Solution: Blocks D and E have a mass of 4 kg and 6 kg,

The members of a truss are pin connected at joint O. Determine the magnitudes of \(F_1\) and \(F_2\) for equilibrium. Set \(\theta = 60^{\circ}\).

The members of a truss are pin connected at joint O. Determine the magnitude of \(F_1\) and its angle \(\theta\) for equilibrium. Set \(F_2 = 6\ kN\).

Determine the magnitude and direction \(\theta\) of F so that the particle is in equilibrium.

The bearing consists of rollers, symmetrically confined within the housing. The bottom one is subjected to a 125-N force at its contact A due to the load on the shaft. Determine the normal reactions \(N_B\) and \(N_C\) on the bearing at its contact points B and C for equilibrium.

The members of a truss are connected to the gusset plate. If the forces are concurrent at point O, determine the magnitudes of F and T for equilibrium. Take \(\theta = 90^{\circ}\).

The gusset plate is subjected to the forces of three members. Determine the tension force in member C and its angle \(\theta\) for equilibrium. The forces are concurrent at point O. Take F = 8 kN.

The man attempts to pull down the tree using the cable and small pulley arrangement shown. If the tension in AB is 60 lb, determine the tension in cable CAD and the angle \(\theta\) which the cable makes at the pulley.

The cords ABC and BD can each support a maximum load of 100 lb. Determine the maximum weight of the crate, and the angle \(\theta\) for equilibrium.

Determine the maximum force F that can be supported in the position shown if each chain can support a maximum tension of 600 lb before it fails.

The block has a weight of 20 lb and is being hoisted at uniform velocity. Determine the angle \(\theta\) for equilibrium and the force in cord AB.

Determine the maximum weight W of the block that can be suspended in the position shown if cords AB and CAD can each support a maximum tension of 80 lb. Also, what is the angle \(\theta\) for equilibrium?

The lift sling is used to hoist a container having a mass of 500 kg. Determine the force in each of the cables AB and AC as a function of \(\theta\). If the maximum tension allowed in each cable is 5 kN, determine the shortest length of cables AB and AC that can be used for the lift. The center of gravity of the container is located at G.

A nuclear-reactor vessel has a weight of \(500(10^3)\ lb\). Determine the horizontal compressive force that the spreader bar AB exerts on point A and the force that each cable segment CA and AD exert on this point while the vessel is hoisted upward at constant velocity.

Determine the stretch in each spring for equilibrium of the 2-kg block. The springs are shown in the equilibrium position.

The unstretched length of spring AB is 3 m. If the block is held in the equilibrium position shown, determine the mass of the block at D.

Determine the mass of each of the two cylinders if they cause a sag of s = 0.5 m when suspended from the rings at A and B. Note that s = 0 when the cylinders are removed.

Determine the stiffness \(k_T\) of the single spring such that the force F will stretch it by the same amount s as the force F stretches the two springs. Express \(k_T\) in terms of stiffness \(k_1\) and \(k_2\) of the two springs.

If the spring DB has an unstretched length of 2 m, determine the stiffness of the spring to hold the 40-kg crate in the position shown.

Determine the unstretched length of DB to hold the 40-kg crate in the position shown. Take k = 180 N/m.

A vertical force P = 10 lb is applied to the ends of the 2-ft cord AB and spring AC. If the spring has an unstretched length of 2 ft, determine the angle \(\theta\) for equilibrium. Take k = 15 lb/ft.

Determine the unstretched length of spring AC if a force P = 80 lb causes the angle \(\theta = 60^{\circ}\) for equilibrium. Cord AB is 2 ft long. Take k = 50 lb/ft.

The springs BA and BC each have a stiffness of 500 N/m and an unstretched length of 3 m. Determine the horizontal force F applied to the cord which is attached to the small ring B so that the displacement of AB from the wall is d = 1.5 m.

The springs BA and BC each have a stiffness of 500 N/m and an unstretched length of 3 m. Determine the displacement d of the cord from the wall when a force F = 175 N is applied to the cord.

Determine the distances x and y for equilibrium if \(F_1 = 800\ N\) and \(F_2 = 1000\ N\).

Determine the magnitude of \(F_1\) and the distance y if x = 1.5 m and \(F_2 = 1000\ N\).

The 30-kg pipe is supported at A by a system of five cords. Determine the force in each cord for equilibrium.

Each cord can sustain a maximum tension of 500 N. Determine the largest mass of pipe that can be supported.

The street-lights at A and B are suspended from the two poles as shown. If each light has a weight of 50 lb, determine the tension in each of the three supporting cables and the required height h of the pole DE so that cable AB is horizontal.

Determine the tension developed in each cord required for equilibrium of the 20-kg lamp.

Determine the maximum mass of the lamp that the cord system can support so that no single cord develops a tension exceeding 400 N.

Blocks D and E have a mass of 4 kg and 6 kg, respectively. If x = 2 m determine the force F and the sag s for equilibrium.

Blocks D and E have a mass of 4 kg and 6 kg, respectively. If F = 80 N, determine the sag s and distance x for equilibrium.

The lamp has a weight of 15 lb and is supported by the six cords connected together as shown. Determine the tension in each cord and the angle \(\theta\) for equilibrium. Cord BC is horizontal.

Each cord can sustain a maximum tension of 20 lb. Determine the largest weight of the lamp that can be supported. Also, determine \(\theta\) of cord DC for equilibrium.

The ring of negligible size is subjected to a vertical force of 200 lb. Determine the required length l of cord AC such that the tension acting in AC is 160 lb. Also, what is the force in cord AB? Hint: Use the equilibrium condition to determine the required angle \(\theta\) for attachment, then determine l using trigonometry applied to triangle ABC.

Cable ABC has a length of 5 m. Determine the position x and the tension developed in ABC required for equilibrium of the 100-kg sack. Neglect the size of the pulley at B.

A 4-kg sphere rests on the smooth parabolic surface. Determine the normal force it exerts on the surface and the mass \(m_B\) of block B needed to hold it in the equilibrium position shown.

Determine the forces in cables AC and AB needed to hold the 20-kg ball D in equilibrium. Take F = 300 N and d = 1 m.

The ball D has a mass of 20 kg. If a force of F = 100 N is applied horizontally to the ring at A, determine the dimension d so that the force in cable AC is zero.

The 200-lb uniform container is suspended by means of a 6-ft-long cable, which is attached to the sides of the tank and passes over the small pulley located at O. If the cable can be attached at either points A and B, or C and D, determine which attachment produces the least amount of tension in the cable. What is this tension?

The single elastic cord ABC is used to support the 40-lb load. Determine the position x and the tension in the cord that is required for equilibrium. The cord passes through the smooth ring at B and has an unstretched length of 6ft and stiffness of k = 50 lb/ft.

A “scale” is constructed with a 4-ft-long cord and the 10-lb block D. The cord is fixed to a pin at A and passes over two small pulleys. Determine the weight of the suspended block B if the system is in equilibrium when s = 1.5 ft.

The three cables are used to support the 40-kg flowerpot. Determine the force developed in each cable for equilibrium.

Determine the magnitudes of \(F_1\), \(F_2\), and \(F_3\) for equilibrium of the particle.

If the bucket and its contents have a total weight of 20 lb, determine the force in the supporting cables DA, DB, and DC.

Determine the stretch in each of the two springs required to hold the 20-kg crate in the equilibrium position shown. Each spring has an unstretched length of 2 m and a stiffness of k = 300 N/m.

Determine the force in each cable needed to support the 20-kg flowerpot.

Determine the tension in the cables in order to support the 100-kg crate in the equilibrium position shown.

Determine the maximum mass of the crate so that the tension developed in any cable does not exceeded 3 kN.

Determine the force in each cable if F = 500 lb.

Determine the greatest force F that can be applied to the ring if each cable can support a maximum force of 800 lb.

Determine the tension developed in cables AB and AC and the force developed along strut AD for equilibrium of the 400-lb crate.

If the tension developed in each cable cannot exceed 300 lb, determine the largest weight of the crate that can be supported. Also, what is the force developed along strut AD?

Determine the tension developed in each cable for equilibrium of the 300-lb crate.

Determine the maximum weight of the crate that can be suspended from cables AB, AC, and AD so that the tension developed in any one of the cables does not exceed 250 lb.

The 25-kg flowerpot is supported at A by the three cords. Determine the force acting in each cord for equilibrium.

If each cord can sustain a maximum tension of 50 N before it fails, determine the greatest weight of the flowerpot the cords can support.

Determine the tension developed in the three cables required to support the traffic light, which has a mass of 15 kg. Take h = 4 m.

Determine the tension developed in the three cables required to support the traffic light, which has a mass of 20 kg. Take h = 3.5 m.

The 800-lb cylinder is supported by three chains as shown. Determine the force in each chain for equilibrium. Take d = 1 ft.

Determine the tension in each cable for equilibrium.

If the maximum force in each rod can not exceed 1500 N, determine the greatest mass of the crate that can be supported.

The crate has a mass of 130 kg. Determine the tension developed in each cable for equilibrium.

If cable AD is tightened by a turnbuckle and develops a tension of 1300 lb, determine the tension developed in cables AB and AC and the force developed along the antenna tower AE at point A.

If the tension developed in either cable AB or AC can not exceed 1000 lb, determine the maximum tension that can be developed in cable AD when it is tightened by the turnbuckle. Also, what is the force developed along the antenna tower at point A?

Determine the tension developed in cables AB, AC, and AD required for equilibrium of the 300-lb crate.

Determine the maximum weight of the crate so that the tension developed in any cable does not exceed 450 lb.