Archives: Solution Manual

CHAPTER 5 PROBLEM 5.1 Locate the centroid of the plane area shown. SOLUTION Area 1: Rectangle 72 mm by 45 mm. Area 2: Triangle b = 27 mm, h = 45 mm. 2 ,mmA ,mm x ,mm y 3 ,mmxA […]

PROBLEM 4.152 The rectangular plate shown weighs 75 lb and is held in the position shown by hinges at A and B and by cable EF. Assuming that the hinge at B does not exert any axial thrust, determine (a) […]

PROBLEM 4.142 A 3200-lb forklift truck is used to lift a 1700-lb crate. Determine the reaction at each of the two (a) front wheels A, (b) rear wheels B. SOLUTION Free-Body Diagram: (a) Front wheels: 0: (1700 lb)(52 in.) (3200 […]

PROBLEM 4.134 (Continued) // (0.5 m) ; (1 m) ; (268 N) BA CA ririPj To eliminate the reactions at A and D, we shall write /// 0: ( ) ( ) ( ) 0 AD AD B A BG […]

PROBLEM 4.129 (Continued) 0: ( ) ( ) 0 xxCFBExDGx FATTT     12 24 600 N 975 N 625 N 0 13 25 x A      2100 N x A 0: ( ) […]

PROBLEM 4.124 Solve Problem 4.123, assuming that the 1.8- kN load is applied at C. PROBLEM 4.123 The rigid L-shaped member ABC is supported by a ball-and- socket joint at A and by three cables. If a 1.8- kN load […]

PROBLEM 4.118 (Continued) 0: 0 CE  FABTW Coefficient of i: 270 (621.31) 0 855 x A 196.2 N x A Coefficient of j: 675 113.186 (621.31) 981 0 855 y A  377.3 N y A Coefficient of k: […]

PROBLEM 4.113 (Continued) 0.90 0.88182(19.6203 N) 0; 19.2240 N xx AA  j: 0.90 44.145 0.180(19.6203 N) 0; 45.123 N yy AA i: 19.62 N CD F (19.22N) (45.1 N)  Aij  0: cos11.5370 0 19.2240 19.6203cos11.5370 0 0 […]

PROBLEM 4.108 (Continued) From Eq. (2): 0.92857(2.80) 2.600 kN AD T 2.60 kN AD T  0.8 0.8 0: (2.6 kN) (2.8 kN) 0 0 2.6 2.8 0.6 1.2 0: (2.6 kN) (2.8 kN) (3.6 kN) 0 1.800 kN 2.6 […]

PROBLEM 4.103 The 24-lb square plate shown is supported by three vertical wires. Determine (a) the tension in each wire when 10a  in., (b) the value of a for which the tension in each wire is 8 lb. SOLUTION […]

PROBLEM 4.94 A 48–ft sheet of plywood weighing 34 lb has been temporarily placed among three pipe supports. The lower edge of the sheet rests on small collars at A and B and its upper edge leans against pipe C. […]

PROBLEM 4.85 An 8-kg slender rod of length L is attached to collars that can slide freely along the guides shown. Knowing that the rod is in equilibrium and that   30, determine (a) the angle  that the […]

PROBLEM 4.76 Solve Problem 4.75, assuming that the 170-N force applied at B is horizontal and directed to the left. PROBLEM 4.75 Rod AB is supported by a pin and bracket at A and rests against a frictionless peg at […]

PROBLEM 4.68 (Continued) Force Triangle Law of sines: 150 lb sin 29.745 sin116.565 sin33.690 CD   270.42 lb, 167.704 lb C D   270 lbC 56.3 ; 167.7 lbD26.6  Copyright © McGraw-Hill Education. Permission required for reproduction […]

PROBLEM 4.60 The bracket ABC can be supported in the eight different ways shown. All connections consist of smooth pins, rollers, or short links. For each case, answer the questions listed in Problem 4.59, and, wherever possible, compute the reactions, […]

PROBLEM 4.53 A slender rod AB, of weight W, is attached to blocks A and B, which move freely in the guides shown. The blocks are connected by an elastic cord that passes over a pulley at C. (a) Express […]

PROBLEM 4.43 (Continued) (b) 0: (3600 lb)(12 ft) (1200 lb)(6.5 ft) 0 EE MM     51,000 lb ft E M   00 xx FE   0: 3600 lb 1200 lb 0 yy FE   […]

PROBLEM 4.35 Bar AC supports two 400-N loads as shown. Rollers at A and C rest against frictionless surfaces and a cable BD is attached at B. Determine (a) the tension in cable BD, (b) the reaction at A, (c) […]

PROBLEM 4.27 Determine the reactions at A and B when (a)   0, (b)   90, (c)   30. SOLUTION (a) 0   0: (20 in.) 75 lb(10 in.) 0 37.5 lb A MB B  […]

PROBLEM 4.19 The bracket BCD is hinged at C and attached to a control cable at B. For the loading shown, determine (a) the tension in the cable, (b) the reaction at C. SOLUTION At B: 0.18 m 0.24 m […]

PROBLEM 4.9 Three loads are applied as shown to a light beam supported by cables attached at B and D. Neglecting the weight of the beam, determine the range of values of Q for which neither cable becomes slack when […]

CHAPTER 4 PROBLEM 4.1 A gardener uses a 60-N wheelbarrow to transport a 250-N bag of fertilizer. What force must she exert on each handle? SOLUTION Free-Body Diagram:   0: (2 )(1m) (60 N)(0.15 m) (250 N)(0.3 m) 0 […]

PROBLEM 3.156 (Continued) (b) 21 (42 42 49 ) N== +−FF i j k or 2 (42.0 N) (42.0 N) (49.0 N)=+−F ijk  2 /11 2 (0.1350) 0.03 0.07 0.31 0.0233 0 (31 N m) 0.155000 42 42 49 […]

PROBLEM 3.147 A 300–N force P is applied at Point A of the bell crank shown. (a) Compute the moment of the force P about O by resolving it into horizontal and vertical components. (b) Using the result of part […]

PROBLEM 3.142* (Continued) Substituting ? 160 ( 42 18 8 ) ( 3 ) 0 11 − + − ⋅ −− + =i j k ij k or ? 160 [( 42)( 1) (18)( 1) ( 8)(3)] 0 11 − […]

PROBLEM 3.138* Two bolts at A and B are tightened by applying the forces and couples shown. Replace the two wrenches with a single equivalent wrench and determine (a) the resultant R, (b) the pitch of the single equivalent wrench, […]

PROBLEM 3.131 A concrete foundation mat of 5–m radius supports four equally spaced columns, each of which is located 4 m from the center of the mat. Determine the magnitude and the point of application of the resultant of the […]

PROBLEM 3.122 In order to unscrew the tapped faucet A, a plumber uses two pipe wrenches as shown. By exerting a 40–lb force on each wrench, at a distance of 10 in. from the axis of the pipe and in […]

PROBLEM 3.113 A truss supports the loading shown. Determine the equivalent force acting on the truss and the point of intersection of its line of action with a line drawn through Points A and G. SOLUTION We have (240 lb)(cos70 […]

PROBLEM 3.105 The weights of two children sitting at ends A and B of a seesaw are 84 lb and 64 lb, respectively. Where should a third child sit so that the resultant of the weights of the three children […]

PROBLEM 3.96 To keep a door closed, a wooden stick is wedged between the floor and the doorknob. The stick exerts at B a 175–N force directed along line AB. Replace that force with an equivalent force–couple system at C. […]

PROBLEM 3.86 A worker tries to move a rock by applying a 360–N force to a steel bar as shown. If two workers attempt to move the same rock by applying a force at A and a parallel force at […]

PROBLEM 3.78 Replace the two couples shown with a single equivalent couple, specifying its magnitude and the direction of its axis. SOLUTION Replace the couple in the ABCD plane with two couples P and Q shown: 160 mm (50 N) […]

PROBLEM 3.68 In Problem 3.59, determine the perpendicular distance between cable AE and the line joining Points D and B. PROBLEM 3.59 The triangular plate ABC is supported by ball–and–socket joints at B and D and is held in the […]

PROBLEM 3.58 In Problem 3.57, determine the moment about the diagonal AD of the force exerted on the frame by portion BG of the cable. PROBLEM 3.57 The frame ACD is hinged at A and D and is supported by […]

PROBLEM 3.49 To loosen a frozen valve, a force F of magnitude 70 lb is applied to the handle of the valve. Knowing that 25 , θ = ° Mx 61lb ft,=−⋅ and 43 lb ft, z M=−⋅ determine φ […]

PROBLEM 3.39 Knowing that the tension in cable AC is 280 lb, determine (a) the angle between cable AC and the boom AB, (b) the projection on AB of the force exerted by cable AC at point A. SOLUTION (a) […]

PROBLEM 3.29 In Prob. 3.24, determine the perpendicular distance from point B to wire AE. PROBLEM 3.24 The wire AE is stretched between the corners A and E of a bent plate. Knowing that the tension in the wire is […]

PROBLEM 3.19 Determine the moment about the origin O of the force F = 4i − 3j + 5k that acts at a Point A. Assume that the position vector of A is (a) r = 2i + 3j − […]

PROBLEM 3.9 Rod AB is held in place by the cord AC. Knowing that the tension in the cord is 1350 N and that c = 360 mm, determine the moment about B of the force exerted by the cord […]

CHAPTER 3 PROBLEM 3.1 A crate of mass 80 kg is held in the position shown. Determine (a) the moment produced by the weight W of the crate about E, (b) the smallest force applied at B that creates a […]

PROBLEM 2.F4 A chairlift has been stopped in the position shown. Knowing that each chair weighs 250 N and that the skier in chair E weighs 765 N, draw the free–body diagrams needed to determine the weight of the skier […]

PROBLEM 2.133 The end of the coaxial cable AE is attached to the pole AB, which is strengthened by the guy wires AC and AD. Knowing that the tension in wire AC is 120 lb, determine (a) the components of […]

PROBLEM 2.124 Knowing that the tension in cable AE of Prob. 2.123 is 75 lb, determine (a) the magnitude of the load P, (b) the tension in cables BAC and AD. PROBLEM 2.123 Cable BAC passes through a frictionless ring […]

PROBLEM 2.117 For the cable system of Problems 2.107 and 2.108, determine the tension in each cable knowing that 2880 NP= and 576 N.Q= SOLUTION See Problem 2.116 for the analysis leading to the linear algebraic Equations (1), (2), and […]

PROBLEM 2.111 A transmission tower is held by three guy wires attached to a pin at A and anchored by bolts at B, C, and D. If the tension in wire AB is 840 lb, determine the vertical force P […]

PROBLEM 2.104 (Continued) Equilibrium condition: 0: (36 lb) 0 DA DB DC FΣ= + + + =TTT j DA DB DC Substituting the expressions obtained for , , and DA DB DC TT T and factoring i, j, and k: […]

PROBLEM 2.98 For the boom and loading of Problem. 2.97, determine the magnitude of the load P. PROBLEM 2.97 The boom OA carries a load P and is supported by two cables as shown. Knowing that the tension in cable […]

PROBLEM 2.89 A rectangular plate is supported by three cables as shown. Knowing that the tension in cable AB is 408 N, determine the components of the force exerted on the plate at B. SOLUTION We have: (320 mm) (480 […]

PROBLEM 2.79 Determine the magnitude and direction of the force F = (240 N)i – (270 N)j + (680 N)k. SOLUTION 222 222 (240 N) ( 270 N) ( 680 N) xyz F FFF F = ++ = +− +− […]