15. Rotational Equilibrium

Center of Mass & Simple Balance

Multiple Choice
A 70 kg, 1.90 m man doing push-ups holds himself in place making 20° with the floor. His feet and arms are, respectively, 1.15 m below and 0.4 m above his center of mass. You may model him as a thin, long board, and assume his arms and feet are perpendicular to the floor. How much force does the floor apply to each of his hands? (Use g=10 m/s².)
Open Question
A uniform rod is 2.00 m long and has mass 1.80 kg. A 2.40-kg clamp is attached to the rod. How far should the center of gravity of the clamp be from the left-hand end of the rod in order for the center of gravity of the composite object to be 1.20 m from the left-hand end of the rod?
Open Question
The three masses shown in FIGURE EX12.15 are connected by massless, rigid rods.(a) Find the coordinates of the center of mass.
Open Question
The four masses shown in FIGURE EX12.13 are connected by massless, rigid rods. (a) Find the coordinates of the center of mass.
Open Question
Two balls are connected by a 150-cm-long massless rod. The center of mass is 35 cm from a 75 g ball on one end. What is the mass attached to the other end?
Open Question
A small 300 g ball and a small 600 g ball are connected by a 40-cm-long, 200 g rigid rod.a. How far is the center of mass from the 600 g ball?
Open Question
Your task in a science contest is to stack four identical uniform bricks, each of length L, so that the top brick is as far to the right as possible without the stack falling over. Is it possible, as FIGURE P12.60 shows, to stack the bricks such that no part of the top brick is over the table? Answer this question by determining the maximum possible value of d.
Open Question
(II) Three children are trying to balance on a seesaw, which includes a fulcrum rock acting as a pivot at the center, and a very light board 3.2 m long (Fig. 12–60). Two playmates are already on either end. Boy A has a mass of 45 kg, and boy B a mass of 35 kg. Where should girl C, whose mass is 25 kg, place herself so as to balance the seesaw?
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Open Question
(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. 12–65). The two scales read, respectively, 35.1 and 31.6 kg. What distance is the center of gravity of this person from the top of her head?
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Open Question
(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.
Open Question
(II) The center of gravity of a loaded truck depends on how the truck is packed. If it is 4.0 m high and 2.4 m wide, and its cg is 2.2 m above the ground, on how steep a slope can the truck be parked without tipping over (Fig. 12–77)?
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Open Question
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 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: 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.]
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Open Question
The forces acting on an 85,000-kg aircraft flying at constant velocity are shown in Fig. 12–108. The engine thrust, F_T = 5.0 x 10⁵ N, acts on a line 1.6 m below the cm. Determine the drag force F_D and the distance above the cm that it acts. Assume F→_D and F→_T are horizontal. ( F→_L is the “lift” force on the wing.)
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