A 2.0-m-high box with a 1.0-m-square base is moved across a rough floor as in Fig. 9–89. The uniform box weighs 250N and has a coefficient of static friction with the floor of 0.60. What minimum force must be 1.0 m exerted on the box to make it slide? What is the maximum height h above the floor that this force can be applied without tip- ping the box over? Note that as the box tips, the normal force CG 2.0 m FN and the friction force will act at the lowest corner. Fir FIGURE 9-89 Problem 74.

(III) A uniform ladder of mass m and length l leans at an angle 0 against a frictionless wall, Fig. 9–70. If the coefficient of static friction between the ladder and the ground is µs, determine a formula for the minimum angle at which the ladder will not slip. FIGURE 9-70 Problem 30.

(II) Figure 9–50 shows a pair of forceps used to hold a thin plastic rod firmly. If the thumb and finger each squeeze with a force Fr = FF = 11.0 N, what force do the forceps jaws exert on the plastic rod? Jaws Rod Fr P FIGURE 9-50 8.50 cm 2.70 cm Problem 6.

(II) A 172-cm-tall person lies on a light (massless) board which is supported by two scales, one under the top of her head and one beneath the bottom of her feet (Fig. 9–64). The two scales read, respectively, 35.1 and 31.6 kg. What distance is the center of gravity of this person from the bottom of her feet? 35.1 31.6 KILOGRAMS KILOGRAMS FIGURE 9-64 Problem 24.

(II) The Leaning Tower of Pisa is 55 m tall and about 7.7 m in radius. The top is 4.5 m off center. Is the tower in stable equilibrium? If so, how much farther can it lean before it becomes unstable? Assume the tower is of uniform composition.

A uniform meter stick with a mass of 180 g is supported horizontally by two vertical strings, one at the 0-cm mark and the other at the 90-cm mark (Fig. 9–82). What is the tension in the string (a) at 0 cm? (b) at 90 cm? ib 20 30 40 50 60 70 90 loo FIGURE 9-82 Problem 63.

In a mountain-climbing technique called the "Tyrolean tra- verse," a rope is anchored on both ends (to rocks or strong trees) across a deep chasm, and then a climber traverses the rope while attached by a sling as in Fig. 9–91. This technique generates tremendous forces in the rope and anchors, so a basic understanding of physics is crucial for safety. A typical climbing rope can undergo a tension force of perhaps 29 kN before breaking, and a “safety factor" of 10 is usually recom- mended. The length of rope used in the Tyrolean traverse must allow for some “sag" to remain in the recommended safety range. Consider a 75-kg climber at the center of a Tyrolean traverse, spanning a 25-m chasm. (a) To be within its recommended safety range, what minimum distance x must the rope sag? (b) If the Tyrolean traverse is set up incorrectly so that the rope sags by only one-fourth the distance found in (a), determine the tension in the rope. Ignore stretching of the rope. Will the rope break? 25 m…

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 10° N. Suppose a 200-km/h wind exerts a force of 950 N/m² over the 76.0-m-wide face (Fig. 9–80). Calculate the torque about the potential pivot point, the rear edge_ of the building (where Fp acts in Fig. 9–80), and determine whether the building will topple. Assume the total force of the wind acts at I口 the midpoint of the build- ing's face, and that the building is not anchored in bedrock. [Hint: Fe in Fig. 9-80 represents the force that the Earth would ... mg exert on the building in the case where the building would just begin to tip.] FIGURE 9-80 Forces on a building subjected to wind (FA), gravity (mg), and the force FE on the building due to the Earth if the building were just about to tip. Problem 61.

(II) Find the tension in the two cords shown in Fig. 9-45. Neglect the mass of the cords, and assume 9. that the angle 6 is 33° and the mass m is 170 kg. FIGURE 9-45 Problem 11.