Antwoordenboek statica

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1. 11. Round off the following numbers to three significant figures: (a) 4.65735 m, (b) 55.578 s, (c) 4555 N, and (d) 2768 kg. . 2. 1 . Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) , (b) , and (c) .MN>(kg # ms)Mg>mN kN>ms SOLUTION a) Ans. b) Ans. c) Ans.MN>(kg # ms) = (106 ) N kg # (10-3 ) s = (109 ) N kg # s = GN>(kg # s) Mg>mN = (106 ) g (10-3 ) N = (109 ) g N = Gg>N kN>ms = (103 ) N (10-6 ) s = (109 ) N s = GN>s 2 3. 1 . SOLUTION a) Ans. b) Ans. c) Ans. d) Ans.km # mN = 10 3 m 10 -6 N = 10 -3 m = mm ks>mg = 11023 s 1102-6 kg = 11029 s kg = Gs>kg mkm = 1102-6 11023 m = 1102-3 m = mm m>ms = m 1102-3 s = 11023 m s = km>s Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) (b) (c) ks and (d) km # mN.mkm, # N # N >mg, m>ms, 3 4. A concrete column has diameter d and length L. If the density (mass/volume) of concrete is U, determine the weight of the column in . Units Used: Mg 10 3 kg kip 10 3 lb Given: d 350 mm L 2 m U 2.45 Mg m 3 Solution: V S d 2 2 L V W U V W 1-4 newtons 0.19242 m 3 1 2 g 0.471 (103 ) (9.81) 4.62 N(103 ) 4.62kN . Ans. 5. 15. Represent each of the following combinations of units in the correct SI form: (a) , (b) , and (c) .mN>(kg # ms) N>mmMg>ms . . . 6. 1 . Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) ,(b) ,and (c) .>(kg s)#Mg>kN> 6 ms kN kN ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) MN / b) Mg / kN kg / N c) kN / (kg GN kg kgkg N a) kN / ms = = = = = = = = Ans. Ans. 3 6 3 6 3 3 3 9 6 10 10 N s10 s 10 g 10 g N10 N 10 N 10 N s) = / ( s) s10 s Ans. m m s 7. 1 . A rocket has a mass of 3.529(10 ) kg on earth. Specify (a) its mass in SI units and (b) its weight in SI units. If the rocket is on the moon, where the acceleration due to gravity is , determine to three significant figures (c) its weight in SI units and (d) its mass in SI units. gm = . >s2 SOLUTION 7 6 1 6 m1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) 6 2 2 a) 3.529 10 kg = 3.53Gg b) m / s kg m / s c) m / s N d) Sin = = = = = = = = = = = Ans. 6 6 2 6 6 2 2 3.529 10 kg 9.81 34.619 10 34.6MN 3.529 10 kg 1.61 5.682 10 5.68MN Or 1.61m / s (34.619MN) 5.68MN 9.81m / s e m m m m e W mg W mg g W W g Ans. Ans. ce the mass is independent of tis location, then = = 3.53Ggm em m Ans. 8. 1 . SOLUTION a) Ans. b) Ans.(35 mm)2 (48 kg)3 = C35A10-3 B mD2 (48 kg)3 = 135 m2 kg3 = 8.53A103 B m>kg2 = 8.53 km>kg2 (0.631 Mm) 2 = a 0.631A106 B m (8.60)2 kg2 b = 8532 m kg2 Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a) , (b) .(35 mm)2 (48 kg)3 (0.631 Mm)>(8.60 kg)2 # >(8.60 kg) 8 9. 19. Determine the mass in kilograms of an object that has a weight of (a) 0 mN, (b) 50 kN, and (c) 0 MN. Express the answer to three significant figures. 5 2 8 Applying Eq. 1 3, we have ( ) ( ) ( ) m / s a) = g m / s m / s b) = Mg m / s m / s c) = g m / s m m m = = = = = = Ans. Ans. 3 2 2 3 2 2 6 2 2 50 10 kg 5.10 9.81 250 10 kg 25.5 9.81 80 10 kg 8.15 G 9.81 W g W g W g Ans. 10. 11 . Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a) , (b) , and (c) .(400 m)3 (0.005 mm)2 (200 kN)2 0 . . . 11. 11 . Evaluate each of the following and express with an appropriate prefix: (a) (b) and (c) 1230 m23 . 10.002 mg22 ,1430 kg22 , SOLUTION a) Ans. b) Ans. c) Ans.230 m 3 = 0.23 103 m 3 = 0.0122 km3 10.002 mg22 = 32110-6 2 g42 = 4 mg2 1430 kg22 = 0.1851106 2 kg2 = 0.185 Mg2 1 12. 11 . SOLUTION Applying Eq. 13, we have a) Ans. b) Ans. c) Ans.m = W g = 60A106 B kg # m>s2 9.81 m>s2 = 6.12 Gg m = W g = 150A103 B kg # m>s2 9.81 m>s2 = 15.3 Mg m = W g = 20A10-3 B kg # m>s2 9.81 m>s2 = 2.04 g Determine the mass of an object that has a weight of (a) 20 mN, (b) 150 kN, and (c) 60 MN. Express the answer to three significant figures. 2 13. 1- Represent each of the following with SI units having an appropriate prefix: (a) S1, (b) S2, (c) S3. Units Used: kg 1000 g ms 10 3 s kN 10 3 N Given: S1 8653 ms S2 8368 N S3 0.893 kg Solution: a( ) S1 8.653 s b( ) S2 8.368 kN c( ) S3 893g 13. Ans. Ans. Ans. 14. 11 . Evaluate (204 mm)(0.00457 kg) (34.6 N) to three significant figures and express the answer in SI units using an appropriate prefix. 4 . 15. 1 . Two particles have a mass of 8 kg and 12 kg, respectively. If they are 800 mm apart, determine the force of gravity acting between them. Compare this result with the weight of each particle. SOLUTION Where Ans. Ans. Ans.W2 = 12(9.81) = 118 N W1 = 8(9.81) = 78.5 N F = 66.73A10-12 B B 8(12) (0.8)2 R = 10.0A10-9 B N = 10.0 nN G = 66.73A10-12 B m3 (kg # s2 ) F = G m1 m2 r2 15 16. 1 . If a man weighs on earth, specify (a) his mass in kilograms If the man is on the moon, where the acceleration due to gravity is determine ( ) his weight in and ( ) his mass in kilograms. gm = . s ,2 SOLUTION a) Ans. Ans. Ans.m = = 70. kg W = c d = m = = . 16 690 newtons . 1 61 m b cnewtons 690 9.81 70 3 kg b) 690 1.61 9.81 113 N c) 690 9.81 3 17. . . 18. SOLUTION The parallelogram law of addition and the triangular rule are shown in Figs. a and b, respectively. Applying the law of consines to Fig. b, Ans. This yields Thus, the direction of angle of measured counterclockwise from the positive axis, is Ans.f = a + 60 = 95.19 + 60 = 155 x FRf sin a 700 = sin 45 497.01 a = 95.19 = 497.01 N = 497 N FR = 27002 + 4502 - 2(700)(450) cos 45 22. If and , determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive x axis. F = 450 Nu = 60 x y 700 N F u 15 19. SOLUTION The parallelogram law of addition and the triangular rule are shown in Figs. a and b, respectively. Applying the law of cosines to Fig. b, Ans. Applying the law of sines to Fig. b, and using this result, yields Ans.u = 45.2 sin (90 + u) 700 = sin 105 959.78 = 959.78 N = 960 N F = 25002 + 7002 - 2(500)(700) cos 105 23. If the magnitude of the resultant force is to be 500 N, directed along the positive y axis, determine the magnitude of force F and its direction .u x y 700 N F u 15 20. 24. Determine the magnitude of the resultant force and its direction, measured clockwise from the positive u axis. FR = F1 + F2 SOLUTION Ans. Ans.f = 55.40 + 30 = 85.4 u = 55.40 605.1 sin 95 = 500 sin u FR = 2(300)2 + (500)2 - 2(300)(500) cos 95 = 605.1 = 605 N u v 70 30 45 F1 300 N F2 500 N 21. 25. SOLUTION Ans. Ans.F1v = 160 N F1v sin 30 = 300 sin 110 F1u = 205 N F1u sin 40 = 300 sin 110 Resolve the force into components acting along the u and v axes and determine the magnitudes of the components. F1 u v 70 30 45 F1 300 N F2 500 N 22. 26. Resolve the force into components acting along the u and v axes and determine the magnitudes of the components. F2 SOLUTION Ans. Ans.F2v = 482 N F2v sin 65 = 500 sin 70 F2u = 376 N F2u sin 45 = 500 sin 70 u v 70 30 45 F1 300 N F2 500 N 23. 27. If and the resultant force acts along the positive u axis, determine the magnitude of the resultant force and the angle .u FB = 2 kN y x u B FA 3 kN FB A u 30 24. 28. If the resultant force is required to act along the positive u axis and have a magnitude of 5 kN, determine the required magnitude of FB and its direction .u y x u B FA 3 kN FB A u 30 25. 29. Resolve F1 into components along the u and axes and determine the magnitudes of these components. v SOLUTION Sine law: Ans. Ans. F1u sin 45 = 250 sin 105 F1u = 183 N F1v sin 30 = 250 sin 105 F1v = 129 N F1 250 N F2 150 N u v 30 30 105 26. 210. SOLUTION Sine law: Ans. Ans. F2u sin 75 = 150 sin 75 F2u = 150 N F2v sin 30 = 150 sin 75 F2v = 77.6 N Resolve F2 into components along the u and axes and determine the magnitudes of these components. v F1 250 N F2 150 N u v 30 30 105 27. . . 28. . . . 29. x x 21 . The device is used for surgical replacement of the knee joint. If the force acting along the leg is 360 N, determine its components along the x and y axes. 60 360 N 10 y x y x 3 . . 30. 21 . The device is used for surgical replacement of the knee joint. If the force acting along the leg is 360 N, determine its components along the x and y axes. 60 360 N 10 y x y x 4 . . 31. 215. SOLUTION Parallelogram Law: The parallelogram law of addition is shown in Fig. a. Trigonometry: Using law of cosines (Fig. b), we have Ans. The angle can be determined using law of sines (Fig. b). Thus, the direction of FR measured from the x axis is Ans.f = 33.16 - 30 = 3.16 f u = 33.16 sin u = 0.5470 sin u 6 = sin 100 10.80 u = 10.80 kN = 10.8 kN FR = 282 + 62 - 2(8)(6) cos 100 The plate is subjected to the two forces at A and B as shown. If , determine the magnitude of the resultant of these two forces and its direction measured clockwise from the horizontal. u = 60 A B FA 8 kN FB 6 kN 40 u 32. 216. Determine the angle of for connecting member A to the plate so that the resultant force of FA and FB is directed horizontally to the right. Also, what is the magnitude of the resultant force? u SOLUTION Parallelogram Law: The parallelogram law of addition is shown in Fig. a. Trigonometry: Using law of sines (Fig .b), we have Ans. From the triangle, . Thus, using law of cosines, the magnitude of FR is Ans.= 10.4 kN FR = 282 + 62 - 2(8)(6) cos 94.93 f = 180 - (90 - 54.93) - 50 = 94.93 u = 54.93 = 54.9 sin (90 - u) = 0.5745 sin (90 - u) 6 = sin 50 8 A B FA 8 kN FB 6 kN 40 u 33. . . 34. . . . 35. 219. SOLUTION Ans. Ans. 19.18 sin 1.47 = 30.85 sin u ; u = 2.37 FR = 2(30.85)2 + (50)2 - 2(30.85)(50) cos 1.47 = 19.18 = 19.2 N 30.85 sin 73.13 = 30 sin (70 - u ) ; u = 1.47 F = 2(20)2 + (30)2 - 2(20)(30) cos 73.13 = 30.85 N Determine the magnitude and direction of the resultant of the three forces by first finding the resultant a