ࡱ> |q }bjbjt+t+ )4AA2RP6].+.+.+B+B+B+B+8z+,, B+z-@>1"`1`1v1/111111$~rxU%.+{Uy`1v1|-yyyb`1.+v1/B+B+/yy/| .+/v1-L`PTB+B+/Chapter 7. Newtons Second Law Newtons Second Law 7-1. A 4-kg mass is acted on by a resultant force of (a) 4 N, (b) 8 N, and (c) 12 N. What are the resulting accelerations?  (a)  EMBED Equation  1 m/s2 (b)  EMBED Equation  2 m/s2 (c)  EMBED Equation  3 m/s2 7-2. A constant force of 20 N acts on a mass of (a) 2 kg, (b) 4 kg, and (c) 6 kg. What are the resulting accelerations?  (a)  EMBED Equation  10 m/s2 (b)  EMBED Equation  5 m/s2 (c)  EMBED Equation  3.33 m/s2 7-3. A constant force of 60 lb acts on each of three objects, producing accelerations of 4, 8, and 12 N. What are the masses?   EMBED Equation  15 slugs  EMBED Equation  7.5 slugs  EMBED Equation  5 slugs 7-4. What resultant force is necessary to give a 4-kg hammer an acceleration of 6 m/s2? F = ma = (4 kg)(6 m/s2); F = 24 N 7-5. It is determined that a resultant force of 60 N will give a wagon an acceleration of 10 m/s2. What force is required to give the wagon an acceleration of only 2 m/s2?  EMBED Equation ; F = ma = (6 slugs)(2 m/s2); F = 12 N 7-6. A 1000-kg car moving north at 100 km/h brakes to a stop in 50 m. What are the magnitude and direction of the force? Convert to SI units: 100 km/h = 27.8 m/s  EMBED Equation  F = ma = (1000 kg)(7.72 m/s2); F = 772 N, South. The Relationship Between Weight and Mass 7-7. What is the weight of a 4.8 kg mailbox? What is the mass of a 40-N tank? W = (4.8 kg)(9.8 m/s2) = 47.0 N ;  EMBED Equation = 4.08 kg 7-8. What is the mass of a 60-lb child? What is the weight of a 7-slug man?  EMBED Equation = 1.88 slugs ; W = (7 slugs)(32 ft/s2) = 224 lb  7-9. A woman weighs 180 lb on earth. When she walks on the moon, she weighs only 30 lb. What is the acceleration due to gravity on the moon and what is her mass on the moon? On the Earth? Her mass is the same on the moon as it is on the earth, so we first find the constant mass:   EMBED Equation  mm = me = 5.62 slugs ; Wm = mmgm  EMBED Equation ; gm = 5.33 ft/s2 7-10. What is the weight of a 70-kg astronaut on the surface of the earth. Compare the resultant force required to give him or her an acceleration of 4 m/s2 on the earth with the resultant force required to give the same acceleration in space where gravity is negligible? On earth: W = (70 kg)(9.8 m/s2) = 686 N ; FR = (70 kg)(4 m/s2) = 280 N Anywhere: FR = 280 N The mass doesnt change.  7-11. Find the mass and the weight of a body if a resultant force of 16 N will give it an acceleration of 5 m/s2.  EMBED Equation  = 3.20 kg ; W = (3.20 kg)(9.8 m/s2) = 31.4 N 7-12. Find the mass and weight of a body if a resultant force of 200 lb causes its speed to increase from 20 ft/s to 60 ft/s in a time of 5 s.  EMBED Equation = 25.0 slugs W = mg = (25.0 slugs)(32 ft/s2); W = 800 lb  7-13. Find the mass and weight of a body if a resultant force of 400 N causes it to decrease its velocity by 4 m/s in 3 s.  EMBED Equation ;  EMBED Equation  m = 300 kg W = mg = (300 kg)(9.8 m/s2); W = 2940 N Applications for Single-Body Problems: 7-14. What horizontal pull is required to drag a 6-kg sled with an acceleration of 4 m/s2 if a friction force of 20 N opposes the motion?  P 20 N = (6 kg)(4 m/s2); P = 44.0 N 7-15. A 2500-lb automobile is speeding at 55 mi/h. What resultant force is required to stop the car in 200 ft on a level road. What must be the coefficient of kinetic friction? We first find the mass and then the acceleration. (55 mi/h = 80.7 m/s)  EMBED Equation   EMBED Equation  F = ma = (78.1 slugs)(-16.3 ft/s2); F = -1270 lb  EMBED Equation.DSMT4  (k = 0.508 7-16. A 10-kg mass is lifted upward by a light cable. What is the tension in the cable if the acceleration is (a) zero, (b) 6 m/s2 upward, and (c) 6 m/s2 downward?  Note that up is positive and that W = (10 kg)(9.8 m/s2) = 98 N. (a) T  98 N = (10 kg)(0 m/s2) and T = 98 N (b) T  98 N = (10 kg)(6 m/s2) and T = 60 N + 98 N or T = 158 N (c) T  98 N = (10 kg)(-6 m/s2) and T = - 60 N + 98 N or T = 38.0 N 7-17. A 64-lb load hangs at the end of a rope. Find the acceleration of the load if the tension in the cable is (a) 64 lb, (b) 40 lb, and (c) 96 lb.  (a)  EMBED Equation.DSMT4 ; a = 0 (b)  EMBED Equation.DSMT4 ; a = -12.0 ft/s2 (b)  EMBED Equation.DSMT4 ; a = 16.0 ft/s2 7-18. An 800-kg elevator is lifted vertically by a strong rope. Find the acceleration of the elevator if the rope tension is (a) 9000 N, (b) 7840 N, and (c) 2000 N.  Newtons law for the problem is: T mg = ma (up is positive)  (a) 9000 N (800 kg)(9.8 m/s2) = (800 kg)a ; a = 1.45 m/s2  (a) 7840 N (800 kg)(9.8 m/s2) = (800 kg)a ; a = 0  (a) 2000 N (800 kg)(9.8 m/s2) = (800 kg)a ; a = -7.30 m/s2 7-19. A horizontal force of 100 N pulls an 8-kg cabinet across a level floor. Find the acceleration of the cabinet if (k = 0.2.  F = (kN = (k mg F = 0.2(8 kg)(9.8 m/s2) = 15.7 N 100 N  F = ma; 100 N  15.7 N = (8 kg) a; a = 10.5 m/s2 7-20. In Fig. 7-10, an unknown mass slides down the 300 inclined plane. What is the acceleration in the absence of friction?  SFx = max; mg sin 300 = ma ; a = g sin 300 a = (9.8 m/s2) sin 300 = 4.90 m/s2, down the plane  7-21. Assume that (k = 0.2 in Fig 7-10. What is the acceleration? Why did you not need to know the mass of the block? SFx = max; mg sin 300 - (kN = ma ; N = mg cos 300  mg sin 300 - (k mg cos 300 = ma ; a = g sin 300 - (k g cos 300 a = (9.8 m/s2)(0.5) 0.2(9.8 m/s2)(0.866); a = 3.20 m/s2, down the plane.  *7-22. Assume that m = I 0 kg and (k = 0. 3 in Fig. 7- 10. What push P directed up and along the incline in Fig.7-10 will produce an acceleration of 4 m/s2 also up the incline?  F = (kN = (kmg cos 300; F = 0.3(10 kg)(9.8 m/s2)cos 300 = 25.5 N  SFx = ma; P  F  mg sin 300 = ma  P  25.5 N  (10 kg)(9.8 m/s2)(0.5) = (10 kg)(4 m/s2) P  25.5 N  49.0 N = 40 N; P = 114 N  *7-23. What force P down the incline in Fig. 7-10 is required to cause the acceleration DOWN the plane to be 4 m/s2? Assume that in = IO kg and (k = 0. 3. See Prob. 7-22: F is up the plane now. P is down plane (+). SFx = ma; P - F + mg sin 300 = ma ; Still, F = 25.5 N  P - 25.5 N + (10 kg)(9.8 m/s2)(0.5) = (10 kg)(4 m/s2) P - 25.5 N + 49.0 N = 40 N; P = 16.5 N Applications for Multi-Body Problems 7-24. Assume zero friction in Fig. 7-11. What is the acceleration of the system? What is the tension T in the connecting cord?  Resultant force = total mass x acceleration  80 N = (2 kg + 6 kg)a; a = 10 m/s2  To find T, apply F = ma to 6-kg block only: 80 N T = (6 kg)(10 m/s2); T = 20 N  7-25. What force does block A exert on block B in Fig, 7-12?  SF = mTa; 45 N = (15 kg) a; a = 3 m/s2 Force ON B = mB a = (5 kg)(3 m/s2); F = 15 N  *7-26. What are the acceleration of the system and the tension in the connecting cord for the arrangement shown in Fig. 7-13? Assume zero friction and draw free-body diagrams. For total system: m2g = (m1 + m2)a (m1g is balanced by N)   EMBED Equation ; a = 5.88 m/s2 Now, to find T, consider only m1 SF = m1a T = m1a = (4 kg)(5.88 m/s2); T = 23.5 N  *7-27. If the coefficient of kinetic friction between the table and the 4 kg block is 0.2 in Fig. 7-13, what is the acceleration of the system. What is the tension in the cord?  SFy = 0; N = m1g; F = (kN = (km1g For total system: m2g - (km1g = (m1 + m2)a  EMBED Equation  *7-27. (Cont.)  EMBED Equation  or a = 5.10 m/s2 To find T, consider only m2 and make down positive:  SFy = m2a ; m2g  T = m2a; T = m2g  m2a T = (6 kg)(9.8 m/s2)  (6 kg)(5.10 m/s2); T = 28.2 N  *7-28. Assume that the masses m1 = 2 kg and m2 = 8 kg are connected by a cord that passes over a light frictionless pulley as in Fig. 7-14. What is the acceleration of the system and the tension in the cord? Resultant force = total mass of system x acceleration m2g m1g = (m1 + m2)a  EMBED Equation    EMBED Equation  a = 5.88 m/s2 Now look at m1 alone: T - m1g = m1 a; T = m1(g + a) = (2 kg)(9.8 m/s2  5.88 m/s2); T = 31.4 N  *7-29. The system described in Fig. 7-15 starts from rest. What is the acceleration assuming zero friction? (assume motion down plane) SFx = mT a; m1g sin 320  m2g = (m1 + m2) a (10 kg)(9.8 m/s2)sin 320  (2 kg)(9.8 m/s2) = (10 kg + 2 kg)a   EMBED Equation  a = 2.69 m/s2 *7-30. What is the acceleration in Fig. 7-15 as the 10-kg block moves down the plane against friction ((k = 0.2). Add friction force F up plane in figure for previous problem. m1g sin 320  m2g  F = (m1 + m2) a ; SFy = 0 ; N = m1g cos 320 *7-30. (Cont.) m1g sin 320  m2g  F = (m1 + m2) a ; F = (kN = (k m1g cos 320 m1g sin 320 m2g (k m1g cos 320 = (m1 + m2) a ; a = 1.31 m/s2  *7-31 What is the tension in the cord for Problem 7-30? Apply F = ma to mass m2 only: T m2g = m2 a; T = m2(g + a) = (2 kg)(9.8 m/s2 + 1.31 m/s2); T = 22.2 N Challenge Problems 7-32. A 2000-lb elevator is lifted vertically with an acceleration of 8 ft/s2. Find the minimum breaking strength of the cable pulling the elevator?  SFy = ma;  EMBED Equation  T  mg = ma; T = m(g + a); T = (62.5 slugs)(32 ft/s2 + 8 ft/s2); T = 2500 lb  7-33. A 200-lb worker stands on weighing scales in the elevator of Problem 7-32. What is the reading of the scales as he is lifted at 8 m/s?  The scale reading will be equal to the normal force N on worker. N mg = ma; N = m(g + a); T = (62.5 slugs)(32 ft/s2 + 8 ft/s2); T = 2500 lb  7-34. A 8-kg load is accelerated upward with a cord whose breaking strength is 200 N. What is the maximum acceleration?  Tmax mg = ma  EMBED Equation  a = 15.2 m/s2 7-35. For rubber tires on a concrete road (k = 0.7. What is the horizontal stopping distance for a 1600-kg truck traveling at 20 m/s? The stopping distance is determined by the acceleration from a resultant friction force F = (kN, where N = mg: F = -(kmg = ma; a = -(kg = - (0.7)(9.8 m/s2); a = -6.86m/s2 Recall that: 2as = vo2 - vf2;  EMBED Equation ; s = 29.2 km *7-36. Suppose the 4 and 6-kg masses in Fig. 7-13 are switched so that the larger mass is on the table. What would be the acceleration and tension in the cord neglecting friction? For total system: m2g = (m1 + m2); m1 = 6 kg; m2 = 4 kg   EMBED Equation ; a = 3.92 m/s2 SF = m1a T = m1a = (6 kg)(5.88 m/s2); T = 23.5 N  *7-37. Consider two masses A and B connected by a cord and hung over a single pulley. If mass A is twice that of mass B, what is the acceleration of the system?  mA = 2mB ; If the left mass B is m, the right mass A will be 2m.  2mg mg = (2m + m)a mg = 3ma   EMBED Equation  a = 3.27 m/s2 *7-38. A 5-kg mass rests on a 340 inclined plane where (k = 0.2. What push up the incline, will cause the block to accelerate at 4 m/s2? F = (kN = (kmg cos 340; F = 0.2(5 kg)(9.8 m/s2)cos 340 = 8.12 N  SFx = ma; P F mg sin 340 = ma P 8.12 N (5 kg)(9.8 m/s2) sin 340 = (5 kg)(4 m/s2) P = 47.4 N *7-39. A 96-lb block rests on a table where (k = 0.4. A cord tied to this block passes over a light frictionless pulley. What weight must be attached to the free end if the system is to accelerated at 4 ft/s2? F = (kN = 0.2 (96 lb); F = 19.2 lb   EMBED Equation.DSMT4  W 19.2 lb = 12 lb + 0.125 W; W = 35.7 lb Critical Thinking Questions 7-40. In a laboratory experiment, the acceleration of a small car is measured by the separation of spots burned at regular intervals in a paraffin-coated tape. Larger and larger weights are transferred from the car to a hanger at the end of a tape that passes over a light frictionless pulley. In this manner, the mass of the entire system is kept constant. Since the car moves on a horizontal air track with negligible friction, the resultant force is equal to the weights at the end of the tape. The following data are recorded: Weight, N24681012Acceleration, m/s21.42.94.15.67.18.4 Plot a graph of weight (force) versus acceleration. What is the significance of the slope of this curve? What is the mass? The slope is the change in Force over the change in acceleration, which is the mass of the system. Thus, the mass is found to be: m = 1.42 kg 7-41. In the above experiment, a student places a constant weight of 4 N at the free end of the tape. Several runs are made, increasing the mass of the car each time by adding weights. What happens to the acceleration as the mass of the system is increased? What should the value of the product of mass and acceleration be for each run? Is it necessary to include the mass of the constant 4 N weight in these experiments? The acceleration increases with increasing mass. According to Newtons second law, the product of the total mass of the system and the acceleration must always be equal to the resultant force of 4 N for each run. It is necessary to add the mass of the 4-N weight to each of the runs because it is part of the total mass of the system.  7-42. An arrangement similar to that described by Fig. 7-13 is set up except that the masses are replaced. What is the acceleration of the system if the suspended mass is three times that of the mass on the table and (k = 0.3. SFy = 0; N = mg; F = (kN = (kmg For total system: 3mg - (kmg = (3m + m)a ; (3 - (k)mg = 4 ma   EMBED Equation  a = 6.62 m/s2 7-43. Three masses, 2 kg, 4 kg, and 6 kg, are connected (in order) by strings and hung from the ceiling with another string so that the largest mass is in the lowest position. What is the tension in each cord? If they are then detached from the ceiling, what must be the tension in the top string in order that the system accelerate upward at 4 m/s2? In the latter case what are the tensions in the strings that connect masses? 7-43. (Cont.) The tension in each string is due only to the weights BELOW the string. Thus,  TC = (6 kg)(9.8 m/s2) = 58.8 N ; TB = (6 kg + 4 kg)(9.8 m/s2) = 98.0 N ;  TA = (6 kg + 4 kg + 2 kg)(9.8 m/s2) = 118 N  Now consider the upward acceleration of 4 m/s2. SFy = 0; TA = (2 kg + 4 kg + 6 kg)(4 m/s2); TA = 48 N  TB = (4 kg + 6 kg)(4 m/s2) = 40 N ; TC = (6 kg)(4 m/s2) = 24 N  7-44. An 80-kg astronaut on a space walk pushes against a 200-kg solar panel that has become dislodged from a spacecraft. The force causes the panel to accelerate at 2 m/s2. What acceleration does the astronaut receive? Do they continue to accelerate after the push? The force on the solar panel Fp is equal and opposite that on the astronaut Fa. Fp = mpap; Fa = maaa ; Thus, mpap = - maaa ; solve for aa:  EMBED Equation ; a = - 5 m/s2 Acceleration exists only while a force is applied, once the force is removed, both astronaut and solar panel move in opposite directions at the speeds obtained when contact is broken..  7-45. A 400-lb sled slides down a hill ((k = 0.2) inclined at an angle of 600. What is the normal force on the sled? What is the force of kinetic friction? What is the resultant force down the hill? What is the acceleration? Is it necessary to know the weight of the sled to determine its acceleration?  SFy = 0; N  W cos 600 = 0; N = (400 lb)cos 600 = 200 lb ;  F = (kN = (0.2)(200 lb); F = 40 lb SFx = W sin 600  F = (400 lb)sin 600  40 lb; FR = 306 lb 7-45 (Cont.) Since FR = ma; we note that: W sin 600 - (kW = (W/g)a; Thus, the weight divides out and it is not necessary for determining the resultant acceleration. *7-46. Three masses, m1 = 10 kg, m2 = 8 kg, and m3 = 6 kg, are connected as shown in Fig. 7-16. Neglecting friction, what is the acceleration of the system? What are the tensions in the cord on the left and in the cord on the right? Would the acceleration be the same if the middle mass m2 were removed? Total mass of system = (10 + 8 +6) = 24 kg Resultant Force on system = m1g  m3g The normal force N balances m2g; SF = mTa  m1g  m3g = (m1 + m2 +m3)a ; (10 kg)(9.8 m/s2)  (6 kg)(9.8 m/s2) = (24 kg) a (24 kg)a = 98.0 N  58.8 N; a = 1.63 m/s2 ; The acceleration is not affected by m2.  To find TA apply SF = m1a to 10-kg mass: m1g  TA = m1a ; TA = m1g  m1a TA = m1(g  a) = (10 kg)(9.8 m/s2 - 1.63 m/s2); TA = 81.7 N  Now apply to 6-kg mass: TB  m3g = m3a; TB = m3g + m3a TB = (6 kg)(9.8 m/s2 + 1.63 m/s2) ; TB = 68.6 N  *7-47. Assume that (k = 0.3 between the mass m2 and the table in Fig. 7-16. The masses m2 and m3 are 8 and 6 kg, respectively. What mass m1 is required to cause the system to accelerate to the left at 2 m/s2? ( F = (km2g acts to right. ) Apply SF = mTa to total system, left is positive. m1g  F  m3g = (m1 + m2 +m3)a ; F = (km2g = 0.3(8 kg)(9.8 m/s2); F = 23.5 N  m1(9.8 m/s2)  23.5 N - (6 kg)(9.8 m/s2) = (m1 + 14 kg)(2 m/s2) 9.8 m1 23.5 kg 58.8 kg = 2m1 + 28 kg ; m1 = 14.1 kg *7-48. A block of unknown mass is given a push up a 400 inclined plane and then released. It continues to move up the plane (+) at an acceleration of 9 m/s2. What is the coefficient of kinetic friction? Since block is moving up plane, F is directed down plane. F = (kN ; SFy = 0; N = mg cos 400; F = (kmg cos 400 EMBED Equation.DSMT4  EMBED Equation.DSMT4   SFx = ma; -F - mg sin 400 = ma; -(kmg cos 400 - mg sin 400 = ma  a = -(kg cos 400 - g sin 400 ; -9 m/s2 = -(k(9.8 m/s2) cos 400 - (9.8 m/s2) sin 400 Solving for (k we obtain: (k = 0.360  *7-49. Block A in Fig. 7-17 has a weight of 64 lb. What must be the weight of block B if Block A moves up the plane with an acceleration of 6 ft/s2. Neglect friction. SFx = ma: WB  WA sin 600 = (mA + mB) a  EMBED Equation.DSMT4 ;  EMBED Equation.DSMT4   WB  (64 lb)(0.866) = 0.188(64 lb + WB) EMBED Equation.DSMT4  WB  55.4 lb = 12.0 lb + 0.188WB ; WB = 83.0 lb  *7-50. The mass of block B in Fig. 7-17 is 4 kg. What must be the mass of block A if it is to move down the plane at an acceleration of 2 m/s2? Neglect friction. SFx = ma: mAg sin 600 - mBg = (mA + mB) a  (9.8 m/s2)(0.866)mA (4 kg)(9.8 m/s2) = mA(2 m/s2) + (4 kg)(2 m/s2) 8.49 mA 39.2 kg = 2 mA + 8 kg; mA = 7.28 kg. *7-51. Assume that the masses A and B in Fig. 7-17 are 4 kg and 10 kg, respectively. The coefficient of kinetic friction is 0.3. Find the acceleration if (a) the system is initially moving up the plane, and (b) if the system is initially moving down the plane? (a) With upward initial motion, F is down the plane. F = (kN ; SFy = 0; N = mAg cos 600; F = (kmAg cos 600 EMBED Equation.DSMT4  EMBED Equation.DSMT4  Resultant force on entire system = total mass x acceleration mBg  mAg sin 600 - (kmAg cos 600 = (mA + mB)a  (10 kg)(9.8 m/s2)  (4 kg)(9.8 m/s2)(0.866) 0.3(10 kg)(9.8 m/s2)(0.5) = (14 kg)a 98 N 33.9 N 14.7 N = (14 kg)a; or a = 3.53 m/s2  (b) If initial motion is down the plane, then F is up the plane, but the resultant force is still down the plane. The block will side until it stops and then goes the other way. SFx = ma; mBg  mAg sin 600 + (kmAg cos 600 = (mA + mB)a  98 N  33.9 N + 14.7 N = (14 kg)a a = 5.63 m/s2 The greater acceleration results from the fact that the friction force is increasing the resultant force instead of decreasing it as was the case in part (a). Chapter 7 Newton s Second Law Physics, 6th Edition PAGE  PAGE 72 Da DF Acceleration, m/s2 EMBED Excel.Sheet.8 600 N +a mAg 600 T T mBg F 600 N +a mAg 600 T T mBg 600 N +a WA = 64 lb 600 WB T T T T mBg 600 600 F N +a mAg + F F mg 400 F 8 kg m2g m1g m3g TA TB TA TB + + 6 kg 400 N N 6 kg 8 kg 10 kg + + TB TA TB TA m3g m2g m1g W = mg = 400 lb +a N F 600 600 a = + 4 m/s2 2 kg 6 kg 4 kg A B C A B C 6 kg 4 kg 2 kg +a T T 3mg mg N Fk F +a T T W 96 lb N + 340 N mg P 340 F B A 2m m T T mg 2mg +a +a T T m2 g m1 g N 8 kg mg T = 200 N +a 200 lb N +a +a T +a +a T m2g 320 N m1g 2000 lb 320 T m2g m1g T T +a T T m2 g m1 g N Fk Fk +a T T m2 g m1 g N N m1 g m2 g T T +a B 45 N T 80 N 6 kg + + 300 300 N mg F P P 300 300 N mg F F 300 300 N mg mg N 300 mg F 100 N N + m mg T m = W/g T + W + W = mg T 10 kg 6 kg 20 N P 10 kg 5 kg A 2 kg 300  6 jEHUj2: CJUVmH j|EHUj: CJUVmH jOEHUjX: CJUVmH j'EHUj : CJUVmHH* jEHUj: CJUVmH jU jUmH5CJ5CJ 1 !56Iq)p* A $d ~`0!d ~`0!$d `0!d `0!d jPd$ !56Iq)p* A x > ? 9 w j?eU4>L<-pw6DNH &!*!j""x##0$U$$ %6% &$&&&f'j'dFGIJS_`)+,=>?@GP_`  ޠ jEHUjJ: CJUVmH6 jEHUjB: CJUVmH jWEHUj: CJUVmH j EHUj$: CJUVmHmH jUmHH* jU j EHUj<: CJUVmH7     * + , = > ? @ A J \ ] e f q w x     / 0 1 2       ! žjp6EHUj1T: CJUVmH j6U j#EHUjQS: CJUVmH jEHUjR: CJUVmHj6UmH5H* jkEHUjK: CJUVmH jU jUmH67A x > ? 9 }}g$d ~`P d ~`P $0 ~`P $0d ~`P 0d ~`P $0 $0d0d$d ~`0! ! " & ' 9 ; < = A B C D L M ^ _ ` a h i p u v w x } ~   mnjlm~ jZ#EHUjZ: CJUVmH jUH*>*5 jUmHH*j !6EHUjNU: CJUVmH j6Uj6UmH66H*B9 w j?e $vdvd$0 $0d0d $dd$d ~`P ~?ABSTUV]^opqrv}12efgtU塘ܭj-6EHUj: CJUVmH j6U5 jh+EHUjH_: CJUVmH j(EHUj^: CJUVmH jUmHH*6 jU j%EHUj[: CJUVmH8U4>L<-pw6dvd $vdvd0d  !"#)*+45 (*>@Xz|LNfjc; CJUVmHOJQJ H*OJQJj6UmHj5UmHH* jm jT4EHUj4; CJUVmH jU jUmHH*6 j6Uj06EHUjɇ: CJUVmH6  !"#-6:;<= -./LMYfnopqrmnorwH* jmj6UmH5j5UmH j?EHUj6c; CJUVmHH* j;EHUjc; CJUVmH jUmH6 jU j7EHUBwxy{|*,2Hp (8:JLhj5 jm6H*H*j5UmHH*OJQJOJQJ H*OJQJ6H*OJQJ jm6OJQJ6H* jm6 6OJQJ6 jUmHE6DNH &!*!j""x##0$U$$0dd*dv0vdvd   -34789BCDKSThixy56NOQRUVWX[\]_fgkl     OJQJ>*j6UmH5H* jm jUmHH* 6OJQJ6OJQJS  " ( . : < B H J ` !!&!(!*!,!0!""T"V"X"Z"b"d"l""""""####### #&#,#8#:#@#D#P#\#b#d#x#z####### $%$&$0$T$U$V$$$$$$ OJQJmH6mHmH6H* 6OJQJ6>*5H* jm jUmHj6UmHH*OJQJ6L$ %6% &$&&&f'j''B(x(()v*z*+\,,--.x.d0d ~` 0 ~` vd$ % %%"%0%4%5%6%7%k%&&& &"&&&&&&&&&&&&&'''('@'B'f'h'F(((((((((((((((((((((())** **(***2*P*R*t*v*jTC6EHUjg: CJUVmH j6U 6OJQJ6H* 6OJQJ jUmHOJQJ H*OJQJH*j6UmH6Fj''B(x(()v*z*+\,,--.x.../ 0d000D2233844"5567#8{8}88'9(9<999H:::;<U<<<J=x===>>??n@@RA^ASBBBDDVEEFqFGGyGGGG H"J,J.J0J2J4J7J:J;JNJRJVJZJ^JbJfJgJhJJ~K%MuNxNO cv*x*z*|*++,,,,,,&,(,6,8,@,B,D,F,P,R,T,V,X,,,,,,,,,,,,,,,,,,---.-0-R-T-V-X-n-x--------...... .(.*.H* jWIEHUjk: CJUVmH jFEHUj#k: CJUVmH jU jm6 6OJQJ6H*6 6OJQJ jUmHj5UmHD*.:.<.N.P.f.h.r.t.x........2/4/6/>??n@@RA^Ad $0d0d0d0d999:::: :::@:B:D:F::::::::<<<H<I<J<U<V<e<f<z<<<<<<<<<J=K=N=O=R=U=Y=Z=b=c=t=u=v=w=z======>j>k>n>o>p>q>y>Ｓ jm6 jmjU6EHUj: CJUVmH6H*OJQJH*jR6EHUj: CJUVmH j6U6H*OJQJ jUmHCy>z>}>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>? ????@@*@,@4@6@D@H@L@Z@\@^@d@n@p@t@~@@@@@@@@@ȿjG[6EHUj: CJUVmH6mH jUmHjtX6EHUj: CJUVmH j6U6H*j6UmHH*6H* jm6H* jm6OJQJ>@@@@@@@@AAA,A.ARATA^A`ASBTBUBVBWB\B]BBBBBBBBCCCCCD DDDVDXDDDD:EE@EZE\EbEdEfEhEnEpErEvEEEEEEEEEEEú>*OJQJH* jmj^6EHUj: CJUVmH j6Uj6UmH jUmHOJQJ H*OJQJ6H* 6OJQJ6H*D^ASBBBDDVEEFqFGGyGGGG H"J,J.J0J2J4J$$$vd0ddd p0ddEEEEEEEFF F FFFFFF)F*H*6>*H*6H* jUmH6Q`za bbbc(dddefwfgLgghpijXj\jkXlmm(nvvd0d0ddvdbbb,b.b4bPbRbXbhbjblb~bbbbbbbbbbbbbbbbLcNcPcRcTc\c^c`ccccBdDdTdVd\d^d`dbddddddddddddeeeeeeee$e&e4e6ee@eBeDeRenepe|e~ee 6OJQJOJQJCJ5H* jm jUmHH*OJQJ H*OJQJ6H*6Oeeeeeeffff f fffffff=f>f?fBfWfXfYf_fjfkflfofwfxfffggggMgcgegmgng{ggggggggghhhhhh2h4hhDhFhHhZh\h^hhhj)*: CJUVmH jH*UOJQJH* jmOJQJ 6OJQJ6>*CJ5CJ jUmHH*6H*6j6UmHEhhhhhhhhhhhhhhhhiiiii2i4i6i:iHiJiPiVibidijipiri~iiiiiiiiiiiiiiiiiiijjjjj9j:j;jMjNjOjRjXjYj[jjIJĿĿĿ jmj6UmH6H* jm66H*OJQJOJQJ jUmHjkEHH*Ujj*: CJUVmHH* jH*UjiEHH*UDjjllll lll l(l*l8l:lBlDlFlNlPllllllllllllmmm0m2m4m:mzm|m~mmmmmmmmmmmmnn(n*n,n.nNoPozoȿj6UmH jtEHUju5: CJUVmH jU jUmHj`q6EHUj2: CJUVmHjm6EHUji2: CJUVmH j6U6H*6H*OJQJH*;(n,nzoo;p~pqqrLss3twt-uzvvwxvxxxx&`#$ !$vd0d `0@!d0d0zooooooooooooooooooooooooppp pppp p!p"p'p(p8p9pMpNpOp^p_p`papppqprpsptpup~ppqqqqqqqqqqqqqrrrrrr r"r$r&r4r6r>r@rFrHrJrLr jmOJQJ6>*j6UmH5 jUmHH*6H*6H*OJQJSLrNrPr^r`rbrrrrrrrrrrrLs^s`sbslsnsrs~ssssssssssssssssssssstt t!t1t4tTtktutvtwtxtyt~ttttttttvv 6OJQJ6>*j6UmHH* jmOJQJjxEHH*Ujj*: CJUVmHjvEHH*Uj)*: CJUVmH jH*UH*66H*Bvvvv v*v,v0vvDvFvHvJvLvNv\v^vfvhvjvrvtvvvzv|vvvvwww"w2wvxxxxxxxxxxyy yyyyyyyyyyyyyyy z z z zzzzzz jzCJUj0/; UV jUCJH*CJ0JmH0J j0JU 6OJQJj6OJQJUmHH* jmH*6H*6Exxxyyyyyyyy y"y$y&y(y*y,y.y0y2y4y6y8y:yy@yBy&`#$8y:yy@yByDyFyHyJyLyNyPyRyTyVyXyZy\y^y`ybydyfyhyjylynypyrytyvyxyzy|y~yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyz z z z z zzzzzzzzzz#z$z&z'z)z*z/z0z2z3z7z8z:z;z>z?zCzdByDyFyHyJyLyNyPyRyTyVyXyZy\y^y`ybydyfyhyjylynypyrytyvyxyzy|y|y~yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy zzzzzzzzzz#z$z&z'z)z*z/z0z2z3z7z8z:z;z>zzzzzzzzzz!z"z#z$z&z'z)z*z+z,z/z0z1z3z5z6z7z8z9zz?z@zAzCzDzFzGzHzIzKzLzNzOzPzQzTzUzWzXzYzZz[z^z`zazbzczlzmzozpzqzsztzwzyzzz|z}zzzzzzzzzzzzzzzzzzzzzzzH*CJH*56CJH*CJ6H*6OJQJZ>z?zCzDzHzIzKzLzNzOzTzUzYzZz\z]z`zazlzmzqzrzvzwzyzzz|z}zzzCzDzHzIzKzLzNzOzTzUzYzZz\z]z`zazlzmzqzrzvzwzyzzz|z}zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz{{{ { { {{{{{{{{dzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz{ { {{{{{{{{{{{{{{{{{{ {!{"{ CJOJQJ 6OJQJCJH*CJOJQJ6H*6Xzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz{{{ { { {{{{{{{{{ {!{%{&{*{+{;{<{?{@{B{C{E{{{ {!{%{&{*{+{;{<{?{@{B{C{E{F{J{K{O{P{]{^{c{d{i{j{o{p{r{s{u{v{x{y{{{|{~{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{d"{#{%{&{'{({*{+{;{={?{@{A{C{D{F{H{I{J{K{M{N{O{P{[{\{]{^{c{d{i{j{o{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{5H* 5OJQJ556 6CJH*6CJCJH*OJQJCJ66H*TE{F{J{K{O{P{]{^{c{d{i{j{o{p{r{s{u{v{x{y{{{|{~{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{||||||||| | | | ||||||||||||||||!|%|(|)|-|3|4|5|7|8|?|@|A|B|C|D|F|G|H|J|K|M|N|O|P|Q|R|S|T|U| 5OJQJ6H*56OJQJCJH*CJ56Y{{|||| | | | |||||||||$|%|(|)|3|4|7|8|?|@|B|C|F|G|J|K|M|N|Q|R|U|V|X|Y|^|_|c|d|f|g|k|l|t|u|y|z|||}||||||||||||||||||||||||||||||||||||||||||||||d{|||| | | | |||||||||$|%|(|)|3|4|7|8|?|@|B|C|F|F|G|J|K|M|N|Q|R|U|V|X|Y|^|_|c|d|f|g|k|l|t|u|y|z|||}|||||U|V|X|Y|Z|[|\|]|^|_|a|b|c|d|e|g|h|i|j|k|l|t|u|w|x|y|z|||}|~|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||5H* 5OJQJOJQJCJH*CJ566H*65W||||||||||||||||||||||||||||||||||||||||||||||||||||||||||}}}}}}} } } } }}}}}}}}}}}}}!}"}#}$}%}'}*}+},}.}/}1}3}4}5}6}8}9}:};}<}>}A}B}E}F}G}I}K}L}M}N}Q}R}S}\}]}_}a}OJQJCJH*CJ566H*6 5OJQJ5Y|||||||||||||||||||||||||||||}|||||||||||||||||}}} } } } }}}}}}}}}}}#}$}&}'}*}+}-}.}0}1}5}6}:};}=}>}A}B}E}F}H}I}M}N}Q}R}T}U}[}\}^}_}a}b}d}e}h}i}k}l}t}u}w}x}z}{}~}}}}}}}}}}}}}}}}}}}}}d}}} } } } }}}}}}}}}}}#}$}&}'}*}+}-}.}0}1}5}6}:}:};}=}>}A}B}E}F}H}I}M}N}Q}R}T}U}[}\}^}_}a}b}d}e}h}i}k}l}t}u}a}b}d}e}h}i}k}l}t}u}w}{}~}}}}}}}}}}}}}}}}}}}}}}}CJH*CJ56"u}w}x}z}{}~}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} }}}}}}0d'0&PPA/ =!"#$%p!> KTvWNQL5W A`_xݘKTAǿsΞAE]!"X)B2 2AEїXz$ Az,`{E?! S8̙9{ֺ;3fΙ9 B|X,u;&KYQkӒel :9|$w<$t7%>-rVm+7ej="#7gshåihbo5vz|AtOSɖ:+gl]"/Y.o4b~r'NVjxo2aI)F^,E,E,I,I,A,A,F,F,JLDh?^38{:΢NKdͷt4F+k|vBOE^۴~^){_~);7vu\S4#6F,E,E,I,I,A,A,F,F,J,J,k3;Wb= $6Il4b Ė-[#Fvlr EYVKrbd45s*9k=%uw+*1;ԳS8ߢN彩z}WiQ ]!וX⹓y}W#̾?+xY1緐,GdU 3e cR]X,k"zB.>ɲJV%R֪t ,ɲJVŰQ֪ a B"߲l;pj[fN.(+o͸g{wf2vV]߹v5 ~:]שgf"2S $.G+I"q"HG˜JraF#Lf>;Y\o09ܒ$fS..D\0ׂ]KI$rrf O,-r&OKJZ5Zuw΄ ̼Iq*2 J rTj\*9̼u{؂2t! vy3!TgM[ae"AR ]d)UPqXx+:VeXy^ԓTZ G袛ĸV `OC&5ɪD::ug~/2I< mx.V!|)Gۂ3* 5Ye]E ԑk:V?_ʻU-r5E^z3JŇ9M"ozdm̙޿ǰH;]&(ķ0 -םBе2鹨! J&+a(|,(HC!N,vJ_FրY3-:hК D܅V!|)Gۂ3 U홻]w5䚎U}*EhrOc`S0!dTMM:s?=iG`$&<%UἩSp6B&=5DAidt 6Lcv?)e_N˨3|ۭL9 ek.&ȝ,:,@UNMc3aMesIOhI/Kt.DdLB  S A? 2f ln$@ u_t `!lf ln$@ u_$  d:xuP=KA}3wzGH bO0IixFH@,RkE;.2fޛ7CFqXGL$q dUTrhOUmk!t,U)rUF^zSJ%9 $Zoz`ԙ޿ǰI;#]$(70 Mם~k#ds^CF7MN`dQS8nxC^Y|m:=ʔCZN+Yn?eʉ~}ٽil& $lt4r7 -KvSDdxlB  S A? 2Mr1t~6H `!Mr1t~6 _xQ=KAMrR`yD!Xv0IDI4!`?YoZE;v}o#fyD)ބ(:m {Q^b"0VfVAt=zB59>XRVD_H&Z1?imn8yCؿNA"r^aT[T6 Q`8{@6DmAV/rHk3e ʼn2 ;KG^-2$z5t23a.1GiSzgydȣ1فgΘ* ĵj^&nl_]p Brc<|"ϕ]BQDdxlB  S A? 2 [fL"V߾  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~+cRoot Entry F cA6T@]Data WordDocument)4ObjectPoolOTA6T_988354836  FTTOle CompObj\ObjInfo  #&)*-01478;>?BEFGHILOPSVWZ]^adehklorstwz{~ FMathType Equation Equation Equation9q` a=4N4 kg=r%2P&N FMathType Equation Equation Ole10Natived_988354825 F T TOle CompObj \Equation9q` a=8N4 kg=r%2P&N FMathType Equation Equation Equation9qObjInfo Ole10Native d_988354904 F T TOle  CompObj \ObjInfoOle10Nativel_988355102 F T Th a=12N4 kg=%2P&NDD FMathType Equation Equation Equation9q` a=20N2 kg=usbar=1 ScannerOle CompObj\ObjInfoOle10Natived_988355122 F TʛTOle CompObj\ObjInfo FMathType Equation Equation Equation9q` a=20N4 kg=%2P&N FMathType Equation Equation Ole10Natived_988355132" FʛTʛTOle CompObj \Equation9q` a=20N6 kg=%2P&N FMathType Equation Equation Equation9qObjInfo!!Ole10Native"d_988355364$ FʛTʛTOle $CompObj#%%\ObjInfo&'Ole10Native(_988355506;) FlT4T m=60 lb4 ft/s 2 =PCancel FMathType Equation Equation Equation9q m=60 lb8 ft/s Ole +CompObj(*,\ObjInfo+.Ole10Native/2 =PCancel FMathType Equation Equation Equation9q m=60 lb12 ft/s 2 =PCancel_988355650. F4T4TOle 2CompObj-/3\ObjInfo05Ole10Native6_988367588,63 F4T4TOle 9CompObj24:\ FMathType Equation Equation Equation9q m=60 N10 m/s 2 =6 slugsObjInfo5<Ole10Native=_9883678008 F4T4TOle @ FMathType Equation Equation Equation9q` 2as=v f2 -v o2 ;a=v f2 -v o2 2s=(0) 2 -(27.8 m/s) 2 2(50 m);a=CompObj79A\ObjInfo:COle10NativeDd_9883695991E= F\T\T 7.72 m/s 2ebar=1 Statusbar=1 Scanner FMathType Equation Equation Equation9q m=40 N9.8 m/s 2%2PCancelOle JCompObj<>K\ObjInfo?MOle10NativeN FMathType Equation Equation Equation9q m=60 lb32 ft/s 2PCancel_988369745B FTTOle QCompObjACR\ObjInfoDTOle10NativeU_988369969@JG F%T%TOle XCompObjFHY\ FMathType Equation Equation Equation9q m e =180 lb32 ft/s 2 =5.625 slugs;ObjInfoI[Ole10Native\_988370254L F%T%TOle _CompObjKM`\ObjInfoNbOle10Nativec_988371609'Q FTT FMathType Equation Equation Equation9q g m =30 lb5.625 slugscel FMathType Equation Equation Ole fCompObjPRg\ObjInfoSiOle10NativejEquation9q m=16 N5.0 m/s 2%2PCancel FMathType Equation Equation Equation9q_988371851V FTTOle mCompObjUWn\ObjInfoXp a=60 ft/s - 20 ft/s5 s=8 ft/s 2 ;m=200 lb8 ft/s 2 FMathType Equation Equation Equation9qOle10Nativeq_988372683T^[ F@T@TOle uCompObjZ\v\ObjInfo]xOle10Nativey_988372808` F@T@!TOle | a=Dvt=-4 m/s3 s;a=-1.33 m/s 2Upda FMathType Equation Equation Equation9qCompObj_a}\ObjInfobOle10Native_988383112Ye F@!TIT m=-400 N-1.33 m/s 2 ;cel FMathType Equation Equation Equation9q  m=2500 lb32 ft/Ole CompObjdf\ObjInfogOle10Native$s 2 = 78.1 slugs; Now recall that:  2as=v f2 -v 02   FMathType Equation Equation Equation9q_988383177j FITITOle CompObjik\ObjInfolOle10NativeD_999765126oFITITOle CompObjnpi@  a=v f2 -v 02 2s=(0)-(80.7 ft/s) 2 2(200 ft);     and       a= - 16.3 m/s 2le] Toolbar=1  FMathType 4.0 Equation MathType EFEquation.DSMT49qܘ%MU2GxDSMT4WinANSITimes New RomanSymbolCourier NewMT Extra!/'_!!/!"!APAE%B_AC_A %!AHA_D_E_E_A  FF kk ==m kk NN;;   m kk == 11227700 llbbObjInfoqEquation Native _996388845|tF T TOle 22550000 llbb;;V FMathType 4.0 Equation MathType EFEquation.DSMT49q%MU2GxDSMT4WinANSITimes New RomanSymbolCourier NewMT Extra!/'_!!/!"!APAE%B_AC_A %!AHA_D_E_E_A CompObjsuiObjInfovEquation Native _996388888yF T T TT"-WW== WWggaa;;6644 llbb"-6644 llbb == 6644 llbb3322 fftt//ss 22 ()aa FMathType 4.0 Equation MathType EFEquation.DSMT49qOle CompObjxziObjInfo{Equation Native %MU2GxDSMT4WinANSITimes New RomanSymbolCourier NewMT Extra!/'_!!/!"!APAE%B_AC_A %!AHA_D_E_E_A  TT"-WW== WWggaa;;4400 llbb"-6644 llbb == 6644 llbb3322 fftt//ss 22 ()aa FMathType 4.0 Equation MathType EFEquation.DSMT49q%MU2GxDSMT4WinANSITimes New RomanSymbolCourier NewMT Extra!/'_!!/!"!APAE%B_AC_A %!AHA_D_E_E_A _996388918wm~F"T2TOle CompObj}iObjInfoEquation Native _988440553h F{:T{:TOle CompObj\ TT"-WW== WWggaa;;9966 llbb"-6644 llbb == 6644 llbb3322 fftt//ss 22 ()aa4 FMathType Equation Equation Equation9qObjInfoOle10Native_988441379 F{:T{:TOle  a=m 2 gm 1 +m 2 =(6 kg)(9.8 m/s 2 )4 kg + 6 kgAP7.doc? FMathType Equation Equation Equation9qCompObj\ObjInfoOle10Natived_988441556c FCTCT` a=m 2 g-m k m 1 gm 1 +m 2 =(6 kg)(9.8 m/s 2 )-(0.2)(4 kg)(9.8 m/s 2 )4 kg + 6 kgr=1 Statusbar=1 ScannerOle CompObj\ObjInfoOle10Native FMathType Equation Equation Equation9q a=58.8 N-7.84 N10 kgPCancel FMathType Equation Equation _988447095 FDKT`5eTOle CompObj\ObjInfoEquation9q a=m 2 g-m 1 gm 1 +m 2P' PUpda FMathType Equation Equation Equation9qOle10Native_988446967 F`5eT`5eTOle CompObj\ObjInfoOle10Native_988488917 F`5eT`5eTOle  a=(8 kg)(9.8 m/s 2 )-(2 kg)(9.8 m/s 2 )2 kg + 8 kgANSCHAP7.doc? FMathType Equation Equation Equation9qCompObj\ObjInfoOle10Native_988524276 F`5eT`5eT a=51.9 N - 19.6 N12 kgncel FMathType Equation Equation Equation9qOle CompObj\ObjInfoOle10Native m=Wg=2000 lb32 ft/s 2 ;m= 62.5 slugse=C:\Program Files FMathType Equation Equation Equation9q_988525792 FlTlTOle CompObj\ObjInfoOle10Native_988530832 F@uT@uTOle CompObj\    !"#$%&),-.1456=@ABCDEHKLMNOPUXYZ\]^_`abdefghijlmnopqrt a=T max -mgm=200 N - (8 kg)(9.8 m/s 2 )8 kgles\Answers\ANSCHAP7.doc? FMathType Equation Equation Equation9qObjInfoOle10Native_988531390 F@uT@hTOle   s=v f2 -v 02 2a=0-(20 m/s) 2 2(-6.86 m/s 2 )NSCHAP7.doc? FMathType Equation Equation Equation9qCompObj \ObjInfoOle10Native_988545177r F@hT@hT a=m 2 gm 1 +m 2 =(4 kg)(9.8 m/s 2 )6 kg + 4 kgAP7.doc? FMathType Equation Equation Equation9qOle CompObj\ObjInfoOle10Native a=g3=9.8 m/s 2 3PCancel FMathType 4.0 Equation MathType EFEquation.DSMT49q%MU2GxDSMT4WinANSITimes New Rom_996389027FTTOle CompObjiObjInfoEquation Native _988549458 FTTOle 'CompObj(\anSymbolCourier NewMT Extra!/'_!!/!"!APAE%B_AC_A %!AHA_D_E_E_A  WW -- 1199..22 llbb==  9966 llbb ++ WW3322 fftt//ss 22 ()44 fftt//ss 22 () FMathType Equation Equation Equation9q a=(3-m k )g4=(3 - 0.3)(9.8 m/s 2 )4o Equation in C:\WorObjInfo*Ole10Native+_988556570 F 1T!TOle /CompObj0\ObjInfo2Ole10Native3_988621353FTTTT  ) (  !"#$%&'*,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abefghqjklmnopdrstuvwxyz{}~ FMathType Equation Equation Equation9q a a =-m p a p m a =-(200 kg)(2 m/s 2 )80 kgtes\McAfee VirusOle 7ObjInfo8_988621418F`|T`|TOle 9 FMathType 4.0 Equation MathType EFEquation.DSMT49qMݐ%MU2GxDSMT4WinANSITimes New RomObjInfo:_988623465FTTOle ;CompObj<iObjInfo>Equation Native ?_988623497FTTOle FanSymbolCourier NewMT Extra!/'_!!/!"!APAE%B_AC_A %!AHA_D_E_E_A  WW BB "-WW AA ssiinn6600 "o == WW AA ++WW BB gg()aa FMathType 4.0 Equation MathTyCompObjGiObjInfoIEquation Native J_988624245FTTpe EFEquation.DSMT49qM݀%MU2GxDSMT4WinANSITimes New RomanSymbolCourier NewMT Extra!/'_!!/!"!APAE%B_AC_A %!AHA_D_E_E_A   aagg== 66 fftt//ss 22 3322 fftt//ss 22 == 00..118888 FMicrosoft Excel WorksheetBiff8Excel.Sheet.89q Oh+'08Ole QObjInfoR_1005399856 F`|T`TOle SPRINT CompObjTfObjInfoVWorkbooku"H$ X -   I''  Arial---"System-'- I "--  8 "---'--- I- "- $c3c3c "----'--- 3_ 3pp3::3333cc3---'--- I "-c c33c "-cpp::cc322||WW33---'--- 8---'--- AY---'--- >Y -- "-  $---'--- >Ypt $tf~ptzjptf---'--- >Y: $0:D:0---'--- >Y: $:D:0:---'--- >Y $---'--- >Y $---'--- >Y---'--- AY---'--- I-----'--- cT  Arial- 2 ]Force, N-----'--- I---'--- I---'--- I  2 l0 2 l2 2 Yl4 2 #l6 2 l8 2 V10 2 V12 2 LV14---'--- I---'--- I  2 0 2 1 2 '2 2 q3 2 4 2 5 2 L6 2 7 2 8 2 (9---'--- I---'--- I "- -  8-- -4- "-(V---- --- -' I '  ' A\pPaul E. Tippens Ba=<=k <X@"1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_)                + ) , *  ` Chart1Sheet1 Sheet2!Sheet3jb(3  @@  (Acceleration, m/s2Force, N % 56;60_5\ 5W8 5 ( 5)  6b pbxbY0ymm@0Н0b 'd b0bbbʲbpbip06bb6n0 }0 %x8T0bt00`T0zm00b E000bbb߿0bx8bt0b6(bPercent0]hT;|b0\xb0{T0T00Te0Tբ0T|?b10|)*b(b@kT0e0{T0L0b@8b֜z0$Hb$d{0cT0Xb$lb$b}0RT0bbbbz0b$jbb%0(bj$` 0j(  AMHP DeskJet 890C Series (2)7d,,HP DeskJet 890C Series (2)LPT1 ,,"d,,??3`  `   ` >  ( 333  ~  <8 @AA?]8  $ @3Sdd23 M NM4 3Q: Force, NQ ;Q ;Q3_4E4D$% M 3O&Q4$% M 3O& Q4FA  I 3O. 3*?#M43*#M! M4523   43d" 3_ M NM  MM<444% 2M:Z3O*Q'44effffff?333333@ffffff@ffffff@ffffff@ @e@@@ @$@(@e> Sd A  dMbP?_*+%MHP DeskJet 890C Series (2)7d,,HP DeskJet 890C Series (2)LPT1 ,,"d,,??U} T0b *a@ r@y@@0@@@ *@@@ @$@(@< (  p  6NMM?p<`]`\  AMHP DeskJet 890C Series (2)7d,,HP DeskJet 890C Series (2)LPT1 ,,"d,,??3` > `  `  0(  ~  <N @AA?> ]N $3d23 M NM4 3Q: Force, NQ ;Q ;Q3_4E4D$% M 3O&Q4$% M 3O&Q4FA= 2 3O# 3*?#M43*#M! M4523  O43d" 3_ M NM  MM<444% 8uM:Z3O2Q'44eee >@  A  dMbP?_*+%" ??U>@ A  dMbP?_*+%"??U>@ SummaryInformation(WDocumentSummaryInformation8[1TableiSummaryInformation(c@Xp Paul E. TippensPaul E. TippensMicrosoft Excel@U: ՜.+,D՜.+,D PXh px SPSUCh1 Sheet1Sheet2Sheet3Chart1  WorksheetsCharts 6> _PID_GUIDAN{5D56FACC-A667-11D3-B9D0-44455354616F} Oh+'0 ( D P \ ht| Chapter 2 hapPaul E. Tippensaulaul Normal.dotpPaul`! [fL"V߾ ]xQJA`A$ H'Jr&Xڥ"v `auv΄]foog|&%%x HZW-A ü\D[o!wiF0|z>]xƝ 'ՠ'y9u!#B,ׇAΦ^˻nb^SmDdlB   S A ? 23&kn0UB`!3&kn0UyxR=O@ 9# u'Ёv'ED)BXX*1:tf` `"!q%gw LHVWl-FQa·r3ŀb",A鐥, g|y댺#wbAT(ZOl-Y׊>izF+JuXJNpq3Q~1H]xAFIꂿtǺ4;%\=jp,ߚL $:Kqt`Wƃ(Us]TfYMs6 F `"]+͌A8p ǔ#'oGy=A0,yJ߂ 9Mvb5F?xN}dhDd0B   S A ? 2a8يx-R`!a8يx-R+ oCtxMhA&ihELCҺ()* ik [xT%x"x "t$#T#5UX:n:eґYt#uu"QTTcJ,{֋a*_֪5C7YnFS1N߾V׿@f&Ծ:-Vfnpw!ʟ>ӏPZ\h[kMSoq3=چPDdlB   S A ? 2֓Xu? rƖ`!֓Xu? rƖ@ \xQ=KAsh#!6bk J<H@Y؈M_`ggߠZufHDpa73o"d= AN-C%Q$cLKlFu94q&{+̃rp=69(95,SNeEGo wGFQ^8 ~=8a4R^tf[T 20GcvOl%)OT_*c \\M81"k,(v+[~ș-5Dѫ^nZ>"y_YSY_KeAZ_;HTj ?ѼoZcMDd(lB   S A ?2N߯tmg`!N߯tm@ YxQ=KCQ MrbZQ~Tq`}ЂtW.ߠ\kJKE½$'' B!? r|$V/!*d]m";Q^ 9z3%6yX+[HL6݀}&;ETBZ/|"Vؚ$gzD'|!" ja+6.#%KrN{ ![Pf 2I>F~373rG`N,KZ*#(\] Yj<,60KX?h_=Ɍea;ވ%!NUS=+dxiQIDAa)/RܼTQ>mA8<'ǚ@zpŸ5!ܱzjUX),WGo50iFYÞS<ڄ iJՋ:1>piJ`o#ގ@,Q/w.9 GJ^0aDddlB  S A?  2}x>9O#`!}x>9O^ mxJAgr9GI4A|S@g إ ԇHm ֊;w&D=vg7RzDRs2JB\z=[,(u{d qc ux`TBC->ϖfOw4!# 'Qka?hGͳyI6 1At>2J a,𛋵ąa8j!$Eչ;3{#[:.ӬkÉw Gl`<̰rZ,7ˑ.bN<ӍG'_Rc_#Ƞ]y՝$*^%t^^nSK\Sx.W6VԶahj8};E|2('~V}*ԧc\*=[s=>}Kʻ& ϲ w&o@fߝ!ۥTDd lB   S A ? 2'SY *PRɣ1(`!SY *PRɣ1 L"x/A{{aÝ(7G4܉;:J $'d-;:uTZFU: 9k쏻[Hl2޼AHh(zdK""H8KfXa9޹u3-ͥ`\*+rbeUij9qoP6#>G}s|t%mR5*G]v ^[)^jL# mVX9嫌PdWF^{;@nDf*r9dhĞY~gtc5N,(;b-x@V(Ys='_R"@p'~w6Ai%sa$8$qQPUdxp%Fz"o2R #$~S)URϦAQR!7Jͩ׃뉭4cnӣGS=Kv_gT zg3X\T?tJ/h3Km=e@Eفx8ф57dp:DdHlB  S A?  2-+|BBQb\'.`!T-+|BBQb@%9"xT1oPw.IT -[J@" bhw BlRaD (C#,̈=?R^t޻.L?GhUZ 4-դ 1 5ܘ;FֹRN@0JI.3j뫃 |\ K2K}@NWޯz"@h>H/[N?eJcCW ys)(a9 lm=cQjאiY>Va ռk1GE"n2"=:0ҹn'`^i:w0b;jqpm{CΡ#;:kcZl!K]pG|)k3W2H@ DMd/__Qyxx EkD>DFW_KrK?yKJѽ3'd:^EM/5)%=W=ϸTŠ|`7,_rbse~ho8[Dd\B  S A?2Cj2[i=1`!Cj2[i`% 9gxkAG$&i)U IZ,==xiU-$()= ēу<챐xBBR{36BɡL2|߼7;# `K1+-&&PDHb\y)̸d fSػIC<#z<{v!0p޺n!d@_S*RIh׼#EnG0[8 '!4R㱽7M6%̔W㮼 $#iz <0ʎ!!Pfquu /T+(\ukU{\ɓMW}sͶk;AhY }p<"%5d4Wʗm:KGݟ Liž 𴮰T >fiP 3L' .QXnj4y-,"L~IZ s~u}S0#[`no<}JZi;w<)}:9| =5ntPα؃:"}䤕/X$\?W1O6RD#))`'RD;}.I;P1{g[~z#h>equtf >IH9n9JZJ.oDd< lB  S A? 2pnJxPG^:4`!pnJxPG^:(`HbxTkAƦka7EnIKCllC@Ēl+m/ƊP< ! GA7F]arO[Ľft"sS3Ef60{}n8'Ysh:g!hN>G>dwiCI{Bдs| ]ՇN{G![zQj`1mz;,Wc݄sN![*ͤr&-X\Տ~u WdI.0I9#Y@ w2[CE/>*$㈓Л6QÖG+vZv+ _'1H:y_̿i5}I:YTe<ſ9݆Dd,B  S A? 2BGIQpJ c_;`!GIQpJ c_t@p(xTMhQ$-* wi0ٚHji^$UZOG/^ī "Axԓ?ZʢE8OTM޼oahP 48chfhHY#58#)P!tEQ4aN9G=B^.+|pl2\9;ɯiEx]d+]~q}(g0rbWgR:1G"I$:s-N'ZFrޢUDHw%꽳Bh=LQޱ:J{HD*#a߿F,Uw^fZs=qM]!&3wlme$oBy>OOX-l2YeʅiXb?}_v)oU_zkT_vu=w'&^3Mg83f%Dffi )n!!mhTqNR,sd:Gm\t%1=u,}ӰG!Cix;@()H_ FlOAF]f>QgG} WcN![*ͤr&s 9ִo\]J"I}\]4asFxi e_}Q-!d PBdUqIVPQMBaˣX=M-Y=xF%{//%z,T2\EKݶDd,B  S A? 2?@nK&C4?`!@nK&C4t@p(xTKhQ=L?idi)UIRi0B[I2&BJ3bVAj].ݸH .UW~6A2S :ɻp{߇Оs@6ħz.5X\䌤@ 0-&.ijxi`1Vodo-~P<*e*~'5C0w-n0jqevOnU"q@vRZչJaj5& Pc**kTі~o4.jzQEdš)F(S K}1w@mFzD6y4VَU+ \*5a쎪7u)G Q v6W($xM 8??fv(w*X)̀5ۆM=&Rx_/}l'ۍ'xr3D{3clz>};w cQz~ic;o$: .J/Zx+V h*".7SU3EH }T"Ϟ[QvUU5` d S6R({.R`w%f(+;v 1{V?*lKp0}J Һ +X_ ww%9%׬ۣ !]xk榈fVU O|gI{^e;/|U5's[2Sz2vE(Oaqt>9MkzD'o@Efȇ1v *X^u:6H3Ї;DdB  S A?24RZ492I`!y4RZ492B xdGxuQ=KA0F<#ݡ1@LaRZ J<#$ ڥv)??Zug ,BB:*B Rj pS2{y] ҳN jW:V#8&6`7U\0-|4-Gbѱ3޿TM;J׋Q}s};2鹨! Z&k SIp&ݎ- ufkeIܰU4:]iD ~a0Ϭ?X/e]oxE |eBUN3+x' QTDdB  S A? 2#q0tuK`!#q0tu @ `xmK@{6iZ4hRE* .:ظuBEc H6nN:9dwpuy.Iw{?>^J@%Җ6!$m:+M$Li YPZRfqV@pp92v>E9Qwa04x`V+5d>V;3Mw&5x~? Fv2 yCJ-v@v!NK|~Bb[Z>D܈E8Ȣ/*v %1tÝ[FȔh*59WWH_ԣ$+>q-fJlfʇYyNd.ͧhf L)WDd<B  S A?2ͺְCuc@#*N`!ͺְCuc@#``%PxS=KAwIGLaqDbŸIpx&AVl&XZ؊`3{kb\c̛sLUāV4 IC!~ٌH02" frCқ0r_N JzBjCؠV+ebeD+z3?nm=# (4Ϣk9Dyҩ h ۂPh9$U)i=xs>qaGlW'`)! exzGn127]aw` R+:SǼrj'@=ƲM8;z.w{a4lf~*WDd B  S A?2e~c(;QO"@5S`!e~c(;QO"@@ }"dxR=KP%&mmq lD` .i1Vic Hͥ?pEGQOppR4϶^9{y4d15L#lC ˣ)c$ ,;İnf$$ -(wd^CbUnMOb_YƔCk 'LImI,j 5߼*Y:\vOW>nr$Om@zBGqVrT7 Ye/a.Ja6{4U~\"ail"vPb"ck z+PbT% kn,N=i|3s@"\K䖝p0R1."dΎso-ffD'~J\knU uuFS@ '3Y;aP)^x'%3 چxle0l<]c;~*#Ulqϛ ۺ~} pɍ& 1Y|k` qjP-yg PUךJeeY"rq:š,wm:VPkNCI}.;! Ƨ~Fl$9(_3^8eIH&C%h~ESr lFzV&e8=iO zZ!Ys4#;}_i3YGG%ΐ q3.+ݢoN-^.hDdB $ S A$? #2Dd>hQ0zDS^`!Dd>hQ0zD 8>dtxRJAKr^#*&$b"&E"*z&lL-vXRkם8\e̛7+ >`he. YQF*RXdd Ee(b mf!ON˱ž"tǭa/>R_\* <6pdiֱvbort%H% (E׍:q7Uuy@XO]ދgH#~95ksv 2g7uȌEJ/Vaǘk켰,![ #d3Ad,4 jCEب\[h``! G>\[h@S!xKAǿ3T-QCi)lE` B PEH@b^'@/w{sO= = DVmf&j`w/Y`@Wx^W,}ZGCkCh'i7/L2,l(oPV#3l~aؑ=x]wZ<7~yh4{Kac3ovXP͍^ s ى=D[1mF#K҉H`۰t w͚hFNx !yƿŤee:DTDZ#5\܄0Gѝޱ)rr܌!뛴D݋2v$![)&U8fUh|x|y8;c?-" ]u'7E!fVkգgBDdH B  S A?2<Pώm\9g`!<Pώm\@H xKA̮/Ae֡୓?@6 Bt _kgCt :JСy3؋2˛ϼy(/} RT6(!8gmpC2BvBbYDZiݰF |(:O+e5N󴠢cV7 ٮ&[|cu#(3j֕qT [GvO}0䚔U$6ĉ$Y'EIWp*ʔg0gʗȠ!+Sd%엻tO\ePjsbW+a8&iIf>kA=swIG4Yl֨;a|+l8ׄ6 E_zĊ6@&܎I1d"wϋxoQsJyxӁGc}rCJSve^NH~ DdB   S A ? 2wc@/@hġmYSi`!Kc@/@hġmYl ȽHxMQJ@ٴm`["7bPEL!BĂi؞" ڣx)g"|ap>aVj}MʑDYҎ%gUX)W,ȣ5=34,X}~ꖋ^2}Գ ĭa/:#^YY:wgM'g:xMJ/t`}UJJ-CH1pXxo3ŀۺ`w@K[f k;S_(QH DdB   S A ? 2wc@/@hġmYSk`!Kc@/@hġmYl ȽHxMQJ@ٴm`["7bPEL!BĂi؞" ڣx)g"|ap>aVj}MʑDYҎ%gUX)W,ȣ5=34,X}~ꖋ^2}Գ ĭa/:#^YY:wgM'g:xMJ/t`}UJJ-CH1pXxo3ŀۺ`w@K[f k;S_(QHDd B   S A ? 21"ȓOn`!1"ȓO:xxTKkQν>IR룊MV I!@HSݕ ҝPvJ0Н/e(yŤj/39߹y3 ȗа54~h4 5W񬤐+ŪVtCY4&,#š]Lr˜/ˬ/u3_Ď°}\L!%&n]8趘Cr LTg +|3AZˡZ,b Was1^l=`d 9KhҼ;$ԞQ^*ڼff[{<bO?["xE* Uzt>~1:<zi8SuNr7؊~5v&j^WH\S{^$ymh`]Aqb|䫡_-t2S(40gyer$N!Ÿ;kܹZ39t}kgNWQY Q%^px3lG[[{, ۨVj:;=7T,9b1R3ʻ֠e3S7fuslL-+V];uBNi&$X}Zߨm/iQFu`љa"&PmQ0-譾#}6ڤ-XSHbCD8,utO8~,iI'$_@g0ܗwq#R%S~SO; DdB  S A ? !2wc@/@hġmYSu`!Kc@/@hġmYl ȽHxMQJ@ٴm`["7bPEL!BĂi؞" ڣx)g"|ap>aVj}MʑDYҎ%gUX)W,ȣ5=34,X}~ꖋ^2}Գ ĭa/:#^YY:wgM'g:xMJ/t`}UJJ-CH1pXxo3ŀۺ`w@K[f k;S_(QH DdB  S A ? "2wc@/@hġmYSw`!Kc@/@hġmYl ȽHxMQJ@ٴm`["7bPEL!BĂi؞" ڣx)g"|ap>aVj}MʑDYҎ%gUX)W,ȣ5=34,X}~ꖋ^2}Գ ĭa/:#^YY:wgM'g:xMJ/t`}UJJ-CH1pXxo3ŀۺ`w@K[f k;S_(QH DdB  S A ? #2wc@/@hġmYSy`!Kc@/@hġmYl ȽHxMQJ@ٴm`["7bPEL!BĂi؞" ڣx)g"|ap>aVj}MʑDYҎ%gUX)W,ȣ5=34,X}~ꖋ^2}Գ ĭa/:#^YY:wgM'g:xMJ/t`}UJJ-CH1pXxo3ŀۺ`w@K[f k;S_(QHDd < % C A!? 24k#qE|H*{`!4k#qE|Hd_3(xݘKTAǿsΞAE]!"X)B2 2AEїXz$ Az,`{E?! S8̙9{ֺ;3fΙ9 B|X,u;&KYQkӒel :9|$w<$t7%>-rVm+7ej="#7gshåihbo5vz|AtOSɖ:+gl]"/Y.o4b~r'NVjxo2aI)F^,E,E,I,I,A,A,F,F,JLDh?^38{:΢NKdͷt4F+k|vBOE^۴~^){_~);7vu\S4#6F,E,E,I,I,A,A,F,F,J,J,k3;Wb= $6Il4b Ė-[#Fvlr EYVKrbd45s*9k=%uw+*1;ԳS8ߢN彩z}WiQ ]!וX⹓y}W#̾?+xY1緐,GdU 3e cR]X,k"zB.>ɲJV%R֪t ,ɲJVŰQ֪ a B"߲l;pj[fN.(+o͸g{wf2vV]߹v5 ~:]שgf"2S $.G+I"q"HG˜JraF#Lf>;Y\o09ܒ$fS..D\0ׂ]KI$rrf O,-r&OKJZ5?@ABCDEFGHIJKLMNRVj  $),27<AEIMQTW]behnt{~  #&*-03:=@EHLOTWZ]bfilqw{ !%),/5;>AGMPSWZ`cioruz !'*05V        !!""##$$%%&&''(())**++,,--..//00112233445566778899::;;<<==>>??@@AABBCCDDEEFFGGHHIIJJKKLLM                                      z x w   ~ } w v s r q p _ ^ P O N = ; 0 / ) ( ' &                                   X W V M  MN  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNRVj  $),27<AEIMQTW]behnt{~  #&*-03:=@EHLOTWZ]bfilqw{ !%),/5;>AGMPSWZ`cioruz !'*058      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()V06AOOOR ! ~w $v**.279y>@EPzUtZ^behjzoLrvzz"{{U||a}}ILMOQSTUWXZ\]_`bcdfjkmnpqrsuvw}A 9 6$x.(9^A4J~K:V`(nxBy|yy>zzzzE{{{{F|||}:}u}}}JNPRVY^aeghlotxz{|~j'O8yCz{{|}}K[iy+=?+=?/1L^` l ~ A S U ] o q  " "K]_w!!!!!!###&&&3)E)G)***,",$,---000888U>g>i>I2I4I5IMIOIBKZK\KcK{K}KKKKNOOO,O.OV::::::::::::::::::::::::::::::::::::::::::::::6=AHKR!!j~8:( /X2$QL5W A)02$py~史}굛 0e0e     A@ A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@Dx  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSRTUVWXYZ[\]^_`abcdedfghijklmlnopqt(  `  0? l = 0?D r ; 6; ?H `  0? 6`  0? $` s 0? ` t 0? *` u 0? &` v 0? ` w 0? (` x 0? "` y 0?  '` z 0?  U` { 0?  P` | 0?  fB } 6D?fB ~ 6D?fB  6D? fB  6D?fB  6D?`  0? `  0? `  0? `  0? `  0? `  0? `  0? `  0? `  0? `  0? `  0? `  0? fB  6D?fB  6D?fB  6D?fB  6D?`  0?  `  0? `  0? #`  0? "fB  6D?! 0@ ~"$$  %x   0#?"!b# #x   0$?~"V&$ $l2   0̙?#2!P$ l  0?#@!l$~B   BDjJ? #8##~B  B BDjJ?4$4$l   0?$&$$x   0% ?"X"$ $ %fB  6D?&`  0? '$@ #*   )x   0 ?%6 *   TL #<)x   #<)x x   0?#$B x   0!?%'  !x   0"?& <)D  "l  0?$ V&D  xB  <D1?%~% ~B  BDjJ?%P% ~B   BDjJ?% %x xB  <D?# # `  0? *`  0? +r  6? , fB  6D?-@ #~^+  .~   6?R%( ~   6?S#~$ ~   6?S%'H ~   6?S&^+x r  6?S$d&~B  BD1?S%B%B  HDjJ?S%%B   HDjJ?S%|%<~B  BD?S##`  0? /`  0? 0`  0? 2fB  6D?1@ # '(,  3x   0?# 'Z%( x   0?#**h%+ x   0?,&B+(, l   0?%F*&+rB  6D?%'%F*~B  BDjJ?%(%T*~B   BDjJ?%&+%,x   0?:&2(2() xB  <D?$\($*fB  6D?7`  0? 4`  0? 5H@ V4'9  8x   0?J"8>%9 x   0?5!<7 x   0?#`5'7 x   0?."V4l$5 l   0?7%F8l   0̙?x!6"7 ~B   BDjJ?"7%7~B  BDjJ? t7!t7 ~B  BDjJ?<"R5<" 7~B   BDjJ? "J7 "9`  0? 9@ R p)  :x   0?$ R' ~   6?TB$p&L  B   HDjJ?T%: %J  ~B   BD?T $4'  B  HDjJ?TB$%V ~B   BD?T^$ %.  ~B  B BD?T%@ D'.    <*?T !. 4$ *   <?T &V J)  xB  B <D?T& `'R xB   <D?n )xB   <D?))xB  B <D?R p)`  0? ;fB  6D?=.@ 4<)  <x   0 ?r&Z)6  ~   6?UB$& ~   6 ?U#4r&  B   HDjJ?UZ%Z%~B   BD?U#('XB  HDjJ?U#LZ%~B   BD?U#\L%~B  B BD?Uv%&   < ?U x!#l     < ?U &(  xB  B <D?U%&~B   BD?U^<)^~B   BD?U.)P.)l~B  B BD?U4<)^~B  BDjJ?Z%&(fB  @ 6D?AfB  @ 6D??fB  @ 6D?@`  0? >fB  6D?B@ @  *0' " Cx   0?&\(! ~   6 ?V#"V&#  ~   6?V"%~%'0' ~   6?V$R'! B   HDjJ?V:&":&%~B   BD?Vz$ (%B  HDjJ?V$ :&"~B   BD?V$ $,&%~B  B BD?VV&$'%   <?V X"%$'    <?V n'")B$ xB  B <D?Vr&#'#~B   BD?V '* '~B   BD?V**'~B  B BD?V * 'B  HDjJ?V:&N!2(" ~B ! B BDjJ?"%"&# ` # 0? FfB $ 6D?GL @  h,T*3 9 J~ '  6?W&,t)n."  0  <?W '/)*1 ~ &  6?W~#.>%0 ~ (  6?WZ%2'3 ~ )  6?W$h,D'. B *  HDjJ?Wr&2/r&B2~B +  BD?W$,-@(1B , HDjJ?W$-r&N/~B -  BD?W%0d&&2~B . B BD?W&81'&2 /  <?W "&2$3 xB 1 <D?W& 0'X0~B 2  BD?W!3T*3~B 3  BD?WF*,F*3~B 4 B BD?W h,T*3B 5 B HDjJ?W$\/r&0B 6 HDjJ?W&n.|'N/6` 7 0? KlB : @ <D?IlB < <D?E@ z ) Q Lx P  0? 2 "  x N  0?" %x  x M  0)? <  )l H  0?zb' l I  0̙? | T l J  0̙?"\ L%b xB K  <DjJ? "  ~B L  BDjJ?L% D' x O  0?V& )J  ` R 0? M` S 0? NfB T 6D?O@ 4\\(h b P~ ^  6?Y4t & ~ W  6'?YF#:&p '~ X  6&?Y\*# &r Y  6?Y\(h r Z  6̙?YT#8&r [  6̙?Y F# B ]  HDjJ?Y    V  B(̙?Y !" ( _  <̙? #p% ` ` 0? QfB a 6D?R` y 0? T` z 0? SfB { 6D?U N ~&% |  Wx }  0?0~ Z x ~  0?!n " x   0?"$&% x   0?" $J" x   0?,$! x   0?f"$ l   0?" l2   0?2!" l   0?&l   0?!<"F##xB   <D?r"rxB   <D?"6 "<"l2   0?f"""#l2   0?",~B  BDjJ?" ""~B   BDjJ?"#"%~B   BDjJ?r!rxB   <D?hhj!f2   s * 1?!8#D ~B   BDjJ?hhN!~B  BDjJ?hzh, @ :j/T*8  Vx   0?: 0!1 ~ w  6?Zf"j/$F1 ~ v  6?Z!4$5 ~ s  6?Z&7T*8 ~ r  6?Z&3(65 ~ q  6?Zb#0Z%l2 ~ p  6?Z&1 )2 r c  6?Z2:&3r2 d  6?Zh%l2&3r e  6?Z\!1#2r f  6?Z&(5|'6~B g  BD?Z$^2:&^2~B h  BD?Z&"3&(5r2 i  6?Z&5 '6r2 j  6?ZX"2"2B k HDjJ?Z&3&5B l  HDjJ?Z&6&8B m  HDjJ?Z"^2L%^2~B n  BD?Z"0"V4l2 o  0 1?Z,&1n'03B t  HDjJ?Z"2":4B u HDjJ?Z"f0"2~B  B BDjJ? P2"P2 @ 2)p  X~   6?]  ~   6?]$!2# ~   6?] b#n  ~   6?]v% )p ~   6?]%Z '  ~   6?] "$4 ~   6?]Z%'P r   6?]v$L  r2   6?]&$4%  r   6?] b" r   6?]$ :&N  ~B   BD?]"&$& ~B   BD?]%%  r2   6?]Z%` %  r2   6?]!!P B  HDjJ?]% %`  B   HDjJ?]% %  B   HDjJ?]x!& $& ~B   BD?]\!\!  l2   0 1?]$,& B   HDjJ?]\!P\!  B  HDjJ?]\!.\! B  B HDjJ?]N! `  0? Y`  0? Z fB  6D?\`  0? ^`  0? ]fB  6D?v @ "*  [x   0?@(*@  L ":*  ":*~   6?\2(* ~   6?\$& ~   6?\@(F* ~   6?\"d$ r2   6?\^$:x(T ~B   BD?\j(2j(0 ~B   BD?\l$l$ r   6?\#j"%r   6?\|'x)r2   6?\N((Xr2   6?\B$$JB   HDjJ?\j(<j(B  HDjJ?\j(6j(B   HDjJ?\l$Jl$B  HDjJ?\l$6l$e2   BtENGsIAQ 1? tt`Ttt`TA`Tt`TA`T$( r  6?_w x  <?_ u r  6?_t r  6?_s xB  HDjJ?_rrB  BD?_qxB  HDjJ?_prB  BD?_orB  @ BD?_nx  <?_ m lB  <D?_lrB  BD?_krB  @ BD?_jxB  HDjJ?_if2  6?_hr  6?_g r  6?_f f  6?_ef2  6?_dxB  HDjJ?_cxB  HDjJ?_b3rB  BD?_ar  6?_` 2  BǗENGpIgCQ 1?_ Ǘ!Ǘ`TǗ!Ǘ`TgC`T!Ǘ`TgC`T_ `  0? yfB  6D?x`  0? zfB  6D?{`  0? |B@ P$,)   }x   0?&,)  x   0?% ' x   0?P$JN(  l   0?$d&rB  B 6D?%% ~B  BDjJ?%% ~B   BDjJ?%%xB  <D?''N`  0? ~fB  6D? x@ R'*,&  ~   6?a'."T*# ~   6?an'l$*,& ~   6?b')! B  HDjJ?b'6 '"B   HDjJ?b'#'%~B  BD?b) ")#r2   6̙?bR'"'f"r2   6?bR't"'~#~B   BDjJ?b'b#'#~B  B BDjJ?b`'b#n'#q`  0? fB  6D? N@ !)**0  x   0?!,$(. ~L $**0  &$)**0~   6?c&^+)T- ~   6?c%T**, ~   6?c%/x(0 r   6?c$,&. xB  B <D?c%*%, B  HDjJ?c%*%, B   HDjJ?c%-%/ ~B  BD?c','. `  0? `  0? fB  6D? N ~&%   x   0?0~ Z x   0?!n " x   0?"$&% x   0?" $J" x   0?,$! x   0?f"$ l   0?" l2   0?2!" l   0?&l !  0?!<"F##xB "  <D?r"rxB #  <D?"6 "<"l2 $  0?f"""#l2 %  0?",~B & BDjJ?" ""~B '  BDjJ?"#"%~B (  BDjJ?r!rxB )  <D?hhj!f2 *  s * 1?!8#D ~B +  BDjJ?hhN!~B , BDjJ?hzh,` - 0? ` . 0? fB / 6D?  @ #%+/ G x F  0?%*'+ x E  0?) ++, x D  0?&4+t), x C  0?#+$V- ~ 1  6?dJ)&+\( ~ 3  6?ej(-+j/ ~ 4  6?e^$-'/ ~ 5  6?eX)f)^+* ~ 6  6?e~#)%+ r2 7  6?eh%V&)p* ~B 8  BD?et)N(t)L, ~B 9  BD? E. Tippens92lMicrosoft Word 8.0@F@Xp9@Tc@*hT C ՜.+,D՜.+,8 hp  SPSU ";S1  Chapter 2 TitleDocumentSummaryInformation8kCompObjsj 6> _PID_GUIDAN{3ECA96CA-F670-11D2-B9D0-44455354616F}  FMicrosoft Word Document MSWordDocWord.Document.89qev%$(v%", r :  6?ez$+&- r ;  6?e(P+**, r2 <  6?ef)+)0, r2 =  6?e0%",v%v, B >  HDjJ?e),)- B ? HDjJ?e)*)+ B @  HDjJ?eZ%v,Z%(. B A HDjJ?eZ%b*Z%", 2 B  BtENGsIAQ 1?d tt`Ttt`TA`Tt`TA`T%%)5' ` H 0? fB J @ 6D?fB K @ 6D?fB L 6D?` ` 0? L @ !-P+^4 b ~ N  6?f$\/('81  O  <?f (X0*1 ~ P  6?f'H-)/ ~ Q  6?fV&2(^4 ~ R  6?f%-@(. B S  HDjJ?fn'/n'2~B T  BD?f%-<)42B U HDjJ?f%(.n'/~B V  BD?f&81`'2~B W B BD?f'1(2 X  <?f #2%H4 xB Y <D?f'0(1~B Z  BD?f":4P+:4~B [  BD?fB+,-B+H4~B \ B BD?f!-P+:4B ] HDjJ?fn'.X)0B ^ B HDjJ?fd&/|'0x _  0?"/$0 xB a <D?~#/$0 @ ) | x z  0?^f":  ~ d  6?g*#% ~ e  6?g! h%<  ~ f  6?gv%F' ~ g  6?g'( )  ~ h  6?g&$^&  ~ i  6?g`')  r j  6?g| r & r2 k  6?g,& 'n r l  6?g "0 $r r m  6?g& @(~B n  BD?g$ & ~B o  BD?g' ' r2 p  6?g`'. ' r2 q  6?g# # B r HDjJ?g'n '. B s  HDjJ?g' 'B t  HDjJ?g~# & ~B u  BD?gb#^b# l2 v  0 1?g& 2( B w  HDjJ?gb# b# B x HDjJ?gb#b# ~B y B BDjJ?2! F# ` { 0? D`  0?  @ zl+X"  ~   6?hR " ~   6?h~#& ~   6?h "%V ~   6?h' l+X" ~   6?h'B) ~   6?hz$xr& ~   6?h'8*8 r   6?h R'4r2   6?h&'r   6?ht"J$r   6?h6'(6 ~B   BD?h0%R'~B   BD?h''r2   6?h'H$(r2   6?hp##8B  HDjJ?h''HB   HDjJ?h''!B   HDjJ?h#d&~B   BD?h#x#l2   0 1?hD'(B   HDjJ?h#8#B  HDjJ?h##B  B HDjJ?h!# rB  B 6D?D 2! <"rB  B 6D?z$!0<"fB  6D? @ &(,@0  ~   6 ?'h-X). ~   6 ?|'8+J), ~   6 ?|'(J)f*      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ ~   6 ?)l,,- ~   6 ?).,$0 ~   6 ?)),b+ rB   6D?f)@)f)6/ l   0?&(+2) l   0̙?(X**b+ l   0̙?(,*-l   0̙?(.F*@0`  0? `  0? `  0?  `  0?  `  0? `  0?  @ !( p* ~   6 ?! &    < ?i$>&    < ?i%*&    < ?i6' )    < ?in'8*    < ?i'p*    < ?in'8*~ xB   <D?i '( 'R r   6̙?id&t'~ r   6̙?iH&0'dr   6̙?iH&'| ~B  BDjJ? ' 'txB  <D?$J$fB  6D?fB  6D?`  0? * @ 8#**2  x   0?B$p1*2 ZL dz+&2  8#*T*1x   0?d-!/ x   0? z+#r- x   0?"+>%- x   0?2!0b#1 xB  <D? 1L%1xB  <D?>%,>%1 xB  <D? h,Z%1 l2   0?8#.#. ~B   BDjJ?p#.p#2~B  BDjJ?j!-p#.xB   <D?~#.d&1x   0?P$-&@/ rB  6D?#.$/~B  BDjJ?T#d-$.xB  B <D?#<0%P2~B  B BD1?!.!/`  0? `  0? @ ` )  x   0? " x   0?<0$ x   0?d&)$ x   0?V&$( x   0? 4 x   0?V&( x   0?`( x   0?"f $  x   0?t  x   0?#& x   0?fNv l   0?h%Ll   0? "l2   0?<l2   0?$&V&xB   <D?FxB   <D? "%xB   <D?<L<xB   <D?H&H&Jl2   0? !Pl2   0?&6&l2   0?`~B  BDjJ?<<`~B  BDjJ?d&d&6~B   BDjJ?JJt~B   BDjJ?d&d&<~B   BDjJ? F#~B  B BDjJ? ^x   0?"` xB   <D?  l2   0? $!B ~B  BDjJ? J  ~B   BDjJ? ^  `2  B c $ ?p `2   c $ ?%& x   0?( " `  0? fB  6D? @ b,$ g ~ =  6?k#8% ~ ?  6?kf)@!," ~ @  6?kX)&+ ~ A  6?k4 ~ B  6?kX)d+! ~ C  6?kb! ~ D  6?k%' ~ E  6?k" ~ F  6~?k&")# ~~ G  6}?k><"N!# }r H  6?kj( r I  6?k""% r2 J  6?k>R  r2 K  6?k'X)`  ~B L  BD?kH" ~B M  BD?k"%( ~B N  BD?k>>$ ~B O  BD?kJ)rJ)# r2 P  6?k#Z$ r2 Q  6?k )!) " r2 R  6?k!J" B S HDjJ?k>R >! B T HDjJ?kf)( f)! B U  HDjJ?kLf"L# B V  HDjJ?kf)."f)# B W  HDjJ?k#H& B X B HDjJ?k!# ~ Y  6|?k" %! |~B Z  BD?k#8#  r2 [  6?k#L&$ B \ HDjJ?k##L B ]  HDjJ?k##`  f2 ^ B s * ?kH f2 _  s * ?k()r ~ `  6{?k"!"%# {B a  HDjJ?k#L% ~ c  6z?k%'4 zxB e B <D?k$%` h 0? ` i 0? ` j 0? N@ d & | x z  0u?#d v%  ux x  0v?! $  vx w  0w?6 f f"^ wx v  0x?!H&$ xx u  0y?"%> yx n  0?N!: xB k  <D?&xB l <D?&| &xB m <D?"| &l2 o  0?" b#~B p  BDjJ?# #~B q BDjJ?! # ~B r B BDjJ?! #xB s  <D?# &xB t B <D?8#%xB y <D?# Z%  fB } @ 6D?fB ~ @ 6D?fB  @ 6D?`  0? fB  6D? @ "**3  ~   6n?q6'p1)03 n~   6l?qZ%+'- l~   6m?qN(-*@/ m~   6o?q%@/D'0 o~   6t?q#1&3! t~   6s?q'**, s~   6r?q"z+"%r- r~   6p?q8#0h%1 p~B  BD?q"1'1~B  BD?q$(,$(1~B  BD?q"h,`'1r2   6?q>%.%.B   HDjJ?qv%.v%2B  HDjJ?qp#-v%.~B   BD?q%.j(1B  HDjJ?q%:-&.!~B  B BD?q%<0'P2r2   6?q 'v,2(-B  HDjJ?q$(-$(2/B  B HDjJ?q2(/2(0/r2   6?q'2/N(/f2   s * ?q`'+(, `  0? fB  6D?8 N "*#   x   0k?Z%'^ kx   0j?N(z* jx   0i?( *t" ix   0h?%D'|  hx   0g?#!'# gx   0f?'*p fx   0e?"X"%P ex   0d?8#n h%! dxB  <D?"!'!xB  <D?$(p$(!xB  <D?"F`'!l2   0?>%h%~B   BDjJ?v%v%f"~B  BDjJ?p#v%xB   <D?%j( ~B  BDjJ?%&vxB  B <D?% '."l2   0? 'T2(z~B  BDjJ?$($(~B  B BDjJ?2(d2( l2   0?'N(`2   c $ ?`'(`  0?  @ | (X  ~   6q?n| &" q~   6c?p0%' c~   6b?pT# %* b~   6a?pH&F( a~   6`?p#>%H `~   6_?p!$X _~   6^?p% (<  ^~   6]?p $ # ]~   6\?p2!:b# \~B  BD?p `%n~B  BD?p&< &n~B  BD?p  Z%`r2   6?p8#4#B   HDjJ?pp#zp#2B  HDjJ?pj! p#z~B   BD?p~#d&B  HDjJ?p~# z$B~B  B BD?p#%r2   6?p% ,&FB  HDjJ?p&p&B  B HDjJ?p,&0,&r2   6?p%H&Lf2   s * ?pZ% & ~B  B BDjJ?J"Pp#`  0?  @ N!(j(  x   0[?N!"#z$ [x   0Z?&,&(' Zx   0Y?4$ %<" Yx   0X?('X"(# Xx   0W?##&Z% Wx   0V?"&%j( Vx   0U?&(N! Ux   0T?!6 #." Tx   0S?"L%B$& SxB  <D?!r&&&xB  <D?&N!&&xB  <D?!$!:&r&l2   0?$F#l$#~B   BDjJ?P$#P$D'~B  BDjJ?J"!P$#xB   <D?^$#D'%~B  BDjJ?B$!%#xB  B <D?z$$% 'l2   0?%2! 'X"~B  BDjJ?&"&#~B  B BDjJ? 'B$ '%l2   0?&#('^$`2   c $ ?:& n'!~B  BDjJ?P$""%b# rB  6D?#"l$T#`  0? `  0? (6    8 j+(  3 @. `^R^S^R^ST   C A R?j+(T   # Qbr&P$' QTB  C DH&$`B   c $DjJ0#8##`B  c $DjJF# T##Z   3 PF# %" PZ   3 O,#!L% OHB  C DfB  6D?B S  ?o      *  B  v    ^ _     I)**9:w  j k ? @ e 4T<-pwt;=8gLywabW X !!e"f"g"h"i"j"k"l"m"n"o"p"q"r"s"t"u"v"w"x"y"z"{"|"~"##$j%l%&&M'N''}(()*** , ,z,,$-j----.i/q0`33m7p788 9::;|;;C<D<<T>:?f t Jt Rt 6t #t Dt :$t ($t t@t RL t '#'t Yt /'t R"t Jxt ($(t ,t 0 Lt t v#t n$t aYt 7t nN%,t vt t 8 t ,`$t |n%t nt p>t `$t 4dHt d#>t ~t ,b\t Zt n$t H#t ,$"*t ,#zt t B#t 6$6t * t \+ Qt R 5t h ,'t A$At" "|$/ t= t< 1t# jt$ .2%.t; xt:  \"t9 Zt$t7 }tQ n$tR btS #jtT 0j%>tb ~$t` |ta 0@%0tz h=ty <C$t{ 3%3t $ t| x&t Xr#t d@t Bft N% t $t  t >rP$t c"$t #z &t $$ t ($$($t ($b($>t #D$Tt #t$t $&t #&t "$t b !t r#, t , 6$, t !t r: t p !t *F t T t ""&t T T t &!t <L"H t z!J#t %t "t  $ t L Bt @ t HR$t  ot N*# t ! t  #5t 5:#5t k"t V#t @%t V(t ?R$?t v 't  & t. h=t- <C$t/ `$tG n.&W tJ %tK 'tb V% tL -$-tH kt` 4Xt| &6$ t{  t Fm% @ N Rt,$t 1%o t ($t &Tt 8 J&t B!Zt Zt Ft$pt $Tt P @t Ht @($@t t <$<t ."& t @%\t Pt ctF#Ft 2%,t ti Jtj Bt $tg f& th t|  V# t P1It~ #;t} $t <Jt $ t "tt H|$t (|$O t t %t v"t 0Pt rU$# t &T t;=@D|~ikDFQS####$$$$"&*&&&)#)@*B*X*[*......P0R0^8`8}888888< <====>>>>>>!>%>4>8>=>A>P>R>z@|@@@AACCFFHHHHIIVIXIIIJK$K&KLLLLLLLLNNNNNNNNxO{O~OOOOOOPPQQ QQQQ/Q1Q2RRRSS!S$S6S9SFSISzS}SSSTTUUUUV+@+@2La l A V ] r e e f f 3#(*K`w!!!!##&"&&&3)H)**,%,--{00001p7s7u78899f:f:::::|;};;;;;<<C<C<<<U>j>A?B?AAPAAAAAEEEEGGGGIPIKJMJBK]KcK~KKKLLLLLLLL9M9MgMnM|M|MMMN/OQ1R2R2R:R;R=RQRhRpRsR~RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRSS S S S SSSSSSSSS S!S&S'S)S*S.S/S1S2S5S6S:S;S?S@SBSCSESFSKSLSPSQSSSTSWSXScSdShSiSmSnSpSqSsStSvSwSySzSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSTTTTT T TTTTTTTTT!T"T2T3T6T7T9T:TUAUBUDUEUHUIULUMUOUPUUUVUZU[U]U^UbUcUkUlUpUqUsUtUyUzUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUVVVVVV V V VVVVVVVVVV!V"V$V%V'V(V,V-V1V2V4V5V8V9V