A movable bin and its contents have a combined weight of

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.

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.

Two structural members B and C are bolted to bracket A. Knowing that both members are in tension and that P = 10 kN and Q = 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 = 6 kips and Q = 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.

A stake is being pulled out of the ground by means of two ropes as shown. Knowing that \(a=30^{\circ}\), 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.

A trolley that moves along a horizontal beam is acted upon by two forces as shown.(a) Knowing that \(a=25^{\circ}\), determine by trigonometry the magnitude of the force P so that the resultant force exerted on the trolley is vertical. (b) What is the corresponding magnitude of the resultant?

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.

A telephone cable is clamped at A to the pole AB. Knowing that the tension in the left-hand portion of the cable is \(T_1=800\ \mathrm{lb}\), determine by trigonometry (a) the required tension \(T_2\) 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 \(T_2=1000\ \mathrm{lb}\), determine by trigonometry (a) the required tension \(T_1\) 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.

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.

A steel tank is to be positioned in an excavation. Knowing that \(a=20^{\circ}\), 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 a 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. 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.

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.

Solve Prob. 2.2 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.

For the hook support of Prob. 2.10, knowing that P = 75 N and \(a=50^{\circ}\), determine by trigonometry the magnitude and direction of the resultant of the two forces applied to the support.

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

Two forces P and Q are applied to the lid of a storage bin as shown. Knowing that P = 60 N and Q = 48 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.

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.

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.

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 240-lb vertical component, determine (a) the magnitude of the force P, (b) its horizontal component.

The guy wire BD exerts on the telephone AC a force P directed along BD. Knowing that P must have a 720-N component perpendicular to the pole AC, determine (a) the magnitude of the force P, (b) its component along line AC.

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

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

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

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

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

Knowing that \(a=35^{\circ}\), determine the resultant of the three forces shown.

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

Knowing that \(a=40^{\circ}\), determine the resultant of the three forces shown.

Knowing that \(a=75^{\circ}\), determine the resultant of the three forces shown.

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.

For the post of Prob. 2.36, determine (a) the required tension in rope AC if the resultant of the three forces exerted at point C is to be horizontal, (b) the corresponding magnitude of the resultant.

A hoist trolley is subjected to the three forces shown. Knowing that \(\mathrm{a}=40^{\circ}\), 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.

A hoist trolley is subjected to the three forces shown. Knowing that P = 250 lb, determine (a) the required value of a 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 are 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. Determine the tension (a) in cable AC, (b) in cable BC.

Knowing that \(a=20^{\circ}\), determine the tension (a) in cable AC, (b) in rope BC.

Knowing that \(a=55^{\circ}\) and that boom AC exerts on pin C a force directed along line AC, determine (a) the magnitude of that force, (b) the tension 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 = 500 N and \(a=60^{\circ}\), determine the tension (a) in cable AC, (b) in cable BC.

Two forces of magnitude \(T_{A}=8 \mathrm{kips}\) and \(T_{B}=15 \mathrm{kips}\) are applied as shown to a welded connection. Knowing that the connection is in equilibrium, determine the magnitudes of the forces \(T_{C}\) and \(T_{D}\).

Two forces of magnitude \(T_{A}=6 \mathrm{kips}\) and \(T_{C}=9 \mathrm{kips}\) are applied as shown to a welded connection. Knowing that the connection is in equilibrium, determine the magnitudes of the forces \(T_{B}\) and \(T_{D}\).

Two cables are tied together at C and loaded as shown. Knowing that P = 360 N, determine the tension (a) in cable AC, (b) in cable BC.

Two cables are tied together at C and loaded as shown. Determine the range of values of P for which both cables remain taut.

A sailor is being rescued using a boatswain’s 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 \(\mathrm{a}=30^{\circ}\) and \(\mathrm{b}=10^{\circ}\) and that the combined weight of the boatswain’s chair and the sailor is 900 N, determine the tension (a) in the support cable ACB, (b) in the traction cable CD.

A sailor is being rescued using a boatswain’s 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 \(\mathrm{a}=25^{\circ}\) and \(\mathrm{b}=15^{\circ}\) and that the tension in cable CD is 80 N, determine (a) the combined weight of the boatswain’s chair and the sailor, (b) the tension in the support cable ACB.

Two forces P and Q are applied as shown to an aircraft connection. Knowing that the connection is in equilibrium and that P = 500 lb and Q = 650 lb, determine the magnitudes of the forces exerted on the 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 magnitudes of the forces exerted on rods A and B are \(F_A=750\mathrm{\ lb}\) and \(F_B=400\mathrm{\ lb}\), determine the magnitudes of P and Q.

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.

Two cables tied together at C are loaded as shown. Knowing that the maximum allowable tension in each cable is 1200 N in cable AC and 600 N in cable B, determine (a) the magnitude of the largest force P that can be applied at C, (b) the corresponding value of a.

For the situation described in Fig. P2.45, 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.

For the structure and loading of Prob. 2.46, 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.

For the cables of Prob. 2.48, 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.

A 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.

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 = 4.5 in., (b) x = 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 = 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 \(50^{\circ}\). Determine the range of values of a for which the magnitude 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 arrangement shown. Determine the magnitude and direction of the force P that must be exerted on the free end of the rope to maintain equilibrium. (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 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 = 750 N, determine (a) the tension in cable ACB, (b) the magnitude of load Q.

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.

Determine (a) the x, y, and z components of the 900-N force, (b) the angles \(\mathrm{u}_{x}\), \(\mathrm{u}_{y}\), and \(\mathrm{u}_{z}\) that the force forms with the coordinate axes.

Determine (a) the x, y, and z components of the 750-N force, (b) the angles \(\mathrm{u}_{x}\), \(\mathrm{u}_{y}\), and \(\mathrm{u}_{z}\) that the force forms with the coordinate axes.

A gun is aimed at a point A located \(35^{\circ}\) east of north. Knowing that the barrel of the gun forms an angle of \(40^{\circ}\) 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 \(\mathrm{u}_{x}\), \(\mathrm{u}_{y}\), and \(\mathrm{u}_{z}\) 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 \(15^{\circ}\) north of west and that the barrel of the gun forms an angle of \(25^{\circ}\) with the horizontal.

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 \(\mathrm{u}_{x}\), \(\mathrm{u}_{y}\), and \(\mathrm{u}_{z}\) defining the direction of that force.

Cable AC is 70 ft long, and the tension in that cable is 5250 lb. Determine (a) the x, y, and z components of the force exerted by the cable on the anchor C, (b) the angles \(\mathrm{u}_{x}\), \(\mathrm{u}_{y}\), and \(\mathrm{u}_{z}\) defining the direction of that force.

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 \(\mathrm{u}_{x}\), \(\mathrm{u}_{y}\), and \(\mathrm{u}_{z}\) that the force forms with the coordinate axes.

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 \(\mathrm{u}_{x}\), \(\mathrm{u}_{y}\), and \(\mathrm{u}_{z}\) that the force forms with the coordinate axes.

Determine the magnitude and direction of the force F = (690 lb)i + (300 lb)j - (580 lb)k.

Determine the magnitude and direction of the force F = (650 N)i - (320 N)j + (760 N)k.

A force acts at the origin of a coordinate system in a direction defined by the angles \(\mathrm{u}_{x}=75^{\circ}\) and \(\mathrm{u}_{z}=130^{\circ}\). Knowing that the y component of the force is +300 lb, determine (a) the angle \(\mathrm{u}_{y}\), (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 \(\mathrm{u}_{y}=55^{\circ}\) and \(\mathrm{u}_{z}=45^{\circ}\). Knowing that the x component of the force is -500 N, determine (a) the angle \(\mathrm{u}_{x}\), (b) the other components and the magnitude of the force.

A force F of magnitude 230 N acts at the origin of a coordinate system. Knowing that \(\mathrm{u}_{x}=32.5^{\circ}\), \(F_y=-60\mathrm{\ N}\), and \(F_{2}>0\), determine (a) the components \(F_{x}\) and \(F_{z}\), (b) the angles \(\mathrm{u}_{y}\) and \(\mathrm{u}_{z}\).

A force F of magnitude 210 N acts at the origin of a coordinate system. Knowing that \(F_x=80\mathrm{\ N}\), \(\mathrm{u}_{z}=151.2^{\circ}\), and \(F_{y}<0\), determine (a) the components \(F_{y}\) and \(F_{z}\), (b) the angles \(\mathrm{u}_{x}\) and \(\mathrm{u}_{y}\).

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.

Knowing that the tension in cable AB is 1425 N, determine the components of the force exerted on the plate at B.

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

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. 2.89, determine the components of the force exerted by the cable on the support at E.

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

Find the magnitude and direction of the resultant of the two forces shown knowing that P = 450 N and Q = 600 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. 2.89, 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 cables of Prob. 2.87, 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.

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.

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 AD is 4.3 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 crate is supported by three cables as shown. Determine the weight of the crate knowing that the tension in cable AB is 750 lb.

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.

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 = 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 = 1200 N, find 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 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.

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.

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.

In trying to move across a slippery icy surface, a 180-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 = -(60 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 tension in each cable knowing that P = 2880 N and Q = 0.

For the cable system of Probs. 2.107 and 2.108, determine the tension in each cable knowing that P = 2880 N and Q = 576 N.

For the cable system of Probs. 2.107 and 2.108, determine the tension in each cable knowing that P = 2880 N and Q = - 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 2100 lb.

A horizontal circular plate weighing 60 lb is suspended as shown from three wires that are attached to a support at D and form \(30^{\circ}\) angles with the vertical. Determine the tension in each wire.

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. Knowing 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. 2.121 is 75 lb, determine (a) the magnitude of the load P, (b) the tension in cables BAC and AD.

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 = Pi and Q = Qk are applied to the ring to maintain the container in the position shown. Knowing that W = 376 N, determine P and Q. (Hint: The tension is the same in both portions of cable BAC.)

For the system of Prob. 2.123, determine W and Q knowing that P = 164 N.

Collars A and B are connected by a 525-mm-long wire and can slide freely on frictionless rods. If a force P = (341 N)j is applied to collar A, determine (a) the tension in the wire when y = 155 mm, (b) the magnitude of the force Q required to maintain the equilibrium of the system.

Solve Prob. 2.125 assuming that y = 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 trigonometry the magnitude and direction of the resultant of the forces applied to the bracket by members A and B.

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.

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.

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

A welded connection is in equilibrium under the action of the four forces shown. Knowing that \(F_{\mathrm{A}}=8\ \mathrm{kN}\) and \(F_{\mathrm{B}}=16\ \mathrm{kN}\), determine the magnitudes of the other two forces.

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.

A horizontal circular plate is suspended as shown from three wires that are attached to a support at D and form \(30^{\circ}\) angles with the vertical. Knowing that the x component of the force exerted by wire AD on the plate is 110.3 N, determine (a) the tension in wire AD, (b) the angles \(\mathrm{u}_{x}\), \(\mathrm{u}_{y}\), and \(\mathrm{u}_{z}\) that the force exerted at A forms with the coordinate axes.

A force acts at the origin of a coordinate system in a direction defined by the angles \(\mathrm{u}_{y}=55^{\circ}\) and \(\mathrm{u}_{z}=45^{\circ}\). Knowing that the x component of the force is -500 lb, determine (a) the angle \(\mathrm{u}_{x}\), (b) the other components and the magnitude of the force.

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

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.

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 = 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 = 120 lb and Q = 60 lb.