Why can’t you put your heels firmly against a wall and then bend over without falling?

(II) A uniform steel beam has a mass of 940 kg. On it is resting half of an identical beam, as shown in Fig. 9-60. What is the vertical support force at each end? •M •M

A ground retaining wall is shown in Fig. 9–36a. The ground, particularly when wet, can exert a significant force F on the wall. (a) What force produces the torque to keep the wall upright? (b) Explain why the retaining wall in Fig. 9–36b would be much less likely to overturn than that in Fig. 9–36a. -F (a) (b) FIGURE 9-36 Question 5.

(I) A tower crane (Fig. 9–48a) must always be carefully balanced so that there is no net torque tending to tip it. A particular crane at a building site is about to lift a 2800-kg air-conditioning unit. The crane's dimensions are shown in Fig. 9-48b. (a) Where must the crane's 9500-kg counterweight be placed when the load is lifted from the ground? (The counterweight is usually moved auto- matically via sensors and motors to precisely compensate for the load.) (b) Determine the maximum load that can be lifted with this counterweight when it is placed at its full extent. Ignore the mass of the beam. (a) Counterweight M = 9500 kg +3.4 m- 7.7 m m = 2800 kg FIGURE 9-48 (b) Problem 3.

(II) The subterranean tension ring that exerts the balancing horizontal force on the abutments for the dome in Fig. 9–34 is 36-sided, so each segment makes a 10° angle with the adjacent one (Fig. 9–77). 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 9–13). -F 5° 5° FIGURE 9-77 420,000 N Problem 58. Buttress

(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.

(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) The Achilles tendon is attached to the rear of the foot as shown in Fig. 9–73. When a person elevates himself just barely off the floor on the “ball of one foot," estimate the tension Fr in the Achilles tendon (pulling upward), and the (downward) force Fg exerted by the lower leg bone on the foot. Assume the person has a mass of 72 kg and D is twice as long as d. - Leg bone Achilles tendon Ball of foot (pivot point) FB FIGURE 9–73 Problem 36.

FB (I) Three forces are applied to a tree sapling, as shown in Fig. 9–46, to stabilize it. If FA = 385 N and FB = 475 N, find Fc in magnitude 105° and direction. FA FIGURE 9–46 Éc. Problem 1.