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# 2 p2 - 76 —~ Chapter 2 Forces and Moments 2.34 Determine...

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Unformatted text preview: 76 —~ Chapter 2 Forces and Moments 2.34 Determine the total moment about point 0 due to the two forces shown in Fig. P234. Fig. P234 I 325 mm or moment M in vector format if its Cartesian components are: 2.35 Express the force F (a) F, = 2,400 N, F, = —2,600 N, and P, = 1,550 N (b) Fx=731b,Fy=—1801b,ansz= 1191b ‘ (c) Mx = 320 N—m, My = 430 N—m, and M, = 540 N—m (d) M, = 770 in—lb, My = 455 in-lb, and Mz = ~550 in-lb tion, relative to the positive x-axis, for each of the vectors 2.36 Determine the magnitude and direc (a) F, = 1,200 N, P, = 1,050 N and P, = 0 (b) Fx= 4551M:y = 62011) ansz = 0 (c) Mx = 2,800 N—m, My = 2,350 N—m and M, = 0 (d) M, = 695 ft-lb, My = ~385 ft—lb and M, = 0 2.37 A position vector 1‘ is constructed in space between the origin (0, 0, 0) and point P. Write r as a Cartesian vector and determine the magnitude (r) and coordinate direction angles (on, B, y) if: (c) P = (0.220, 0.255, 0.270) m (a) P = (6, 3, 5) in. (d) P : (—9, 2, —7) a (b) P = (120, 75, 80) mm 2.38 Determine the coordinate direction angles (on, [3, y) for thefollowing forces: (0) F=(—5i—-5j+8k)kN (a)F=(3i+5j~—5k)N (d)F=(4i—3j—~5k)kip (b) F=(—4i+3j—7k)lb itude (F) and two known coordinate direction angles (0t, [3). fy the three components (F x, Fy, F2) and prepare a drawing ensional Cartesian coordinate system for: 3 2.39 A spacc force F has a known magn Write a vector equation for F, speci showing the force vector in a three-dim (c) F=24kN,0L= 135° andB =60° (a) F = 1,500 N, on = 60° andB = 30° (d) F= 16 kip,or.=50° and|3 = 140° (b) F =1,2001b,ot = 75° andB = 50° 2.40 Write a vector equation for the summation of two space forces F1 and F2. The force F1 is 33.5 kN in magnitude with coordinate direction angles of on = 60°, [31 = 60° and 71 = 135°. The force F2 is 42.0 kN in magnitude with coordinate direction angles of or; = 60°, [32 = 30° and y; = 90°. Prepare a drawing showing this resultant force vector in a three—dimensional Cartesian coordinate system. Statics —-— 77 2.41 Determine the angle between the following pairs of space forces: (a) F1=(4i+3j~4k)NandF2=(——3i+4j+5k)N (b) F1=(2i—3j+3k)lbandF2=(6i—2j+5k)lb (c) F1=v(—3 i+6j~2k)kNandF2=(—4i+3j-—2k)kN 2.42 Determine the magnitude of a single force component produced by two space forces (F1, E) that is directed along a line of action which lies in the x—y plane and makes an angle of 6 with the positive x-axis: (a); F1=(2i+Sj—4k)lb;F2=(—4i+5j+6k.)lb;and6=30° (b) Fl=(3i+4j~3k)kN;F2=(5i—4j+3k)kN;and9=4O° (c) F1=(3i—63—5k)kip;F2=(—6i+2j—3k)kip;and9=120° 2.43 A force vector F, with components Fx, Fy and FZ is applied to a structure at point Q. Determine - the moment of F about the origin 0 of the coordinate system when: (a) F, = 3,000 N, F, = 1,500 N, F, = 2,500 N and Q = (2.3, 3.4, 4.6) m (b) F, = —2,000 lb, F, = 2,500 lb, F, = 1,200 lb and Q = (4.4, ~45, 6.6) a (c) F, = 3.3 1<:N,Fy = 4.5 kN, F, = 4.3 kN and Q = (1.4, 3.9, 2.6) m 2.44 If a structure is loaded at point Q with a force F, determine the moment M0 about the origin 0. Prepare a drawing showing the moment vector M0 in a three-dimensional Cartesian coordinate system. Values for F and Q are: (a) F=(200i+ 125 j + 75 1;) 1b andQ=(2,—3, 15) ft (b) F = (3.8 r + 3.3 j -— 4.5 k) kN and Q = (—4.2, 3.6, —2.8) m (c) F=(75i—67j+45 k)lbandQ=(—3,4, 8)ft 2.45 The cell phone tower, illustrated in Fig. P245, is supported by three cables that are maintained with tension forces FA = FB = PC = 920 lb. The cables are anchored into the ground plane at locations A, B and C. Because the structural strength and rigidity of the tower is along its axis, we design the cable support system to exhibit a vector sum Sv that is directed along the axis of the tower from point D to the tower support point 0. If the tower height H = 120 ft and the anchor locations are given in Fig. P245, determine the position for the anchor at point B to achieve the design objective. Fig. P245 2.47 7s —— Chapter 2 Forces and Moments 2.46 The cell phone tovver, illustrated in Fig. P2. 5 along its axis, we design the cable support system to exhibit a ve 46, is supported by three cables that are maintained ’é’ with tension forces F A = 1,500 lb and PC = 1,200 lb. The cables are anchored into the ground plane at locations A, B and C. Because the structural strength and rigidity of the tower is ctor sum Sv that is directed 0. If the tower height H = along the axis of the tower from point D to the tower support point 2 120 ft and the anchor locations are given in Fig. P2.46, determine the force FB that must be maintained in cable BD to achieve the design objective. VAEEL‘EEL‘Y~ EVAEEE Fig. P2.46 a, s base at point 0 to its tip at point Q as indicated in Fig. P2.47. A three-dimensional coordinate system has been established in this illustration with the point 0 at the origin and the point Q deﬁned with coordinates (- l, 3, 8). A force with a magnitude of 18 kN is applied by the boom onto a cable that extends from the tip of the boom to point P. Point P is located on the x—y plane with coordinates shown in Fig. P2.47. If the coordinates are expressed in meters, determine the following quantities: The boom of a crane extends ﬁom it The force F (in vector form). The force components Fx, Fy, and F2. The moment M0 (in vector form). ‘ The moment components MK, My, and Ml. The magnitude of the moment (M0). The unit vector giving the direction of M0. The angle between F and boom OQ. The projection of F along boom 0Q. 1. 2. 3. 4. 5 6 7 8 Statics — 79‘ 2.48 The boom of a crane extends from its base at point 0 to its tip at point Q as indicated in Fig. P248. A three-dimensional coordinate system has been established in this illustration with the point 0 at the origin and the point Q deﬁned with coordinates (3, 2, 18). A force with a magnitude of 9,400 1b is applied by the boom onto a cable that extends from the tip of, the boom to point P. Point P is located on the x~yplane with coordinates shown in Fig. P248. If the coordinates are expressed in feet, determine the following quantities: The force F (in vector form). The force components FX, Fy, and F2. The moment M0 (in vector form). The moment components Mx, My, and M2. The magnitude of the moment (M0). . The unit vector giving the direction of M0. The angle between F and boom 0Q. The projection of F along boom 0Q. 908999595)!" ...
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