CEN 202 Problems All Chapters, Spring 2001

190 © 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. •4–1. If A, B, and D are given vectors, prove the distributive law for the vector cross product, i.e., . A : (B + D) = (A : B) + (A : D) 4 Solutions 44918 1/23/09 12:03 PM Page 190 191 © 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. 4–2. Prove the triple scalar product identity . A # B : C = A : B # C 4 Solutions 44918 1/23/09 12:03 PM Page 191 192 © 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. 4–3. Given the three nonzero vectors A, B, and C, show that if , the three vectors must lie in the same plane. A # (B : C) = 0 *4–4. Two men exert forces of and on the ropes. Determine the moment of each force about A. Which way will the pole rotate,clockwise or counterclockwise? P = 50 lb F = 80 lb A P F B C 6 ft 45� 12 ft 3 4 5 •4–5. If the man at B exerts a force of on his rope, determine the magnitude of the force F the man at C must exert to prevent the pole from rotating, i.e., so the resultant moment about A of both forces is zero. P = 30 lb A P F B C 6 ft 45� 12 ft 3 4 5 4 Solutions 44918 1/23/09 12:03 PM Page 192 193 © 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. 4–6. If , determine the moment produced by the 4-kN force about point A. u = 45° 3 m 0.45 m 4 kN A u 4 Solutions 44918 1/23/09 12:03 PM Page 193 194 © 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. 4–7. If the moment produced by the 4-kN force about point A is clockwise, determine the angle , where 0° … u … 90°. u 10 kN # m 3 m 0.45 m 4 kN A u 4 Solutions 44918 1/23/09 12:03 PM Page 194 195 © 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. *4–8. The handle of the hammer is subjected to the force of Determine the moment of this force about the point A. F = 20 lb. F B A 18 in. 5 in. 30� 4 Solutions 44918 1/23/09 12:03 PM Page 195 196 © 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. •4–9. In order to pull out the nail at B, the force F exerted on the handle of the hammer must produce a clockwise moment of about point A. Determine the required magnitude of force F. 500 lb # in. F B A 18 in. 5 in. 30� 4 Solutions 44918 1/23/09 12:03 PM Page 196 197 © 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. 4–10. The hub of the wheel can be attached to the axle either with negative offset (left) or with positive offset (right). If the tire is subjected to both a normal and radial load as shown, determine the resultant moment of these loads about point O on the axle for both cases. 4 kN 800 N 800 N 4 kN Case 1 Case 2 0.4 m 0.05 m 0.05 m 0.4 m O O 4 Solutions 44918 1/23/09 12:03 PM Page 197 198 © 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. 4–11. The member is subjected to a force of . If , determine the moment produced by F about point A. u = 45° F = 6 kN A 6 m 1.5 m u F � 6 kN 4 Solutions 44918 1/23/09 12:03 PM Page 198 199 © 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. *4–12. Determine the angle of the force F so that it produces a maximum moment and a minimum moment about point A. Also, what are the magnitudes of these maximum and minimum moments? u (0° … u … 180°) A 6 m 1.5 m u F � 6 kN 4 Solutions 44918 1/23/09 12:03 PM Page 199 200 © 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. •4–13. Determine the moment produced by the force F about point A in terms of the angle . Plot the graph of versus , where 0° … u … 180°. u MA u A 6 m 1.5 m u F � 6 kN 4 Solutions 44918 1/23/09 12:03 PM Page 200 201 © 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. 4–14. Serious neck injuries can occur when a football player is struck in the face guard of his helmet in the manner shown, giving rise to a guillotine mechanism. Determine the moment of the knee force about point A. What would be the magnitude of the neck force F so that it gives the counterbalancing moment about A? P = 50 lb 2 in. 4 in. 6 in. 30� 60� P � 50 lb F A 4–15. The Achilles tendon force of is mobilized when the man tries to stand on his toes.As this is done, each of his feet is subjected to a reactive force of Determine the resultant moment of and about the ankle joint A. Nf Ft Nf = 400 N. Ft = 650 N 100 mm 65 mm 200 mm A Nf � 400 N Ft 5� 4 Solutions 44918 1/23/09 12:03 PM Page 201 202 © 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. *4–16. The Achilles tendon force is mobilized when the man tries to stand on his toes.As this is done, each of his feet is subjected to a reactive force of If the resultant moment produced by forces and about the ankle joint A is required to be zero, determine the magnitude of Ft. Nt Ft Nt = 400 N. Ft 100 mm 65 mm 200 mm A Nf � 400 N Ft 5� •4–17. The two boys push on the gate with forces of and as shown. Determine the moment of each force about C. Which way will the gate rotate, clockwise or counterclockwise? Neglect the thickness of the gate. FA = 30 lb 60� 6 ft C B A 3 ft 3 4 5 FB FA 4–18. Two boys push on the gate as shown. If the boy at B exerts a force of , determine the magnitude of the force the boy at A must exert in order to prevent the gate from turning. Neglect the thickness of the gate. FA FB = 30 lb 60� 6 ft C B A 3 ft 3 4 5 FB FA 4 Solutions 44918 1/23/09 12:03 PM Page 202 203 © 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. 4–19. The tongs are used to grip the ends of the drilling pipe P. Determine the torque (moment) that the applied force exerts on the pipe about point P as a function of . Plot this moment versus for 0 … u … 90°. u MP u F = 150 lb MP 43 in. 6 in. F P MP u *4–20. The tongs are used to grip the ends of the drilling pipe P. If a torque (moment) of is needed at P to turn the pipe, determine the cable force F that must be applied to the tongs. Set . u = 30° MP = 800 lb # ft 43 in. 6 in. F P MP u 4 Solutions 44918 1/23/09 12:03 PM Page 203 204 © 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. •4–21. Determine the direction for of the force F so that it produces the maximum moment about point A. Calculate this moment. 0° … u … 180° u F � 400 N 3 m 2 m A u 4 Solutions 44918 1/23/09 12:03 PM Page 204 205 © 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. 4–22. Determine the moment of the force F about point A as a function of . Plot the results of M (ordinate) versus (abscissa) for 0° … u … 180°. u u F � 400 N 3 m 2 m A u 4–23. Determine the minimum moment produced by the force F about point A. Specify the angle u … 180°). u (0° … F � 400 N 3 m 2 m A u 4 Solutions 44918 1/23/09 12:03 PM Page 205 206 © 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. *4–24. In order to raise the lamp post from the position shown, force F is applied to the cable. If determine the moment produced by F about point A. F = 200 lb, F 75� C A B 10 ft 20 ft 4 Solutions 44918 1/23/09 12:03 PM Page 206 207 © 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. •4–25. In order to raise the lamp post from the position shown,the force F on the cable must create a counterclockwise moment of about point A. Determine the magnitude of F that must be applied to the cable. 1500 lb # ft F 75� C A B 10 ft 20 ft 4 Solutions 44918 1/23/09 12:03 PM Page 207 208 © 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. 4–26. The foot segment is subjected to the pull of the two plantarflexor muscles. Determine the moment of each force about the point of contact A on the ground. 60� 30� 4 in. A 1 in. 3.5 in. 70� F2 � 30 lb F1 � 20 lb 4–27. The 70-N force acts on the end of the pipe at B. Determine (a) the moment of this force about point A, and (b) the magnitude and direction of a horizontal force,applied at C, which produces the same moment.Take u = 60°. A C 0.3 m 0.7 m 0.9 m B 70 N u 4 Solutions 44918 1/23/09 12:03 PM Page 208 209 © 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. *4–28. The 70-N force acts on the end of the pipe at B. Determine the angles of the force that will produce maximum and minimum moments about point A.What are the magnitudes of these moments? u 10° … u … 180°2 A C 0.3 m 0.7 m 0.9 m B 70 N u •4–29. Determine the moment of each force about the bolt located at A.Take FB = 40 lb, FC = 50 lb. 4 Solutions 44918 1/23/09 12:03 PM Page 209 210 © 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. 4–30. If and determine the resultant moment about the bolt located at A. FC = 45 lb, FB = 30 lb 4–31. The rod on the power control mechanism for a business jet is subjected to a force of 80 N. Determine the moment of this force about the bearing at A. 20� 60� A 80 N 150 mm *4–32. The towline exerts a force of at the end of the 20-m-long crane boom. If determine the placement x of the hook at A so that this force creates a maximum moment about point O.What is this moment? u = 30°, P = 4 kN 1.5 m O 20 m A B P � 4 kN x u 4 Solutions 44918 1/23/09 12:03 PM Page 210 211 © 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. •4–33. The towline exerts a force of at the end of the 20-m-long crane boom. If determine the position of the boom so that this force creates a maximum moment about point O.What is this moment? u x = 25 m, P = 4 kN 1.5 m O 20 m A B P � 4 kN x u 4 Solutions 44918 1/23/09 12:03 PM Page 211 212 © 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. 4–34. In order to hold the wheelbarrow in the position shown, force F must produce a counterclockwise moment of about the axle at A. Determine the required magnitude of force F. 200 N # m B 0.65 m 0.5 m 1.2 m 30� 0.3 m F G A 4 Solutions 44918 1/23/09 12:03 PM Page 212 213 © 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. 4–35. The wheelbarrow and its contents have a mass of 50 kg and a center of mass at G. If the resultant moment produced by force F and the weight about point A is to be zero, determine the required magnitude of force F. B 0.65 m 0.5 m 1.2 m 30� 0.3 m F G A 4 Solutions 44918 1/23/09 12:03 PM Page 213 214 © 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. *4–36. The wheelbarrow and its contents have a center of mass at G. If and the resultant moment produced by force F and the weight about the axle at A is zero, determine the mass of the wheelbarrow and its contents. F = 100 N B 0.65 m 0.5 m 1.2 m 30� 0.3 m F G A 4 Solutions 44918 1/23/09 12:03 PM Page 214 215 © 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. •4–37. Determine the moment produced by about point O. Express the result as a Cartesian vector. F1 y x z 1 ft 2 ft 2 ft A O 3 ft F2 � {�10i � 30j � 50k} lb F1 � {�20i � 10j � 30k} lb 4 Solutions 44918 1/23/09 12:03 PM Page 215 216 © 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. 4–38. Determine the moment produced by about point O. Express the result as a Cartesian vector. F2 y x z 1 ft 2 ft 2 ft A O 3 ft F2 � {�10i � 30j � 50k} lb F1 � {�20i � 10j � 30k} lb 4 Solutions 44918 1/23/09 12:03 PM Page 216 217 © 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. 4–39. Determine the resultant moment produced by the two forces about point O. Express the result as a Cartesian vector. y x z 1 ft 2 ft 2 ft A O 3 ft F2 � {�10i � 30j � 50k} lb F1 � {�20i � 10j � 30k} lb 4 Solutions 44918 1/23/09 12:03 PM Page 217 218 © 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. *4–40. Determine the moment produced by force about point O. Express the result as a Cartesian vector. FB y x z C O B A 6 m 3 m 2 m 2.5 m FC � 420 N FB � 780 N 4 Solutions 44918 1/23/09 12:03 PM Page 218 219 © 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. •4–41. Determine the moment produced by force about point O. Express the result as a Cartesian vector. FC y x z C O B A 6 m 3 m 2 m 2.5 m FC � 420 N FB � 780 N 4 Solutions 44918 1/23/09 12:03 PM Page 219 220 © 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. 4–42. Determine the resultant moment produced by forces and about point O. Express the result as a Cartesian vector. FC FB y x z C O B A 6 m 3 m 2 m 2.5 m FC � 420 N FB � 780 N 4 Solutions 44918 1/23/09 12:03 PM Page 220 221 © 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. 4–43. Determine the moment produced by each force about point O located on the drill bit. Express the results as Cartesian vectors. x z A B O y 150 mm 600 mm 300 mm 150 mm FA � {�40i � 100j � 60k} N FB � {�50i � 120j � 60k} N 4 Solutions 44918 1/23/09 12:03 PM Page 221 222 © 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. *4–44. A force of produces a moment of about the origin of coordinates, point O. If the force acts at a point having an x coordinate of determine the y and z coordinates. x = 1 m, MO = 54i + 5j - 14k6 kN # m F = 56i - 2j + 1k6 kN •4–45. The pipe assembly is subjected to the 80-N force. Determine the moment of this force about point A. 400 mm y 300 mm 200 mm 250 mm x z 30� 40� F � 80 N B C A 4 Solutions 44918 1/23/09 12:03 PM Page 222 223 © 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. 4–47. The force creates a moment about point O of . If the force passes through a point having an x coordinate of 1 m, determine the y and z coordinates of the point. Also, realizing that , determine the perpendicular distance d from point O to the line of action of F. MO = Fd MO = 5-14i + 8j + 2k6 N # m F = 56i + 8j + 10k6 N d z x y O y 1 m z P F MO 4–46. The pipe assembly is subjected to the 80-N force. Determine the moment of this force about point B. 400 mm y 300 mm 200 mm 250 mm x z 30� 40� F � 80 N B C A 4 Solutions 44918 1/23/09 12:03 PM Page 223 224 © 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. *4–48. Force F acts perpendicular to the inclined plane. Determine the moment produced by F about point A. Express the result as a Cartesian vector. z x y 3 m 3 m 4 m A B C F � 400 N 4 Solutions 44918 1/23/09 12:03 PM Page 224 225 © 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. •4–49. Force F acts perpendicular to the inclined plane. Determine the moment produced by F about point B. Express the result as a Cartesian vector. z x y 3 m 3 m 4 m A B C F � 400 N 4 Solutions 44918 1/23/09 12:03 PM Page 225 226 © 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. 4–50. A 20-N horizontal force is applied perpendicular to the handle of the socket wrench. Determine the magnitude and the coordinate direction angles of the moment created by this force about point O. 15� 200 mm 75 mm 20 N A O x y z 4 Solutions 44918 1/23/09 12:03 PM Page 226 227 © 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. 4–51. Determine the moment produced by force F about the diagonal AF of the rectangular block. Express the result as a Cartesian vector. 3 m 1.5 m 3 m x C A B G F y z O D F � {�6i � 3j � 10k} N 4 Solutions 44918 1/23/09 12:03 PM Page 227 228 © 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. *4–52. Determine the moment produced by force F about the diagonal OD of the rectangular block. Express the result as a Cartesian vector. 3 m 1.5 m 3 m x C A B G F y z O D F � {�6i � 3j � 10k} N 4 Solutions 44918 1/23/09 12:03 PM Page 228 229 © 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. •4–53. The tool is used to shut off gas valves that are difficult to access. If the force F is applied to the handle, determine the component of the moment created about the z axis of the valve. x y 0.4 m F � {�60i � 20j � 15k} N 30� z 0.25 m 4–54. Determine the magnitude of the moments of the force F about the x, y, and z axes. Solve the problem (a) using a Cartesian vector approach and (b) using a scalar approach. 4 ft 3 ft 2 ft y z C A B F � {4i � 12j � 3k} lb x 4 Solutions 44918 1/23/09 12:03 PM Page 229 230 © 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. 4–55. Determine the moment of the force F about an axis extending between A and C. Express the result as a Cartesian vector. 4 ft 3 ft 2 ft y z C A B F � {4i � 12j � 3k} lb x 4 Solutions 44918 1/23/09 12:03 PM Page 230 231 © 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. *4–56. Determine the moment produced by force F about segment AB of the pipe assembly. Express the result as a Cartesian vector. y x z 4 m 4 m 3 m A B C F � {�20i � 10j � 15k} N 4 Solutions 44918 1/23/09 12:03 PM Page 231 232 © 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. •4–57. Determine the magnitude of the moment that the force F exerts about the y axis of the shaft. Solve the problem using a Cartesian vector approach and using a scalar approach. 200 mm 250 mm 45� B x y z A O 30� 50 mm � 16 N F 4 Solutions 44918 1/23/09 12:03 PM Page 232 233 © 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. 4–58. If , determine the magnitude of the moment produced by this force about the x axis. F = 450 N 300 mm x y z A B 60� 60� 45� F 100 mm 150 mm 4 Solutions 44918 1/23/09 12:03 PM Page 233 234 © 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. 4–59. The friction at sleeve A can provide a maximum resisting moment of about the x axis. Determine the largest magnitude of force F that can be applied to the bracket so that the bracket will not turn. 125 N # m 300 mm x y z A B 60� 60� 45� F 100 mm 150 mm 4 Solutions 44918 1/23/09 12:03 PM Page 234 235 © 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. *4–60. Determine the magnitude of the moment produced by the force of about the hinged axis (the x axis) of the door. F = 200 N y x z 15� A B 2.5 m 2 m F � 200 N 0.5 m 1 m 4 Solutions 44918 1/23/09 12:03 PM Page 235 236 © 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. •4–61. If the tension in the cable is , determine the magnitude of the moment produced by this force about the hinged axis, CD, of the panel. F = 140 lb 6 ft 4 ft 4 ft 6 ft y z A C F D B 6 ft x 4 Solutions 44918 1/23/09 12:03 PM Page 236 237 © 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. 4–62. Determine the magnitude of force F in cable AB in order to produce a moment of about the hinged axis CD, which is needed to hold the panel in the position shown. 500 lb # ft 6 ft 4 ft 4 ft 6 ft y z A C F D B 6 ft x 4 Solutions 44918 1/23/09 12:03 PM Page 237 238 © 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. 4–63. The A-frame is being hoisted into an upright position by the vertical force of . Determine the moment of this force about the axis passing through points A and B when the frame is in the position shown. y¿ F = 80 lb 30� 15� 6 ft y y¿ x¿ C A B F x z 3 ft 3 ft 4 Solutions 44918 1/23/09 12:03 PM Page 238 239 © 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. *4–64. The A-frame is being hoisted into an upright position by the vertical force of . Determine the moment of this force about the x axis when the frame is in the position shown. F = 80 lb 30� 15� 6 ft y y¿ x¿ C A B F x z 3 ft 3 ft 4 Solutions 44918 1/23/09 12:03 PM Page 239 240 © 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. •4–65. The A-frame is being hoisted into an upright po