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Problems12 - Chapter 12 Problems 1 2 3 = straightforward...

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Chapter 12 Problems 1,  2 3   = straightforward, intermediate,  challenging Section   12.1 The Conditions for Equilibrium  of a Rigid Body 1. A baseball player holds a 36-oz bat  (weight = 10.0 N) with one hand at the point  (Fig. P12.1). The bat is in equilibrium. The  weight of the bat acts along a line 60.0 cm to the  right of  O . Determine the force and the torque  exerted by the player on the bat around an axis  through  O Figure P12.1 2. Write the necessary conditions for  equilibrium of the object shown in Figure P12.2.  Take the origin of the torque equation at the  point  O. Figure P12.2 3. A uniform beam of mass  m b   and length   supports blocks with masses  m 1  and  m 2  at two  positions, as in Figure P12.3. The beam rests on  two knife edges. For what value of  will the  beam be balanced at  P  such that the normal  force at  O  is zero? Figure P12.3 Section 12.2  More on the Center of Gravity Problems 38, 39, 41, 43, and 44 in Chapter 9  can also be assigned with this section.
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4. A circular pizza of radius  R  has a  circular piece of radius  R /2 removed from one  side as shown in Figure P12.4. The center of  gravity has moved from  C  to  C ’ along the  axis.  Show that the distance from  C  to  C ’ is  R /6.  Assume the thickness and density of the  pizza are uniform throughout. Figure P12.4 5. A carpenter's square has the shape of an  L, as in Figure 12.5. Locate its center of gravity.  Figure P12.5 6. Pat builds a track for his model car out  of wood, as in Figure P12.6. The track is 5.00  cm wide, 1.00 m high and 3.00 m long and is  solid.  The runway is cut such that it forms a  parabola with the equation  y =  ( x  – 3) 2 /9 . Locate the horizontal coordinate  of the center of gravity of this track. Figure P12.6 7. Consider the following mass  distribution: 5.00 kg at (0, 0) m, 3.00 kg at  (0, 4.00) m, and 4.00 kg at (3.00, 0) m.  Where  should a fourth object of mass  8.00 kg be placed so that the center of gravity of  the four-object arrangement will be at (0, 0)? 8. Figure P12.8 shows three uniform  objects: a rod, a right triangle, and a square.  Their masses and their coordinates in meters are  given.  Determine the center of gravity for the  three-object system.
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Figure P12.8   Section 12.3 Examples of Rigid Objects in  Static Equilibrium Problems 17, 18, 19, 20, 21, 27, 40, 46, 57,  59, and 73 in Chapter 5 can also be assigned  with this section.
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