Baixe Resolução Hibbeler - Statics 12ªed - hibbeler - statics 12?ed - cap.3 e outras Provas em PDF para Engenharia Mecânica, somente na Docsity! 121 •3–1. Determine the force in each cord for equilibrium of the 200-kg crate. Cord remains horizontal due to the roller at , and has a length of . Set .y = 0.75 m1.5 mABC BC © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. C B A 2 m y 3 Solutions 44918 1/21/09 4:25 PM Page 121 122 3–2. If the 1.5-m-long cord can withstand a maximum force of , determine the force in cord and the distance y so that the 200-kg crate can be supported. BC3500 N AB © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. C B A 2 m y 3 Solutions 44918 1/21/09 4:25 PM Page 122 125 •3–5. 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 .u = 30° © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 5 kN A B C D T O 45 u F 8 kN 3–6. The gusset plate is subjected to the forces of four members. Determine the force in member B and its proper orientation for equilibrium. The forces are concurrent at point O. Take .F = 12 kN u 5 kN A B C D T O 45 u F 8 kN 3 Solutions 44918 1/21/09 4:25 PM Page 125 126 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–7. The towing pendant AB is subjected to the force of 50 kN exerted by a tugboat. Determine the force in each of the bridles, BC and BD, if the ship is moving forward with constant velocity. 30 A B CD 50 kN 20 3 Solutions 44918 1/21/09 4:25 PM Page 126 127 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *3–8. Members and support the 300-lb crate. Determine the tensile force developed in each member. ABAC A BC 4 ft 4 ft 3 ft 3 Solutions 44918 1/21/09 4:25 PM Page 127 130 *3–12. If block weighs and block weighs , determine the required weight of block and the angle for equilibrium. uD 100 lbC200 lbB © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. A B D C u 30 3 Solutions 44918 1/21/09 4:25 PM Page 130 131 •3–13. If block weighs 300 lb and block weighs 275 lb, determine the required weight of block and the angle for equilibrium. uC BD © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. A B D C u 30 3 Solutions 44918 1/21/09 4:25 PM Page 131 132 3–14. Determine the stretch in springs AC and AB for equilibrium of the 2-kg block. The springs are shown in the equilibrium position. © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3 m 3 m 4 m kAC 20 N/m kAB 30 N/m C B A D 3–15. 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. 3 m 3 m 4 m kAC 20 N/m kAB 30 N/m C B A D 3 Solutions 44918 1/21/09 4:25 PM Page 132 135 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–18. Determine the forces in cables AC and AB needed to hold the 20-kg ball D in equilibrium. Take and .d = 1 m F = 300 N A C B F D 2 m 1.5 m d 3 Solutions 44918 1/21/09 4:25 PM Page 135 136 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–19. The ball D has a mass of 20 kg. If a force of is applied horizontally to the ring at A, determine the dimension d so that the force in cable AC is zero. F = 100 N A C B F D 2 m 1.5 m d 3 Solutions 44918 1/21/09 4:25 PM Page 136 137 *3–20. Determine the tension developed in each wire used to support the 50-kg chandelier. © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. A B D C 30 30 45 3 Solutions 44918 1/21/09 4:25 PM Page 137 140 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–23. Determine the unstretched length of spring AC if a force causes the angle for equilibrium. Cord AB is 2 ft long. Take k = 50 lb>ft. u = 60°P = 80 lb 2 ft k 2 ft A B C P u 3 Solutions 44918 1/21/09 4:25 PM Page 140 141 *3–24. If the bucket weighs 50 lb, determine the tension developed in each of the wires. © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. A B E C D4 3 5 30 30 3 Solutions 44918 1/21/09 4:25 PM Page 141 142 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. •3–25. Determine the maximum weight of the bucket that the wire system can support so that no single wire develops a tension exceeding 100 lb. A B E C D4 3 5 30 30 3 Solutions 44918 1/21/09 4:25 PM Page 142 145 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *3–28. 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. Determine the angle the tension in cords AC and BC, and the mass m of each sphere. u, C 30 20 mN 20 mN 30 B u A •3–29. The cords BCA and CD can each support a maximum load of 100 lb. Determine the maximum weight of the crate that can be hoisted at constant velocity and the angle for equilibrium. Neglect the size of the smooth pulley at C. u 12 5 13 B A C D u 3 Solutions 44918 1/21/09 4:25 PM Page 145 146 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–30. The springs on the rope assembly are originally unstretched when . Determine the tension in each rope when . Neglect the size of the pulleys at B and D. F = 90 lb u = 0° F A B C E D 2 ft 2 ft k 30 lb/ft k 30 lb/ft θθ 3 Solutions 44918 1/21/09 4:25 PM Page 146 147 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–31. The springs on the rope assembly are originally stretched 1 ft when . Determine the vertical force F that must be applied so that .u = 30° u = 0° F A B C E D 2 ft 2 ft k 30 lb/ft k 30 lb/ft θθ 3 Solutions 44918 1/21/09 4:25 PM Page 147 150 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–34. The wire forms a loop and passes over the small pulleys at A, B, C, and D. If the maximum resultant force that the wire can exert on each pulley is 120 N, determine the greatest force P that can be applied to the wire as shown. P A B D C 30 30 3 Solutions 44918 1/21/09 4:25 PM Page 150 151 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–35. The picture has a weight of 10 lb and is to be hung over the smooth pin B. If a string is attached to the frame at points A and C, and the maximum force the string can support is 15 lb, determine the shortest string that can be safely used. CA 9 in. 9 in. B 3 Solutions 44918 1/21/09 4:25 PM Page 151 152 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *3–36. 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? A O C 1 ft B 2 ft F D 2 ft 2 ft 3 Solutions 44918 1/21/09 4:25 PM Page 152 155 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. •3–39. 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 at B and C. Determine the weight of the suspended block at B if the system is in equilibrium. C D B A 1 ft 1.5 ft •*3–40. The spring has a stiffness of and an unstretched length of 200 mm. Determine the force in cables BC and BD when the spring is held in the position shown. k = 800 N>m A Bk 800 N/m D 500 mm 400 mm 400 mm 300 mm C 3 Solutions 44918 1/21/09 4:25 PM Page 155 156 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. •3–41. A continuous cable of total length 4 m is wrapped around the small pulleys at A, B, C, and D. If each spring is stretched 300 mm, determine the mass m of each block. Neglect the weight of the pulleys and cords. The springs are unstretched when d = 2 m. B C A k 500 N/m k 500 N/m d D 3–42. Determine the mass of each of the two cylinders if they cause a sag of when suspended from the rings at A and B. Note that when the cylinders are removed. s = 0 s = 0.5 m 1 m 2 m2 m 1.5 m s BA C D k 100 N/m k 100 N/m 3 Solutions 44918 1/21/09 4:25 PM Page 156 157 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. •3–43. The pail and its contents have a mass of 60 kg. If the cable BAC is 15 m long, determine the distance y to the pulley at A for equilibrium. Neglect the size of the pulley. 2 m y C B A 10 m 3 Solutions 44918 1/21/09 4:25 PM Page 157 160 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–46. Determine the maximum mass of the crate so that the tension developed in any cable does not exceeded 3 kN. 2.5 m 2 m 2 m 2 m 1 mA z D y x B C 3 Solutions 44918 1/21/09 4:25 PM Page 160 161 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–47. The shear leg derrick is used to haul the 200-kg net of fish onto the dock. Determine the compressive force along each of the legs AB and CB and the tension in the winch cable DB.Assume the force in each leg acts along its axis. 4 m 4 m 2 m 2 m 5.6 m D B C A x y z 3 Solutions 44918 1/21/09 4:25 PM Page 161 162 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *3–48. Determine the tension developed in cables , , and required for equilibrium of the 300-lb crate.AD ACAB A D C x 1 ft 3 ft 2 ft 1 ft 2 ft 2 ft y z 2 ft B 3 Solutions 44918 1/21/09 4:25 PM Page 162 165 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–51. Determine the force in each cable needed to support the 3500-lb platform. Set .d = 4 ft 3 ft d yx C D B A 3500 lb 4 ft 3 ft 10 ft 4 ft 2 ft z 3 Solutions 44918 1/21/09 4:25 PM Page 165 166 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *3–52. Determine the force in each of the three cables needed to lift the tractor which has a mass of 8 Mg. 2 m 1.25 m 1.25 m 1 m 3 m A D C B y x z 3 Solutions 44918 1/21/09 4:25 PM Page 166 167 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. •3–53. Determine the force acting along the axis of each of the three struts needed to support the 500-kg block. 0.75 m 1.25 m 3 m 2.5 m z A B C D x y 2 m 3 Solutions 44918 1/21/09 4:25 PM Page 167 170 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *3–56. The ends of the three cables are attached to a ring at A and to the edge of a uniform 150-kg plate. Determine the tension in each of the cables for equilibrium. z A B x y D C 10 m 6 m 6 m 6 m 4 m 2 m 2 m 12 m 2 m •3–57. The ends of the three cables are attached to a ring at A and to the edge of the uniform plate. Determine the largest mass the plate can have if each cable can support a maximum tension of 15 kN. z A B x y D C 10 m 6 m 6 m 6 m 4 m 2 m 2 m 12 m 2 m 3 Solutions 44918 1/21/09 4:25 PM Page 170 171 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–58. Determine the tension developed in cables , , and required for equilibrium of the 75-kg cylinder.AD ACAB 1 m 3 m 3 m 4 m 1.5 m 2 m 2 m 1 m A C z y x B D 3 Solutions 44918 1/21/09 4:25 PM Page 171 172 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–59. If each cable can withstand a maximum tension of 1000 N, determine the largest mass of the cylinder for equilibrium. 1 m 3 m 3 m 4 m 1.5 m 2 m 2 m 1 m A C z y x B D 3 Solutions 44918 1/21/09 4:25 PM Page 172 175 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–62. A force of holds the 400-lb crate in equilibrium. Determine the coordinates (0, y, z) of point A if the tension in cords AC and AB is 700 lb each. F = 100 lb B C A F y z x 4 ft 5 ft 5 ft zy 3 Solutions 44918 1/21/09 4:25 PM Page 175 176 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–63. If the maximum allowable tension in cables AB and AC is 500 lb, determine the maximum height z to which the 200-lb crate can be lifted. What horizontal force F must be applied? Take .y = 8 ft B C A F y z x 4 ft 5 ft 5 ft zy 3 Solutions 44918 1/21/09 4:25 PM Page 176 177 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *3–64. 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 , determine the tension in each cable.z = 600 mm x y z z 0.5 m 120 120 120 A B C D 3 Solutions 44918 1/21/09 4:25 PM Page 177 180 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–67. Three cables are used to support a 900-lb ring. Determine the tension in each cable for equilibrium. A B C D F 120 120 120 3 ft y z x 4 ft 3 Solutions 44918 1/21/09 4:25 PM Page 180 181 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *3–68. The three outer blocks each have a mass of 2 kg, and the central block E has a mass of 3 kg. Determine the sag s for equilibrium of the system. s 6030 30 1 m 1 m A D E B C 3 Solutions 44918 1/21/09 4:25 PM Page 181 182 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. •3–69. Determine the angle such that an equal force is developed in legs OB and OC. What is the force in each leg if the force is directed along the axis of each leg? The force F lies in the plane. The supports at A, B, C can exert forces in either direction along the attached legs. x-y u 120 5 ft 10 ft 120 120 yx z O B C A F = 100 lb u 3 Solutions 44918 1/21/09 4:25 PM Page 182 185 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. •3–73. Two electrically charged pith balls, each having a mass of 0.15 g, are suspended from light threads of equal length. Determine the magnitude of the horizontal repulsive force, F, acting on each ball if the measured distance between them is .r = 200 mm A B 50 mm 150 mm 150 mm r 200 mm F–F 3 Solutions 44918 1/21/09 4:25 PM Page 185 186 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–74. 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. x 1.5 m 1.5 m 2 m 4 m A z B y 6 m O C 3 Solutions 44918 1/21/09 4:25 PM Page 186 187 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–75. Determine the magnitude of P and the coordinate direction angles of required for equilibrium of the particle. Note that acts in the octant shown.F3 F3 z y x 20 F3 200 lb P (1 ft, 7 ft, 4 ft) F4 300 lb F1 360 lb F2 120 lb 3 Solutions 44918 1/21/09 4:25 PM Page 187