Solved: The springs BA and BC each have a stiffness of 500

The members of a truss are pin connected at joint O. Determine the magnitudes of \(\mathbf{F}_1\) and \(\mathbf{F}_2\) for equilibrium. Set \(\theta = 60^{\circ}\).

The members of a truss are pin connected at joint O. Determine the magnitude of \(\mathbf{F}_1\) and its angle \(\theta\) for equilibrium. Set \(F_2 = 6\ kN\).

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 lengths of cables AB and AC that can be used for the lift. The center of gravity of the container is located at G.

Cords AB and AC can each sustain a maximum tension of 800 lb. If the drum has a weight of 900 lb, determine the smallest angle \(\theta\) at which they can be attached to the drum.

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 \(\theta = 30^{\circ}\).

The gusset plate is subjected to the forces of four members. Determine the force in member B and its proper orientation \(\theta\) for equilibrium. The forces are concurrent at point O. Take F = 12 kN.

The device shown is used to straighten the frames of wrecked autos. Determine the tension of each segment of the chain, i.e., AB and BC, if the force which the hydraulic cylinder DB exerts on point B is 3.50 kN, as shown.

Two electrically charged pith balls, each having a mass of 0.2 g, are suspended from light threads of equal length. Determine the resultant horizontal force of repulsion, F, acting on each ball if the measured distance between them is r = 200 mm.

Determine the maximum weight of the flowerpot that can be supported without exceeding a cable tension of 50 lb in either cable AB or AC.

Determine the tension developed in wires CA and CB required for equilibrium of the 10-kg cylinder. Take \(\theta = 40^{\circ}\).

If cable CB is subjected to a tension that is twice that of cable CA, determine the angle \(\theta\) for equilibrium of the 10-kg cylinder. Also, what are the tensions in wires CA and CB?

The concrete pipe elbow has a weight of 400 lb and the center of gravity is located at point G. Determine the force \(\mathbf{F}_{AB}\) and the tension in cables BC and BD needed to support it.

Blocks D and F weigh 5 lb each and block E weighs 8 lb. Determine the sag s for equilibrium. Neglect the size of the pulleys.

If blocks D and F weigh 5 lb each, determine the weight of block E if the sag s = 3 ft. Neglect the size of the pulleys.

The spring has a stiffness of k = 800 N/m and an unstretched length of 200 mm. Determine the force in cables BC and BD when the spring is held in the position shown.

The 10-lb lamp fixture is suspended from two springs, each having an unstretched length of 4 ft and stiffness of k = 5 lb/ft. Determine the angle \(\theta\) for equilibrium.

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 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.

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 the ring 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.

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 on the rope assembly are originally unstretched when \(\theta = 0^{\circ}\). Determine the tension in each rope when F = 90 lb. Neglect the size of the pulleys at B and D.

The springs on the rope assembly are originally stretched 1 ft when \(\theta = 0^{\circ}\). Determine the vertical force F that must be applied so that \(\theta = 30^{\circ}\).

The 10-lb weight A is supported by the cord AC and roller C, and by the spring that has a stiffness of k = 10 lb/in. If the unstretched length of the spring is 12 in. determine the distance d to where the weight is located when it is in equilibrium.

The 10-lb weight A is supported by the cord AC and roller C, and by spring AB. If the spring has an unstretched length of 8 in. and the weight is in equilibrium when d = 4 in., determine the stiffness k of the spring.

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.

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.

If the bucket weighs 50 lb, determine the tension developed in each of the wires.

Determine the maximum weight of the bucket that the wire system can support so that no single wire develops a tension exceeding 100 lb.

Determine the tension developed in each wire which is needed to support the 50-lb flowerpot.

If the tension developed in each of the wires is not allowed to exceed 40 lb, determine the maximum weight of the flowerpot that can be safely supported.

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.

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 6 ft and stiffness of k = 50 lb/ft.

The 200-lb uniform tank 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 sling BAC is used to lift the 100-lb load with constant velocity. Determine the force in the sling and plot its value T (ordinate) as a function of its orientation \(\theta\) where \(0\ \leq\ \theta\ \leq\ 90^{\circ}\).

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 load has a mass of 15 kg and is lifted by the pulley system shown. Determine the force F in the cord as a function of the angle \(\theta\). Plot the function of force F versus the angle \(\theta\) for \(0\ \leq\ \theta\ \leq\ 90^{\circ}\).

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.

Determine the magnitude and direction of the force P required to keep the concurrent force system in equilibrium.

If cable AB is subjected to a tension of 700 N, determine the tension in cables AC and AD and the magnitude of the vertical force F.

Determine the magnitudes of \(\mathbf{F}_1\), \(\mathbf{F}_2\), and \(\mathbf{F}_3\) 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.

If the balloon is subjected to a net uplift force of F = 800 N, determine the tension developed in ropes AB, AC, AD.

If each one of the ropes will break when it is subjected to a tensile force of 450 N, determine the maximum uplift force F the balloon can have before one of the ropes breaks.

The lamp has a mass of 15 kg and is supported by a pole AO and cables AB and AC. If the force in the pole acts along its axis, determine the forces in AO, AB, and AC for equilibrium.

Cables AB and AC can sustain a maximum tension of 500 N, and the pole can support a maximum compression of 300 N. Determine the maximum weight of the lamp that can be supported in the position shown. The force in the pole acts along the axis of the pole.

The 50-kg pot is supported from A by the three cables. Determine the force acting in each cable for equilibrium. Take d = 2.5 m.

Determine the height d of cable AB so that the force in cables AD and AC is one-half as great as the force in cable AB. What is the force in each cable for this case? The flower pot has a mass of 50 kg.

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 of the cables 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 force in each cable needed to support the 3500-lb platform. Set d = 2 ft.

Determine the force in each cable needed to support the 3500-lb platform. Set d = 4 ft.

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

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 exceeded 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?

The thin ring can be adjusted vertically between three equally long cables from which the 100-kg chandelier is suspended. If the ring remains in the horizontal plane and z = 600 mm, determine the tension in each cable.

The thin ring can be adjusted vertically between three equally long cables from which the 100-kg chandelier is suspended. If the ring remains in the horizontal plane and the tension in each cable is not allowed to exceed 1 kN, determine the smallest allowable distance z required for equilibrium.

The 80-lb chandelier is supported by three wires as shown. Determine the force in each wire for equilibrium.

If each wire can sustain a maximum tension of 120 lb before it fails, determine the greatest weight of the chandelier the wires will support in the position shown.

The 80-lb ball is suspended from the horizontal ring using three springs each having an unstretched length of 1.5 ft and stiffness of 50 lb/ft. Determine the vertical distance h from the ring to point A for equilibrium.