12.2, p.364

Figure 12. 3 Three forces act on an object Figure 12.3 Three forces act on an object. Notice that the lines of action of all three forces pass through a common point. Fig. 12.3, p.364

Figure 12.4  Construction showing that if the net torque is zero about origin O, it is also zero about any other origin, such as O’. Fig. 12.4, p.365

Figure 12.5  An object can be divided into many small particles each having a specific mass and specific coordinates. These particles can be used to locate the center of mass. Fig. 12.5, p.365

Figure 12.6  The center of gravity of an object is located at the center of mass if g is constant over the object. Fig. 12.6, p.365

Figure 12.7 This one-bottle wine holder is a surprising display of static equilibrium. The center of gravity of the system (bottle plus holder) is directly over the support point. (Charles D. Winters) Fig. 12.7, p.366

Figure 12.8 A balanced system. Fig. 12.8, p.367

Figure 12.9  (a) The biceps muscle pulls upward with a force F that is essentially at a right angle to the forearm. Fig. 12.9a, p.368

Figure 12.9  (b) The mechanical model for the system described in part (a). Fig. 12.9b, p.368

Figure 12. 10 (a) A uniform beam supported by a cable Figure 12.10  (a) A uniform beam supported by a cable. A person walks outward on the beam. Fig. 12.10a, p.369

Figure 12. 10 (b) The free-body diagram for the beam Figure 12.10   (b) The free-body diagram for the beam. (c) The free-body diagram for the beam showing the components of R and T. Fig. 12.10bc, p.369

Figure 12.10  (b) The free-body diagram for the beam. Fig. 12.10b, p.369

Figure 12.10   (c) The free-body diagram for the beam showing the components of R and T. Fig. 12.10c, p.369

Figure 12.11 (a) A uniform ladder at rest, leaning against a smooth wall. The ground is rough. (b) The free-body diagram for the ladder. (c) A person of mass M begins to climb the ladder when it is at the minimum angle found in part (a) of the example. Will the ladder slip? Fig. 12.11ab, p.370

Figure 12.11 (a) A uniform ladder at rest, leaning against a smooth wall. The ground is rough. Fig. 12.11a, p.370

Figure 12.11 (b) The free-body diagram for the ladder. Fig. 12.11b, p.370

Figure 12.11 (c) A person of mass M begins to climb the ladder when it is at the minimum angle found in part (a) of the example. Will the ladder slip? Fig. 12.11c, p.370

Figure 12.12  (a) A wheelchair and person of total weight mg being raised over a curb by a force F. Fig. 12.12a, p.371

Figure 12. 12 (b) Details of the wheel and curb Figure 12.12  (b) Details of the wheel and curb. (c) The free-body diagram for the wheel when it is just about to be raised. Three forces act on the wheel at this instant: F, which is exerted by the hand; R, which is exerted by the curb; and the gravitational force mg. (d) The vector sum of the three external forces acting on the wheel is zero. Fig. 12.12bcd, p.371

Figure 12.12  (b) Details of the wheel and curb. Fig. 12.12b, p.371

Figure 12.12  (c) The free-body diagram for the wheel when it is just about to be raised. Three forces act on the wheel at this instant: F, which is exerted by the hand; R, which is exerted by the curb; and the gravitational force mg. (d) The vector sum of the three external forces acting on the wheel is zero. Fig. 12.12c, p.371

Figure 12.12  (d) The vector sum of the three external forces acting on the wheel is zero. Fig. 12.12d, p.371

Figure 12. 13 (a) Truss structure for a bridge Figure 12.13  (a) Truss structure for a bridge. (b) The forces acting on the pins at points A, B, C, and E. Force vectors are not to scale. Fig. 12.13, p.372

Figure 12.13  (a) Truss structure for a bridge. Fig. 12.13a, p.372

Figure 12.13  (b) The forces acting on the pins at points A, B, C, and E. Force vectors are not to scale. Fig. 12.13b, p.372

Active Figure 12.14 A long bar clamped at one end is stretched by an amount ∆L under the action of a force F. At the Active Figures link at http://www.pse6.com, you can adjust the values of the applied force and Young’s modulus to observe the change in length of the bar. Fig. 12.14, p.373

Figure 12.15  Stress-versus-strain curve for an elastic solid. Fig. 12.15, p.374

Active Figure 12.16   (a) A shear deformation in which a rectangular block is distorted by two forces of equal magnitude but opposite directions applied to two parallel faces. (b) A book under shear stress. At the Active Figures link at http://www.pse6.com, you can adjust the values of the applied force and the shear modulus to observe the change in shape of the block in part (a). Fig. 12.16, p.374

Active Figure 12.16   (a) A shear deformation in which a rectangular block is distorted by two forces of equal magnitude but opposite directions applied to two parallel faces. Fig. 12.16a, p.374

Fig. 12.16b, p.374 Active Figure 12.16 (b) A book under shear stress. At the Active Figures link at http://www.pse6.com, you can adjust the values of the applied force and the shear modulus to observe the change in shape of the block in part (a). Fig. 12.16b, p.374

Table 12.1, p.374

Active Figure 12.17  When a solid is under uniform pressure, it undergoes a change in volume but no change in shape. This cube is compressed on all sides by forces normal to its six faces. At the Active Figures link at http://www.pse6.com, you can adjust the values of the applied force and the bulk modulus to observe the change in volume of the cube. Fig. 12.17, p.375

Figure 12.18   (a) A concrete slab with no reinforcement tends to crack under a heavy load. (b) The strength of the concrete is increased by using steel reinforcement rods. (c) The concrete is further strengthened by prestressing it with steel rods under tension. Fig. 12.18, p.376

Fig. P12.1, p.378

Fig. P12.2, p.378

Fig. P12.3, p.378

Fig. P12.4, p.378

Fig. P12.5, p.378

Fig. P12.6, p.378

Fig. P12.8, p.379

Fig. P12.9, p.379

Fig. P12.10, p.379

Fig. P12.12, p.379

Fig. P12.15, p.380

Fig. P12.19, p.380

Fig. P12.20, p.380

Fig. P12.22, p.381

Fig. P12.23, p.381

Fig. P12.24, p.381

Fig. P12.25, p.381

Fig. P12.38, p.382

Fig. P12.39, p.382

Fig. P12.42, p.383

Fig. P12.43, p.383

Fig. P12.44, p.383

Fig. P12.45, p.383

Fig. P12.46, p.383

Fig. P12.47, p.384

Fig. P12.49, p.384

Fig. P12.50, p.384

Fig. P12.51, p.384

Fig. P12.52, p.385

Fig. P12.53, p.385

Fig. P12.55, p.385

Fig. P12.56, p.385

Fig. P12.57, p.385

Fig. P12.59, p.386

Fig. P12.60, p.386

Fig. P12.62, p.386

Fig. P12.63, p.386

Fig. P12.68, p.387

Fig. P12.69, p.387

Fig. P12.71, p.387

Fig. P12.73, p.387