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- Question : 1P - Two forces P and Q are applied as shown at point A of a hook support. Knowing that P 5 75 N and Q 5 125 N, determine graphically the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule.
- Question : 2P - Two forces P and Q are applied as shown at point A of a hook support. Knowing that P 5 60 lb and Q 5 25 lb, determine graphically the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule.
- Question : 3P - The cable stays AB and AD help support pole AC. Knowing that the tension is 120 lb in AB and 40 lb in AD, determine graphically the magnitude and direction of the resultant of the forces exerted by the stays at A using (a) the parallelogram law, (b) the triangle rule.
- Question : 4P - Two forces are applied at point B of beam AB. Determine graphically the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule.
- Question : 5P - The 300-lb force is to be resolved into components along lines a-a9 and b-b9. (a) Determine the angle a by trigonometry knowing that the component along line a-a9 is to be 240 lb. (b) What is the corresponding value of the component along b-b9?
- Question : 6P - The 300-lb force is to be resolved into components along lines a-a9 and b-b9. (a) Determine the angle a by trigonometry knowing that the component along line b-b9 is to be 120 lb. (b) What is the corresponding value of the component along a-a9?
- Question : 7P - Two forces are applied as shown to a hook support. Knowing that the magnitude of P is 35 N, determine by trigonometry (a) the required angle a if the resultant R of the two forces applied to the support is to be horizontal, (b) the corresponding magnitude of R.
- Question : 8P - For the hook support of Prob. 2.1, knowing that the magnitude of P is 75 N, determine by trigonometry (a) the required magnitude of the force Q if the resultant R of the two forces applied at A is to be vertical, (b) the corresponding magnitude of R.
- Question : 9P - A trolley that moves along a horizontal beam is acted upon by two forces as shown. (a) Knowing that a 5 25
- Question : 10P - A trolley that moves along a horizontal beam is acted upon by two forces as shown. Determine by trigonometry the magnitude and direction of the force P so that the resultant is a vertical force of 2500 N.
- Question : 11P - A steel tank is to be positioned in an excavation. Knowing that a 5 20
- Question : 12P - A steel tank is to be positioned in an excavation. Knowing that the magnitude of P is 500 lb, determine by trigonometry (a) the required angle a if the resultant R of the two forces applied at A is to be vertical, (b) the corresponding magnitude of R.
- Question : 13P - For the hook support of Prob. 2.7, determine by trigonometry (a) the magnitude and direction of the smallest force P for which the resultant R of the two forces applied to the support is horizontal, (b) the corresponding magnitude of R.
- Question : 14P - For the steel tank of Prob. 2.11, determine by trigonometry (a) the magnitude and direction of the smallest force P for which the resultant R of the two forces applied at A is vertical, (b) the corresponding magnitude of R.
- Question : 15P - Solve Prob. 2.2 by trigonometry.
- Question : 16P - Solve Prob. 2.3 by trigonometry.
- Question : 17P - Solve Prob. 2.4 by trigonometry.
- Question : 18P - Two structural members A and B are bolted to a bracket as shown. Knowing that both members are in compression and that the force is 15 kN in member A and 10 kN in member B, determine by trigonometry the magnitude and direction of the resultant of the forces applied to the bracket by members A and B.
- Question : 19P - Two structural members A and B are bolted to a bracket as shown. Knowing that both members are in compression and that the force is 10 kN in member A and 15 kN in member B, determine by trigonometry the magnitude and direction of the resultant of the forces applied to the bracket by members A and B
- Question : 20P - For the hook support of Prob. 2.7, knowing that P 5 75 N and a 5 50
- Question : 2.21 and 2.22P - Determine the x and y components of each of the forces shown.
- Question : 2.23 and 2.24P - Determine the x and y components of each of the forces shown.
- Question : 25P - Member BD exerts on member ABC a force P directed along line BD. Knowing that P must have a 300-lb horizontal component, determine (a) the magnitude of the force P, (b) its vertical component.
- Question : 26P - The hydraulic cylinder BD exerts on member ABC a force P directed along line BD. Knowing that P must have a 750-N component perpendicular to member ABC, determine (a) the magnitude of the force P, (b) its component parallel to ABC.
- Question : 27P - The guy wire BD exerts on the telephone pole AC a force P directed along BD. Knowing that P must have a 120-N component perpendicular to the pole AC, determine (a) the magnitude of the force P, (b) its component along line AC
- Question : 28P - The guy wire BD exerts on the telephone pole AC a force P directed along BD. Knowing that P has a 180-N component along line AC, determine (a) the magnitude of the force P, (b) its component in a direction perpendicular to AC.
- Question : 29P - Member CB of the vise shown exerts on block B a force P directed along line CB. Knowing that P must have a 1200-N horizontal component, determine (a) the magnitude of the force P, (b) its vertical component.
- Question : 30P - Cable AC exerts on beam AB a force P directed along line AC. Knowing that P must have a 350-lb vertical component, determine (a) the magnitude of the force P, (b) its horizontal component.
- Question : 31P - Determine the resultant of the three forces of Prob. 2.22.
- Question : 32P - Determine the resultant of the three forces of Prob. 2.24.
- Question : 33P - Determine the resultant of the three forces of Prob. 2.23.
- Question : 34P - Determine the resultant of the three forces of Prob. 2.21.
- Question : 35P - Knowing that a 5 35
- Question : 36P - Knowing that the tension in cable BC is 725 N, determine the resultant of the three forces exerted at point B of beam AB.
- Question : 37P - Knowing that a 5 40
- Question : 38P - Knowing that a 5 75
- Question : 39P - For the collar of Prob. 2.35, determine (a) the required value of a if the resultant of the three forces shown is to be vertical, (b) the corresponding magnitude of the resultant.
- Question : 40P - For the beam of Prob. 2.36, determine (a) the required tension in cable BC if the resultant of the three forces exerted at point B is to be vertical, (b) the corresponding magnitude of the resultant.
- Question : 41P - Determine (a) the required tension in cable AC, knowing that the resultant of the three forces exerted at point C of boom BC must be directed along BC, (b) the corresponding magnitude of the resultant.
- Question : 42P - For the block of Probs. 2.37 and 2.38, determine (a) the required value of a if the resultant of the three forces shown is to be parallel to the incline, (b) the corresponding magnitude of the resultant.
- Question : 43P - Two cables are tied together at C and are loaded as shown. Knowing that a 5 20
- Question : 44P - Two cables are tied together at C and are loaded as shown. Determine the tension (a) in cable AC, (b) in cable BC.
- Question : 45P - Two cables are tied together at C and are loaded as shown. Knowing that P 5 500 N and a 5 60
- Question : 46P - Two cables are tied together at C and are loaded as shown. Determine the tension (a) in cable AC, (b) in cable BC.
- Question : 47P - Knowing that a 5 20
- Question : 48P - Knowing that a 5 55
- Question : 49P - Two forces P and Q are applied as shown to an aircraft connection. Knowing that the connection is in equilibrium and that P 5 500 lb and Q 5 650 lb, determine the magnitudes of the forces exerted on the rods A and B.
- Question : 50P - Two forces P and Q are applied as shown to an aircraft connection. Knowing that the connection is in equilibrium and that the magnitudes of the forces exerted on rods A and B are FA 5 750 lb and FB 5 400 lb, determine the magnitudes of P and Q.
- Question : 51P - A welded connection is in equilibrium under the action of the four forces shown. Knowing that FA 5 8 kN and FB 5 16 kN, determine the magnitudes of the other two forces.
- Question : 52P - A welded connection is in equilibrium under the action of the four forces shown. Knowing that FA 5 5 kN and FD 5 6 kN, determine the magnitudes of the other two forces.
- Question : 53P - Two cables tied together at C Problems are loaded as shown. Knowing that Q 5 60 lb, determine the tension (a) in cable AC, (b) in cable BC.
- Question : 54P - Two cables tied together at C are loaded as shown. Determine the range of values of Q for which the tension will not exceed 60 lb in either cable.
- Question : 55P - A sailor is being rescued using a boatswain
- Question : 56P - A sailor is being rescued using a boatswain
- Question : 57P - For the cables of Prob. 2.45, it is known that the maximum allowable tension is 600 N in cable AC and 750 N in cable BC. Determine (a) the maximum force P that can be applied at C, (b) the corresponding value of a.
- Question : 58P - For the situation described in Fig. P2.47, determine (a) the value of a for which the tension in rope BC is as small as possible, (b) the corresponding value of the tension.
- Question : 59P - For the structure and loading of Prob. 2.48, determine (a) the value of a for which the tension in cable BC is as small as possible, (b) the corresponding value of the tension.
- Question : 60P - Knowing that portions AC and BC of cable ACB must be equal, determine the shortest length of cable that can be used to support the load shown if the tension in the cable is not to exceed 870 N.
- Question : 61P - Two cables tied together at C are loaded as shown. Knowing that the maximum allowable tension in each cable is 800 N, determine (a) the magnitude of the largest force P that can be applied at C, (b) the corresponding value of a.
- Question : 62P - Two cables tied together at C are loaded as shown. Knowing that the maximum allowable tension is 1200 N in cable AC and 600 N in cable BC, determine (a) the magnitude of the largest force P that can be applied at C, (b) the corresponding value of a.
- Question : 63P - Collar A is connected as shown to a 50-lb load and can slide on a frictionless horizontal rod. Determine the magnitude of the force P required to maintain the equilibrium of the collar when (a) x 5 4.5 in., (b) x 5 15 in.
- Question : 64P - Collar A is connected as shown to a 50-lb load and can slide on a frictionless horizontal rod. Determine the distance x for which the collar is in equilibrium when P 5 48 lb.
- Question : 65P - A 160-kg load is supported by the rope-and-pulley arrangement shown. Knowing that b 5 20
- Question : 66P - A 160-kg load is supported by the rope-and-pulley arrangement shown. Knowing that a 5 40
- Question : 67P - A 600-lb crate is supported by several rope-and-pulley arrangements as shown. Determine for each arrangement the tension in the rope. (See the hint for Prob. 2.65.)
- Question : 68P - Solve parts b and d of Prob. 2.67, assuming that the free end of the rope is attached to the crate.
- Question : 69P - A load Q is applied to the pulley C, which can roll on the cable ACB. The pulley is held in the position shown by a second cable CAD, which passes over the pulley A and supports a load P. Knowing that P 5 750 N, determine (a) the tension in cable ACB, (b) the magnitude of load Q.
- Question : 70P - An 1800-N load Q is applied to the pulley C, which can roll on the cable ACB. The pulley is held in the position shown by a second cable CAD, which passes over the pulley A and supports a load P. Determine (a) the tension in cable ACB, (b) the magnitude of load P.
- Question : 71P - Determine (a) the x, y, and z components of the 750-N force, (b) the angles ux, uy, and uz that the force forms with the coordinate axes.
- Question : 72P - Determine (a) the x, y, and z components of the 900-N force, (b) the angles ux, uy, and uz that the force forms with the coordinate axes.
- Question : 73P - A horizontal circular plate is suspended as shown from three wires that are attached to a support at D and form 30
- Question : 74P - A horizontal circular plate is suspended as shown from three wires that are attached to a support at D and form 30
- Question : 75P - A horizontal circular plate is suspended as shown from three wires that are attached to a support at D and form 30
- Question : 76P - A horizontal circular plate is suspended as shown from three wires that are attached to a support at D and form 30
- Question : 77P - 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 the force exerted by this wire on the pole, (b) the angles ux, uy, and uz that the force forms with the coordinate axes.
- Question : 78P - 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 AD is 85 lb, determine (a) the components of the force exerted by this wire on the pole, (b) the angles ux, uy, and uz that the force forms with the coordinate axes.
- Question : 79P - Determine the magnitude and direction of the force F 5 (320 N)i 1 (400 N)j 2 (250 N)k.
- Question : 80P - Determine the magnitude and direction of the force F 5 Problems (240 N)i 2 (270 N)j 1 (680 N)k.
- Question : 81P - A force acts at the origin of a coordinate system in a direction defined by the angles ux 5 70.9
- Question : 82P - A force acts at the origin of a coordinate system in a direction defined by the angles uy 5 55
- Question : 83P - A force F of magnitude 210 N acts at the origin of a coordinate system. Knowing that Fx 5 80 N, uz 5 151.2
- Question : 84P - A force F of magnitude 230 N acts at the origin of a coordinate system. Knowing that ux 5 32.5
- Question : 85P - A transmission tower is held by three guy wires anchored by bolts at B, C, and D. If the tension in wire AB is 525 lb, determine the components of the force exerted by the wire on the bolt at B.
- Question : 86P - A transmission tower is held by three guy wires anchored by bolts at B, C, and D. If the tension in wire AD is 315 lb, determine the components of the force exerted by the wire on the bolt at D.
- Question : 87P - A frame ABC is supported in part by cable DBE that passes through a frictionless ring at B. Knowing that the tension in the cable is 385 N, determine the components of the force exerted by the cable on the support at D.
- Question : 88P - For the frame and cable of Prob. 2.87, determine the components of the force exerted by the cable on the support at E.
- Question : 89P - Knowing that the tension in cable AB is 1425 N, determine the components of the force exerted on the plate at B.
- Question : 90P - Knowing that the tension in cable AC is 2130 N, determine the components of the force exerted on the plate at C.
- Question : 91P - Find the magnitude and direction of the resultant of the two forces shown knowing that P 5 300 N and Q 5 400 N.
- Question : 92P - Find the magnitude and direction of the resultant of the two forces shown knowing that P 5 400 N and Q 5 300 N.
- Question : 93P - Knowing that the tension is 425 lb in cable AB and 510 lb in cable AC, determine the magnitude and direction of the resultant of the forces exerted at A by the two cables.
- Question : 94P - Knowing that the tension is 510 lb in cable AB and 425 lb in cable AC, determine the magnitude and direction of the resultant of the forces exerted at A by the two cables.
- Question : 95P - For the frame of Prob. 2.87, determine the magnitude and direction of the resultant of the forces exerted by the cable at B knowing that the tension in the cable is 385 N.
- Question : 96P - For the cables of Prob. 2.89, knowing that the tension is 1425 N in cable AB and 2130 N in cable AC, determine the magnitude and direction of the resultant of the forces exerted at A by the two cables.
- Question : 97P - 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 AC is 150 lb and that the resultant of the forces exerted at A by wires AC and AD must be contained in the xy plane, determine (a) the tension in AD, (b) the magnitude and direction of the resultant of the two forces.
- Question : 98P - 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 AD is 125 lb and that the resultant of the forces exerted at A by wires AC and AD must be contained in the xy plane, determine (a) the tension in AC, (b) the magnitude and direction of the resultant of the two forces.
- Question : 99P - Three cables are used to tether a balloon as shown. Determine the vertical force P exerted by the balloon at A knowing that the tension in cable AB is 259 N.
- Question : 100P - Three cables are used to tether a balloon as shown. Determine the vertical force P exerted by the balloon at A knowing that the tension in cable AC is 444 N.
- Question : 101P - Three cables are used to tether a balloon as shown. Determine the vertical force P exerted by the balloon at A knowing that the tension in cable AD is 481 N.
- Question : 102P - Three cables are used to tether a balloon as shown. Knowing that the balloon exerts an 800-N vertical force at A, determine the tension in each cable.
- Question : 103P - A crate is supported by three cables as shown. Determine the weight of the crate knowing that the tension in cable AB is 750 lb.
- Question : 104P - A crate is supported by three cables as shown. Determine the weight of the crate knowing that the tension in cable AD is 616 lb.
- Question : 105P - A crate is supported by three cables as shown. Determine the weight of the crate knowing that the tension in cable AC is 544 lb.
- Question : 106P - A 1600-lb crate is supported by three cables as shown. Determine the tension in each cable.
- Question : 107P - Three cables are connected at A Problems , where the forces P and Q are applied as shown. Knowing that Q 5 0, find the value of P for which the tension in cable AD is 305 N.
- Question : 108P - Three cables are connected at A, where the forces P and Q are applied as shown. Knowing that P 5 1200 N, determine the values of Q for which cable AD is taut.
- Question : 109P - 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 630 lb, determine the vertical force P exerted by the tower on the pin at A.
- Question : 110P - 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 AC is 920 lb, determine the vertical force P exerted by the tower on the pin at A.
- Question : 111P - A rectangular plate is supported by three cables as shown. Knowing that the tension in cable AC is 60 N, determine the weight of the plate.
- Question : 112P - A rectangular plate is supported by three cables as shown. Knowing that the tension in cable AD is 520 N, determine the weight of the plate.
- Question : 113P - For the transmission tower of Probs. 2.109 and 2.110, determine the tension in each guy wire knowing that the tower exerts on the pin at A an upward vertical force of 2100 lb.
- Question : 114P - A horizontal circular plate weighing 60 lb is suspended as shown from three wires that are attached to a support at D and form 30
- Question : 115P - For the rectangular plate of Probs. 2.111 and 2.112, determine the tension in each of the three cables knowing that the weight of the plate is 792 N.
- Question : 116P - For the cable system of Probs. 2.107 and 2.108, determine the tension in each cable knowing that P 5 2880 N and Q 5 0.
- Question : 117P - For the cable system of Probs. 2.107 and 2.108, determine the tension in each cable knowing that P 5 2880 N and Q 5 576 N.
- Question : 118P - For the cable system of Probs. 2.107 and 2.108, determine the tension in each cable knowing that P 5 2880 N and Q 5 2576 N (Q is directed downward).
- Question : 119P - Using two ropes and a roller chute, two workers are unloading a 200-lb cast-iron counterweight from a truck. Knowing that at the instant shown the counterweight is kept from moving and that the positions of points A, B, and C are, respectively, A(0, 220 in., 40 in.), B(240 in., 50 in., 0), and C(45 in., 40 in., 0), and assuming that no friction exists between the counterweight and the chute, determine the tension in each rope. (Hint: Since there is no friction, the force exerted by the chute on the counterweight must be perpendicular to the chute.)
- Question : 120P - Solve Prob. 2.119 assuming that a third worker is exerting a force P 5 2(40 lb)i on the counterweight.
- Question : 121P - A container of weight W is suspended from ring A. Cable BAC passes through the ring and is attached to fixed supports at B and C. Two forces P 5 Pi and Q 5 Qk are applied to the ring to maintain the container in the position shown. Knowing that W 5 376 N, determine P and Q. (Hint: The tension is the same in both portions of cable BAC.)
- Question : 122P - For the system of Prob. 2.121, determine W Problems and Q knowing that P 5 164 N.
- Question : 123P - A container of weight W is suspended from ring A, to which cables AC and AE are attached. A force P is applied to the end F of a third cable that passes over a pulley at B and through ring A and that is attached to a support at D. Knowing that W 5 1000 N, determine the magnitude of P. (Hint: The tension is the same in all portions of cable FBAD.)
- Question : 124P - Knowing that the tension in cable AC of the system described in Prob. 2.123 is 150 N, determine (a) the magnitude of the force P, (b) the weight W of the container.
- Question : 125P - Collars A and B are connected by a 25-in.-long wire and can slide freely on frictionless rods. If a 60-lb force Q is applied to collar B as shown, determine (a) the tension in the wire when x 5 9 in., (b) the corresponding magnitude of the force P required to maintain the equilibrium of the system.
- Question : 126P - Collars A and B are connected by a 25-in.-long wire and can slide freely on frictionless rods. Determine the distances x and z for which the equilibrium of the system is maintained when P 5 120 lb and Q 5 60 lb.
- Question : 127RP - The direction of the 75-lb forces may vary, but the angle between the forces is always 50
- Question : 128RP - A stake is being pulled out of the ground by means of two ropes as shown. Knowing the magnitude and direction of the force exerted on one rope, determine the magnitude and direction of the force P that should be exerted on the other rope if the resultant of these two forces is to be a 40-lb vertical force.
- Question : 129RP - Member BD exerts on member ABC a force P directed along line BD. Knowing that P must have a 240-lb vertical component, determine (a) the magnitude of the force P, (b) its horizontal component.
- Question : 130RP - Two cables are tied together at C and loaded as shown. Determine the tension (a) in cable AC, (b) in cable BC.
- Question : 131RP - Two cables are tied together at C and loaded as shown. Knowing that P 5 360 N, determine the tension (a) in cable AC, (b) in cable BC.
- Question : 132RP - Two cables are tied together at C and loaded as shown. Determine the range of values of P for which both cables remain taut.
- Question : 133RP - A force acts at the origin of a coordinate system in a direction defined by the angles ux 5 69.3
- Question : 134RP - Cable AB is 65 ft long, and the tension in that cable is 3900 lb. Determine (a) the x, y, and z components of the force exerted by the cable on the anchor B, (b) the angles ux, uy, and uz defining the direction of that force.
- Question : 135RP - In order to move a wrecked truck, two cables are attached at A and pulled by winches B and C as shown. Knowing that the tension is 10 kN in cable AB and 7.5 kN in cable AC, determine the magnitude and direction of the resultant of the forces exerted at A by the two cables.
- Question : 136RP - A container of weight W 5 1165 N is supported by three cables as shown. Determine the tension in each cable.
- Question : 137RP - Collars A and B are connected by a 525-mm-long wire and can slide freely on frictionless rods. If a force P 5 (341 N)j is applied to collar A, determine (a) the tension in the wire when y 5 155 mm, (b) the magnitude of the force Q required to maintain the equilibrium of the system.
- Question : 1CP - Write a computer program that can be used to determine the magnitude and direction of the resultant of n coplanar forces applied at a point A. Use this program to solve Probs. 2.32, 2.33, 2.35, and 2.38.
- Question : 2CP - A load P is supported by two cables as shown. Write a computer program that can be used to determine the tension in each cable for any given value of P and for values of u ranging from u1 5 b 2 90
- Question : 3CP - An acrobat is walking on a tightrope of length L 5 20.1 m attached to supports A and B at a distance of 20.0 m from each other. The combined weight of the acrobat and his balancing pole is 800 N, and the friction between his shoes and the rope is large enough to prevent him from slipping. Neglecting the weight of the rope and any elastic deformation, write a computer program to calculate the deflection y and the tension in portions AC and BC of the rope for values of x from 0.5 m to 10.0 m using 0.5-m increments. From the data obtained, determine (a) the maximum deflection of the rope, (b) the maximum tension in the rope, (c) the smallest values of the tension in portions AC and BC of the rope.
- Question : 4CP - Write a computer program that can be used to determine the magni- Computer Problems tude and direction of the resultant of n forces Fi , where i 5 1, 2, . . . , n, that are applied at point A0 of coordinates x0, y0, and z0, knowing that the line of action of Fi passes through point Ai of coordinates xi, yi, and zi. Use this program to solve Probs. 2.93, 2.94, 2.95, and 2.135.
- Question : 5CP - Three cables are attached at points A1, A2, and A3, respectively, and are connected at point A0, to which a given load P is applied as shown. Write a computer program that can be used to determine the tension in each of the cables. Use this program to solve Probs. 2.102, 2.106, 2.107, and 2.115.

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