For the situation described in Fig. P2.48, determine (a) the value of for which the

Two forces are applied as shown to a hook. Determine graphically the magnitude and direction of their resultant using (a) the parallelo-gram law, (b) the triangle rule.

Two forces are applied as shown to a bracket support. Determine graphically the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule.

Two structural members B and C are bolted to bracket A. Knowing that both members are in tension and that P 5 10 kN and Q 5 15 kN, determine graphically the magnitude and direction of the resultant force exerted on the bracket using (a) the parallelogram law, (b) the triangle rule.

Two structural members B and C are bolted to bracket A. Knowing that both members are in tension and that P 5 6 kips and Q 5 4 kips, determine graphically the magnitude and direction of the resultant force exerted on the bracket using (a) the parallelogram law, (b) the triangle rule.

stake is being pulled out of the ground by means of two ropes as shown. Knowing that 5 30, determine by trigonometry (a) the magnitude of the force P so that the resultant force exerted on the stake is vertical, (b) the corresponding magnitude of the resultant.

telephone cable is clamped at A to the pole AB. Knowing that the tension in the left-hand portion of the cable is T1 5 800 lb, determine by trigonometry (a) the required tension T2 in the right-hand portion if the resultant R of the forces exerted by the cable at A is to be vertical, (b) the corresponding magnitude of R.

A telephone cable is clamped at A to the pole AB. Knowing that the tension in the right-hand portion of the cable is T2 5 1000 lb, deter- mine by trigonometry (a) the required tension T1 in the left-hand portion if the resultant R of the forces exerted by the cable at A is to be vertical, (b) the corresponding magnitude of R.

A disabled automobile is pulled by means of two ropes as shown. The tension in rope AB is 2.2 kN, and the angle is 25. Knowing that the resultant of the two forces applied at A is directed along the axis of the automobile, determine by trigonometry (a) the tension in rope AC, (b) the magnitude of the resultant of the two forces applied at A.

A disabled automobile is pulled by means of two ropes as shown. Knowing that the tension in rope AB is 3 kN, determine by trigo- nometry the tension in rope AC and the value of so that the resul- tant force exerted at A is a 4.8-kN force directed along the axis of the automobile.

A steel tank is to be positioned in an excavation. Knowing that 5 20, determine by trigonometry (a) the required magnitude of the force P if the resultant R of the two forces applied at A is to be vertical, (b) the corresponding magnitude of R.

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 if the resultant R of the two forces applied at A is to be vertical, (b) the corresponding magnitude of R.

steel tank is to be positioned in an excavation. Determine by trigo- nometry (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.

For the hook support of Prob. 2.10, 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.

For the hook support shown, determine by trigonometry the magni- tude and direction of the resultant of the two forces applied to the support.

Solve Prob. 2.1 by trigonometry.

Solve Prob. 2.4 by trigonometry.

For the stake of Prob. 2.5, knowing that the tension in one rope is 120 N, determine by trigonometry the magnitude and direction of the force P so that the resultant is a vertical force of 160 N.

Two forces P and Q are applied to the lid of a storage bin as shown. Knowing that P 5 48 N and Q 5 60 N, determine by trigonometry the magnitude and direction of the resultant of the two forces.

Determine the x and y components of each of the forces shown.

Determine the x and y components of each of the forces shown."

Determine the x and y components of each of the forces shown.

Determine the x and y components of each of the forces shown.

Member BC exerts on member AC a force P directed along line BC. Knowing that P must have a 325-N horizontal component, determine (a) the magnitude of the force P, (b) its vertical component.

Member BD exerts on member ABC a force P directed along line BD. Knowing that P must have a 300-lb horizontal component, deter- mine (a) the magnitude of the force P, (b) its vertical component.

The hydraulic cylinder BC exerts on member AB a force P directed along line BC. Knowing that P must have a 600-N component per- pendicular to member AB, determine (a) the magnitude of the force P, (b) its component along line AB.

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.

The hydraulic cylinder BD exerts on member ABC a force P directed along line BD. Knowing that P must have a 750-N component per- pendicular to member ABC, determine (a) the magnitude of the force P, (b) its component parallel to ABC.

Determine the resultant of the three forces of Prob. 2.21.

Determine the resultant of the three forces of Prob. 2.23.

Determine the resultant of the three forces of Prob. 2.24.

Determine the resultant of the three forces of Prob. 2.22.

Knowing that 5 35, determine the resultant of the three forces shown.

Knowing that the tension in rope AC is 365 N, determine the resul- tant of the three forces exerted at point C of post BC.

Knowing that 5 40, determine the resultant of the three forces shown.

Knowing that 5 75, determine the resultant of the three forces shown.

For the collar of Prob. 2.35, determine (a) the required value of if the resultant of the three forces shown is to be vertical, (b) the corresponding magnitude of the resultant.

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.

For the block of Probs. 2.37 and 2.38, determine (a) the required value of if the resultant of the three forces shown is to be parallel to the incline, (b) the corresponding magnitude of the resultant.

Two cables are tied together at C and are loaded as shown. Deter- mine the tension (a) in cable AC, (b) in cable BC.

Two cables are tied together at C and are loaded as shown. Knowing that 5 30, determine the tension (a) in cable AC, (b) in cable BC.

Two cables are tied together at C and loaded as shown. Determine the tension (a) in cable AC, (b) in cable BC.

Two cables are tied together at C and are loaded as shown. Knowing that P 5 500 N and 5 60, determine the tension in (a) in cable AC, (b) in cable BC.

Two cables are tied together at C and are loaded as shown. Deter- mine the tension (a) in cable AC, (b) in cable BC.

Knowing that 5 20, determine the tension (a) in cable AC, (b) in rope BC.

Two cables are tied together at C and are loaded as shown. Knowing that P 5 300 N, determine the tension in cables AC and BC.

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 rods A and B.

Two forces P and Q are applied as shown to an aircraft connection. Knowing that the connection is in equilibrium and that the magni- tudes 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.

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.

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.

A sailor is being rescued using a boatswains chair that is suspended from a pulley that can roll freely on the support cable ACB and is pulled at a constant speed by cable CD. Knowing that 5 30 and 5 10 and that the combined weight of the boatswains chair and the sailor is 200 lb, determine the tension (a) in the support cable ACB, (b) in the traction cable CD.

A sailor is being rescued using a boatswains chair that is suspended from a pulley that can roll freely on the support cable ACB and is pulled at a constant speed by cable CD. Knowing that 5 25 and 5 15 and that the tension in cable CD is 20 lb, determine (a) the combined weight of the boatswains chair and the sailor, (b) the ten- sion in the support cable ACB.

For the cables of Prob. 2.44, find the value of for which the ten- sion is as small as possible (a) in cable BC, (b) in both cables simul- taneously. In each case determine the tension in each cable.

For the cables of Prob. 2.46, 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 corre- sponding value of .

For the situation described in Fig. P2.48, determine (a) the value of for which the tension in rope BC is as small as possible, (b) the corresponding value of the tension.

movable bin and its contents have a combined weight of 2.8 kN. Determine the shortest chain sling ACB that can be used to lift the loaded bin if the tension in the chain is not to exceed 5 kN.

For W 5 800 N, P 5 200 N, and d 5 600 mm, determine the value of h consistent with equilibrium.

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.

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.

Three forces are applied to a bracket as shown. The directions of the two 150-N forces may vary, but the angle between these forces is always 50. Determine the range of values of for which the mag- nitude of the resultant of the forces acting at A is less than 600 N.

A 200-kg crate is to be supported by the rope-and-pulley arrange- ment shown. Determine the magnitude and direction of the force P that must be exerted on the free end of the rope to maintain equilib- rium. (Hint: The tension in the rope is the same on each side of a simple pulley. This can be proved by the methods of Chap. 4.)

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. 2.66.)

Solve parts b and d of Prob. 2.67, assuming that the free end of the rope is attached to the crate.

A load Q is applied to 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 magni- tude of load Q.

Determine (a) the x, y, and z components of the 600-N force, (b) the angles x, y, and z that the force forms with the coordinate axes.

Determine (a) the x, y, and z components of the 450-N force, (b) the angles x, y, and z that the force forms with the coordinate axes.

A gun is aimed at a point A located 35 east of north. Knowing that the barrel of the gun forms an angle of 40 with the horizontal and that the maximum recoil force is 400 N, determine (a) the x, y, and z components of that force, (b) the values of the angles x, y, and z defining the direction of the recoil force. (Assume that the x, y, and z axes are directed, respectively, east, up, and south.)

Solve Prob. 2.73 assuming that point A is located 15 north of west and that the barrel of the gun forms an angle of 25 with the horizontal.

The angle between spring AB and the post DA is 30. Knowing that the tension in the spring is 50 lb, determine (a) the x, y, and z com- ponents of the force exerted on the circular plate at B, (b) the angles x, y, and z defining the direction of the force at B.

The angle between spring AC and the post DA is 30. Knowing that the tension in the spring is 40 lb, determine (a) the x, y, and z com- ponents of the force exerted on the circular plate at C, (b) the angles x, y, and z defining the direction of the force at C.

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 x, y, and z defining the direc- tion of that force.

Cable AC is 70 ft long, and the tension in that cable is 5250 lb. Deter- mine (a) the x, y, and z components of the force exerted by the cable on the anchor C, (b) the angles x, y, and z defining the direction of that force.

Determine the magnitude and direction of the force F 5 (240 N)i (270 N)j 1 (680 N)k.

A force acts at the origin of a coordinate system in a direction defined by the angles x 5 69.3 and z 5 57.9. Knowing that the y component of the force is 174.0 lb, determine (a) the angle y, (b) the other components and the magnitude of the force.

A force acts at the origin of a coordinate system in a direction defined by the angles x 5 70.9 and y 5 144.9. Knowing that the z component of the force is 252.0 lb, determine (a) the angle z, (b) the other components and the magnitude of the force.

A force F of magnitude 210 N acts at the origin of a coordinate system. Knowing that Fx 5 80 N, z 5 151.2, and Fy < 0, determine (a) the components Fy and Fz, (b) the angles x and y.

A force F of magnitude 1200 N acts at the origin of a coordinate system. Knowing that x 5 65, y 5 40, and Fz > 0, determine (a) the components of the force, (b) the angle z.

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.

For the frame and cable of Prob. 2.85, determine the components of the force exerted by the cable on the support at E.

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 in cable AB is 2 kips, determine the components of the force exerted at A by the cable.

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 in cable AC is 1.5 kips, determine the components of the force exerted at A by the cable.

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.

Find the magnitude and direction of the resultant of the two forces shown knowing that P 5 300 N and Q 5 400 N.

Find the magnitude and direction of the resultant of the two forces shown knowing that P 5 400 N and Q 5 300 N.

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.

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.

For the frame of Prob. 2.85, 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.

For the plate of Prob. 2.89, determine the tensions in cables AB and AD knowing that the tension in cable AC is 54 N and that the resul- tant of the forces exerted by the three cables at A must be vertical.

The boom OA carries a load P and is supported by two cables as shown. Knowing that the tension in cable AB is 183 lb and that the resultant of the load P and of the forces exerted at A by the two cables must be directed along OA, determine the tension in cable AC.

For the boom and loading of Prob. 2.97, determine the magnitude of the load P.

A container is supported by three cables that are attached to a ceiling as shown. Determine the weight W of the container knowing that the tension in cable AB is 6 kN.

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.

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.

A 36-lb triangular plate is supported by three wires as shown. Deter- mine the tension in each wire, knowing that a 5 6 in.

Solve Prob. 2.103, assuming that a 5 8 in.

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.

A 1600-lb crate is supported by three cables as shown. Determine the tension in each cable.

Three cables are connected at A, 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.

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.

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.

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 exerted by the tower on the pin at A.

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 590 lb, determine the vertical force P exerted by the tower on the pin at A.

In trying to move across a slippery icy surface, a 175-lb man uses two ropes AB and AC. Knowing that the force exerted on the man by the icy surface is perpendicular to that surface, determine the tension in each rope.

Solve Prob. 2.113 assuming that a friend is helping the man at A by pulling on him with a force P 5 2(45 lb)k.

For the rectangular plate of Probs. 2.109 and 2.110, determine the tension in each of the three cables knowing that the weight of the plate is 792 N.

For the cable system of Probs. 2.107 and 2.108, determine the ten- sion in each cable knowing that P 5 2880 N and Q 5 0.

For the cable system of Probs. 2.107 and 2.108, determine the ten- sion in each cable knowing that P 5 2880 N and Q 5 576 N.

For the cable system of Probs. 2.107 and 2.108, determine the ten- sion in each cable knowing that P 5 2880 N and Q 5 576 N (Q is directed downward).

For the transmission tower of Probs. 2.111 and 2.112, determine the tension in each guy wire knowing that the tower exerts on the pin at A an upward vertical force of 1800 lb.

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.

Knowing that the tension in cable AC of the system described in Prob. 2.121 is 150 N, determine (a) the magnitude of the force P, (b) the weight W of the container.

Cable BAC passes through a frictionless ring A and is attached to fixed supports at B and C, while cables AD and AE are both tied to the ring and are attached, respectively, to supports at D and E. Know- ing that a 200-lb vertical load P is applied to ring A, determine the tension in each of the three cables.

Knowing that the tension in cable AE of Prob. 2.123 is 75 lb, deter- mine (a) the magnitude of the load P, (b) the tension in cables BAC and AD.

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.

Solve Prob. 2.125 assuming that y 5 275 mm.

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 trigo- nometry the magnitude and direction of the resultant of the forces applied to the bracket by members A and B.

Determine the x and y components of each of the forces shown.

A hoist trolley is subjected to the three forces shown. Knowing that 5 40, determine (a) the required magnitude of the force P if the resultant of the three forces is to be vertical, (b) the corresponding magnitude of the resultant.

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.

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 .

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 x, y, and z that the force forms with the coordinate axes.

Knowing that the tension in cable AC is 2130 N, determine the components of the force exerted on the plate at C.

Find the magnitude and direction of the resultant of the two forces shown knowing that P 5 600 N and Q 5 450 N.

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 main- tain 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.)

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.

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.