94CHAPTER 3 EQUILIBRIUM OF A PA R T I C L E FUNDAMENTAL PROBLEMS All problem solutions must include an FBD. F3–1. The crate has a weight of 550 lb. Determine the force in each supporting cable. F3–4. The block has a mass of 5 kg and rests on the smooth plane. Determine the unstretched length of the spring. 0.3 m C B 5 3 3 4 30 k 200 N/m A 0.4 m D 45 F3–1 F3–4 F3–2. The beam has a weight of 700 lb. Determine the shortest cable ABC that can be used to lift it if the maximum force the cable can sustain is 1500 lb. F3–5. If the mass of cylinder C is 40 kg, determine the mass of cylinder A in order to hold the assembly in the position shown. B B u 30 E D u C A C 40 kg 10 ft A F3–2 F3–3. If the 5-kg block is suspended from the pulley B and the sag of the cord is d = 0.15 m, determine the force in cord ABC. Neglect the size of the pulley. 0.4 m F3–6. Determine the tension in cables AB, BC, and CD, necessary to support the 10-kg and 15-kg traffic lights at B and C, respectively. Also, find the angle u. D A C A F3–5 d 0.15m 15 B C B D F3–3 F3–6 u 3. 3–6. The members of a truss are connected to the gusset plate. Set y = 0. 3–7.3 95 COPLANAR FORCE SYSTEMS PROBLEMS All problem solutions must include an FBD. determine the maximum mass of the girder that can be suspended from cable AB so that neither cable will fail. if the ship is moving forward with constant velocity.75 m. 3–3/4 Prob. The center of mass of the girder is located at point G.5-m-long cord AB can withstand a maximum force of 3500 N. Determine the force in each cord for equilibrium of the 200-kg crate. Take u = 30°. determine the tension developed in cables AB. If the mass of the girder is 3 Mg and its center of mass is located at point G. Take F = 12 kN. Cord BC remains horizontal due to the roller at C. If the 1. and AB has a length of 1. Determine the force in member B and its proper orientation u for equilibrium. 3–7 3 . The gusset plate is subjected to the forces of four members. determine the force in cord BC and the distance y so that the 200-kg crate can be supported. D C 30 FAB A 20 45 B B 30 D C A G 50 kN Probs. 3–5/6 3–3. Determine the force in each of the bridles. •3–5.5 m. 3–2. 2m A A O 8 kN u y 45 D B C B T 5 kN C F Probs. determine the magnitudes of F and T for equilibrium. and BD for equilibrium. *3–4. If the forces are concurrent at point O. The towing pendant AB is subjected to the force of 50 kN exerted by a tugboat. BC. BC and BD. •3–1. If cables BD and BC can withstand a maximum tensile force of 20 kN. The forces are concurrent at point O. 3–1/2 Probs. •3–13. 3–10/11 Probs. determine the magnitudes of F and T for equilibrium. If the block is held in the equilibrium position shown. 3–14. determine the largest weight of the crate that can be safely supported. Take F = 8 kN. 3–8/9 3–10. •3–9. Determine the stretch in springs AC and AB for equilibrium of the 2-kg block. If members AC and AB can support a maximum tension of 300 lb and 250 lb. The unstretched length of spring AB is 3 m. If block B weighs 200 lb and block C weighs 100 lb. determine the mass of the block at D. If block D weighs 300 lb and block B weighs 275 lb. 3–15. determine the required weight of block C and the angle u for equilibrium. The springs are shown in the equilibrium position. 3m y 4m C 9 kN 3m F B kAC 20 N/m kAB 30 N/m A 5 3 B 4 O A u x D C T Probs. 3–11. Members AC and AB support the 300-lb crate. 4 ft B C 3 4 ft u 30 A A B C D Probs.96 CHAPTER 3 EQUILIBRIUM OF A PA R T I C L E *3–8. Determine the tension force in member C and its angle u for equilibrium. The gusset plate is subjected to the forces of three members. 3–12/13 Probs. Take u = 90°. determine the required weight of block D and the angle u for equilibrium. 3 ft *3–12. respectively. 3–14/15 . The members of a truss are connected to the gusset plate. The forces are concurrent at point O. Determine the tensile force developed in each member. If the forces are concurrent at point O. The ball D has a mass of 20 kg. Take k = 50 lb>ft. 3–20/21 3–18. 3–19.5 m B 2 ft u C C k d A A F 2m D P Probs. determine the angle u for equilibrium.3. 3–18/19 Probs. Take k = 15 lb>ft. determine the maximum mass of the chandelier that can be supported. If cable CB is subjected to a tension that is twice that of cable CA. A B A 30 u 30° 3 C B 30 45 C D Probs. B 2 ft 1. Determine the unstretched length of spring AC if a force P = 80 lb causes the angle u = 60° for equilibrium. 3–16/17 Prob. Also. •3–17. •3–21. 3–22/23 . Take u = 40°. Determine the forces in cables AC and AB needed to hold the 20-kg ball D in equilibrium. A vertical force P = 10 lb is applied to the ends of the 2-ft cord AB and spring AC. determine the dimension d so that the force in cable AC is zero. what are the tensions in wires CA and CB? 97 COPLANAR FORCE SYSTEMS *3–20. 쐍3–22.3 *3–16. If the tension developed in each of the four wires is not allowed to exceed 600 N. determine the angle u for equilibrium of the 10-kg cylinder. Determine the tension developed in each wire used to support the 50-kg chandelier. If the spring has an unstretched length of 2 ft. If a force of F = 100 N is applied horizontally to the ring at A. 3–23. Take F = 300 N and d = 1 m. Determine the tension developed in wires CA and CB required for equilibrium of the 10-kg cylinder. Cord AB is 2 ft long. 3–27. determine the weight of cylinder F. If the bucket weighs 50 lb. Determine the angle u. and the mass m of each sphere. Neglect the size of the smooth pulley at C. The cords BCA and CD can each support a maximum load of 100 lb. 3–24/25 Prob. 3–29 A . and BA and the angle u required for equilibrium of the 30-lb cylinder E and the 60-lb cylinder F. 3–26/27 Prob. C C 3 u 30 B 30 A B 5 4 D 3 30 E 20 mN A 20 mN 30 Probs. the tension in cords AC and BC. CB. •3–25. 3–28 3–26. If cylinder E weighs 30 lb and u = 15°. Determine the maximum weight of the bucket that the wire system can support so that no single wire develops a tension exceeding 100 lb. Two spheres A and B have an equal mass and are electrostatically charged such that the repulsive force acting between them has a magnitude of 20 mN and is directed along line AB.98 CHAPTER 3 EQUILIBRIUM OF A PA R T I C L E *3–24. *3–28. Determine the maximum weight of the crate that can be hoisted at constant velocity and the angle u for equilibrium. •3–29. determine the tension developed in each of the wires. Determine the tensions developed in wires CD. D D A 30 C u C 45 u B 13 E 12 5 F B Probs.