Solved: Determine the x and y components of each of the forces shown

Determine graphically the magnitude and direction of the resultant of the two forces shown using (a) the parallelogram law, (b) the triangle rule.

Determine graphically the magnitude and direction of the resultant of the two forces shown using (a) the parallelogram law, (b) the triangle rule.

Two structural members B and C are bolted to the bracket A. Knowing that the tension in member B is 6 kN and that the tension in C is 10 kN, determine graphically the magnitude and direction of the resultant force acting on the bracket.

Two structural members B and C are bolted to the bracket A. Knowing that the tension in member B is 2500 lb and that the tension in C is 2000 lb, determine graphically the magnitude and direction of the resultant force acting on the bracket.

The force F of magnitude 100 lb is to be resolved into two components along the lines a-a and b-b. Determine by trigonometry the angle \(\alpha\), knowing that the component of F along line a-a is 70 lb.

The force F of magnitude 800 N is to be resolved into two components along the lines a-a and b-b. Determine by trigonometry the angle \(\alpha\), knowing that the component of F along line b-b is 120 N.

A trolley that moves along a horizontal beam is acted upon by two forces as shown. (a) Knowing that \(\alpha = 25^\circ\), 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 disabled automobile is pulled by means of two ropes as shown. The tension in AB is 500 lb, and the angle \(\alpha\) is \(25^\circ\). 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.

Determine by trigonometry the magnitude of the force P so that the resultant of the two forces applied at A is vertical. What is the corresponding magnitude of the resultant?

A disabled automobile is pulled by means of two ropes as shown. Knowing that the tension in rope AB is 750 lb, determine by trigonometry the tension in rope AC and the value of \(\alpha\) so that the resultant force exerted at A is a 1200-lb force directed along the axis of the automobile.

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.

Knowing that P = 30 lb, determine by trigonometry the resultant of the two forces applied at point A.

Solve Prob. 2.1 by trigonometry.

Solve Prob. 2.4 by trigonometry.

If the resultant of the two forces exerted on the trolley of Prob. 2.7 is to be vertical, determine (a) the value of \(\alpha\) for which the magnitude of P is minimum, (b) the corresponding magnitude of P.

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 tension in the support wire AB is 65 lb. Determine the horizontal and vertical components of the force acting on the pin at A.

The hydraulic cylinder GE exerts on member DF a force P directed along line GE. Knowing that P must have a 600-N component perpendicular to member DF, determine the magnitude of P and its component parallel to DF.

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 perpendicular to member ABC, determine (a) the magnitude of the force P, (b) its component parallel to ABC.

Using x and y components, solve Prob. 2.1.

Using x and y components, solve Prob. 2.2.

Determine the resultant of the three forces of Prob. 2.17.

Determine the resultant of the three forces of Prob. 2.19.

Two cables of known tensions are attached to the top of pylon AB. A third cable AC is used as a guy wire. Determine the tension in AC, knowing that the resultant of the forces exerted at A by the three cables must be vertical.

A hoist trolley is subjected to the three forces shown. Knowing that \(\alpha = 40^\circ\), determine (a) the magnitude of the force P for which the resultant of the three forces is 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 value of the angle \(\alpha\) for which the resultant of the three forces is vertical, (b) the corresponding magnitude of the resultant.

A collar that can slide on a vertical rod is subjected to the three forces shown. The direction of the force F may be varied. If possible, determine the direction of the force F so that the resultant of the three forces is horizontal, knowing that the magnitude of F is (a) 2.4 kN, (b) 1.4 kN.

Two cables are tied together at C and loaded as shown. Determine the tension in AC and BC.

Two cables are tied together at C and loaded as shown. Determine the tension in AC and BC.

Two cables are tied together at C and loaded as shown. Determine the tension in AC and BC.

Two cables are tied together at C and loaded as shown. Determine the tension in AC and BC.

Two cables are tied together at C and loaded as shown. Knowing that P = 500 N and \(\alpha = 60^\circ\), determine the tension in AC and BC.

Two forces of magnitude \(T_A= 8\) kips and \(T_B= 15\) 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 \(T_A= 6\) kips and \(T_C= 9\) 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 forces of magnitude \(T_A= 5000 \ \mathrm N\) and \(T_B=2500 \ \mathrm N\) are applied as shown to a welded connection. Knowing that the connection is in equilibrium, determine the magnitudes of the forces \(T_C\) and \(T_D\).

Determine the range of values of P for which both cables remain taut.

For the cables of Prob. 2.36, 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 \(\alpha\).

Two ropes are tied together at C. If the maximum permissible tension in each rope is 2.5 kN, what is the maximum force F that can be applied? In what direction must this maximum force act?

A 600-lb block is supported by two cables AC and BC. (a) For what value of a is the tension in cable AC maximum? (b) What are the corresponding values of the tension in cables AC and BC?

A 600-lb block is supported by two cables AC and BC. Determine (a) the value of a for which the larger of the cable tensions is as small as possible, (b) the corresponding values of the tension in cables AC and BC.

Two cables are tied together at C as shown. Find the value of \(\alpha\) for which the tension is as small as possible (a) in cable BC, (b) in both cables simultaneously. In each case determine the tension in both cables.

The 60-lb collar A can slide on a frictionless vertical rod and is connected as shown to a 65-lb counterweight C. Determine the value of h for which the system is in equilibrium.

The force P is applied to a small wheel that rolls on the cable ACB. Knowing that the tension in both parts of the cable is 750 N, determine the magnitude and direction of P.

The directions of the 60-lb forces may vary, but the angle between the forces is always \(45^\circ\). Determine the value of \(\alpha\) for which the resultant of the forces acting at A is directed vertically upward.

A 3.6-m length of steel pipe of mass 300 kg is lifted by a crane cable CD. Determine the tension in the cable sling ACB, knowing that the length of the sling is (a) 4.5 m, (b) 6 m.

A movable bin and its contents weigh 700 lb. 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 1250 lb.

A 250-kg crate is supported by several rope-and-pulley arrangements as shown. Determine for each arrangement the tension in the rope. (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.)

Solve parts b and d of Prob. 2.51 assuming that the free end of the rope is attached to the crate.

A 450-lb crate is to be supported by the rope-and-pulley arrangement shown. Determine the magnitude and direction of the force F that should be exerted on the free end of the rope.

For W = 800 N, P = 200 N, and d = 600 mm, determine the value of h to maintain equilibrium.

The collar A can slide freely on the horizontal smooth rod. Determine the magnitude of the force P required to maintain equilibrium when (a) c = 9 in., (b) c = 16 in.

Determine (a) the x, y, and z components of the 250-N force, (b) the angles \(\theta_x, \theta_y\), and \(\theta_z\) that the force forms with the coordinate axes.

Determine (a) the x, y, and z components of the 300-N force, (b) the angles \(\theta_x, \theta_y\), and \(\theta_z\) that the force forms with the coordinate axes.

The angle between the guy wire AB and the mast is \(20^\circ\). Knowing that the tension in AB is 300 lb, determine (a) the x, y, and components of the force exerted on the boat at B, (b) the angles \(\theta_x, \theta_y\), and \(\theta_z\) defining the direction of the force exerted at B.

The angle between the guy wire AC and the mast is \(20^\circ\). Knowing that the tension in AC is 300 lb, determine (a) the x, y, and components of the force exerted on the boat at C, (b) the angles \(\theta_x, \theta_y\), and \(\theta_z\) defining the direction of the force exerted at C.

A gun is aimed at a point A located \(20^{\circ}\) west of north. Knowing that the barrel of the gun forms an angle of \(35^{\circ}\) with the horizontal and that the maximum recoil force is 800 N, determine (a) the x, y, and z components of the force, (b) the angles \(\theta_x, \theta_y\), and \(\theta_z\) defining the direction of the recoil force. (Assume that the x, y, and z axes are directed, respectively, cast, up, and south.)

Solve Prob. 2,60 , assuming that point A is located \(25^{\circ}\) north of west and that the barrel of the gun forms an angle of \(30^{\circ}\) with the horizontal.

Determine the magnitude and direction of the force F = -(240 lb)i - (320 lb)j + (600 lb)k.

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

A force acts at the origin in a direction defined by the angles \(\theta_y=120^{\circ}\) and \(\theta_z=75^{\circ}\). It is known that the x component of the force is +40 N. Determine the magnitude of the force and the value of \(\theta_x\).

A 250-lb force acts at the origin in a direction defined by the angles \(\theta_x=65^{\circ}\) and \(\theta_y=40^{\circ}\). It is known that the z component of the force is positive. Determine the value of \(\theta_x\) and the components of the force.

A force acts at the origin in a direction defined by the angles \(\theta_x=70^{\circ}\) and \(\theta_z=130^{\circ}\). Knowing that the y component of the force is +400 lb, determine (a) the other components and the magnitude of the force, (b) the value of \(\theta_y\).

A force acts at the origin in a direction defined by the angles \(\theta_y=65^{\circ}\) and \(\theta_z=40^{\circ}\). Knowing that the x component of the force is -750 N, determine (a) the other components and the magnitude of the force, (b) the value of \(\theta_x\).

Knowing that the tension in cable AB is 900 N, determine the components of the force exerted on the plate at A.

Knowing that the tension in cable BC is 450 N, determine the components of the force exerted on the plate at C.

Knowing that the tension in cable AB is 285 lb, determine the components of the force exerted on the plate at B.

Knowing that the tension in cable AC is 426 lb, determine the components of the force exerted on the plate at C.

Determine the resultant of the two forces shown.

Knowing that the tension is 285 lb in cable AB and 426 lb in cable AC, determine the magnitude and direction of the resultant of the forces exerted at A by the two cables.

The angle between each of the springs AB and AC and the post DA is \(30^\circ\). Knowing that the tension is 50 lb in spring AB and 40 lb in spring AC, determine the magnitude and direction of the resultant of the forces exerted by the springs on the post at A.

Determine the two possible values of \(\theta_y\) for a force F, (a) if the force forms equal angles with the positive x, y, and z axes, (b) if the force forms equal angles with the positive y and z axes and an angle of \(45^\circ\) with the positive x axis.

Knowing that the tension in AB is 39 kN, determine the required values of the tension in AC and AD so that the resultant of the three forces applied at A is vertical.

Knowing that the tension in AC is 28 kN, determine the required values of the tension in AB and AD so that the resultant of the three forces applied at A is vertical.

The boom OA carries a load P and is supported by two cables as shown. Knowing that the tension in cable AB is 732 N 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. 2.78, 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.

A container of weight W = 9.32 kN is supported by three cables that are attached to a ceiling as shown. Determine the tension in each cable.

A load W is supported by three cables as shown. Determine the value of W knowing that the tension in cable BD is 975 lb.

A load W is supported by three cables as shown. Determine the value of W knowing that the tension in cable CD is 300 lb.

A load W of magnitude 555 lb is supported by three cables as shown. Determine the tension in each cable.

Three wires are connected at point D, which is located 18 in. below the T-shaped pipe support ABC. Determine the tension in each wire when a 180-lb container is suspended from point D as shown.

A triangular plate of weight 18 lb is supported by three wires as shown. Determine the tension in each wire.

Three cables are connected at A, where the forces P and Q are applied as shown. Determine the tension in each of the cables when P = 0 and Q = 36.4 kN.

Three cables are connected at A, where the forces P and Q are applied as shown. Knowing that Q = 36.4 kN and that the tension in cable AD is zero, determine (a) the magnitude and sense of P, (b) the tension in cables AB and AC.

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. 2.90, assuming that a friend is helping the man at A by pulling on him with a force P = 2(45 lb)k.

A container of weight W = 360 N is supported by cables AB and AC, which are tied to ring A. Knowing that Q = 0, determine (a) the magnitude of the force P that must be applied to the ring to maintain the container in the position shown, (b) the corresponding values of the tension in cables AB and AC.

Solve Prob. 2.92 knowing that Q = (60 N)k.

A container is supported by a single cable that passes through a frictionless ring A and is attached to fixed points 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 the weight of the container is W = 660 N, determine the magnitudes of P and Q. (Hint: The tension must be the same in portions AB and AC of the cable.)

Determine the weight W of the container of Prob. 2.94 knowing that P = 478 N.

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, deter- mine the tension in each of the three cables.

Knowing that the tension in cable AE of Prob. 2.96 is 75 lb, determine (a) the magnitude of the load P, (b) the tension in cables BAC and AD.

The uniform circular ring shown has a mass of 20 kg and a diameter of 300 mm. It is supported by three wires each of length 250 mm. If \(\alpha = 120^\circ, \beta = 150^\circ\), and \(\gamma = 90^\circ\), determine the tension in each wire.

Collar A weighs 5.6 lb and may slide freely on a smooth vertical rod; it is connected to collar B by wire AB. Knowing that the length of wire AB is 18 in., determine the tension in the wire when (a) c = 2 in., (b) c = 8 in.

Solve Prob. 2.99 when (a) c = 14 in., (b) c = 16 in.

Two wires are attached to the top of pole CD. It is known that the force exerted by the pole is vertical and that the 500-lb force applied to point C is horizontal. If the 500-lb force is parallel to the z axis \((\alpha = 90^\circ)\), determine the tension in each cable.

Three cables are connected at D, where an upward force of 30 kN is applied. Determine the tension in each cable.

A 6-kg circular plate of 200-mm radius is supported as shown by three wires of length L. Knowing that \(\alpha = 30^\circ\), determine the smallest permissible value of the length L if the tension is not to exceed 35 N in any of the wires.

A cable loop of length 1.5 m is placed around a crate. Knowing that the mass of the crate is 300 kg, determine the tension in the cable for each of the arrangements shown.

Knowing that the magnitude of the force P is 75 lb, determine the resultant of the three forces applied at A.

Determine the range of values of P for which the resultant of the three forces applied at A does not exceed 175 lb.

The directions of the 300-N forces may vary, but the angle between the forces is always \(40^\circ\). Determine the value of \(\alpha\) for which the resultant of the forces acting at A is directed parallel to the plane b-b.

Knowing that P = 300 lb, determine the tension in cables AC and BC.

Determine the range of values of P for which both cables remain taut.

A container is supported by three cables as shown. Determine the weight W of the container knowing that the tension in cable AB is 500 N.

In Prob. 2.110, determine the angles \(\theta_x, \theta_y\), and \(\theta_z\) for the force exerted at D by cable AD.

A 1200-N force acts at the origin in a direction defined by the angles \(\theta_x = 65^\circ\) and \(\theta_y = 40^\circ\). It is also known that the z component of the force is positive. Determine the value of \(\theta_z\) and the components of the force.

Two cables BG and BH are attached to frame ACD as shown. Knowing that the tension is 540 N in cable BG and 750 N in cable BH, determine the magnitude and direction of the resultant of the forces exerted by the cables on the frame at B.

A crate is supported by three cables as shown. Determine the weight W of the crate knowing that the tension in cable AD is 924 lb.

A triangular steel plate is supported by three wires as shown. Knowing that a = 6 in. and that the tension in wire AD is 17 lb, determine the weight of the plate.