2 Solutions 44918 1/21/09 12:01 PM Page © 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 •2–1 If u = 30° and T = kN, determine the magnitude of the resultant force acting on the eyebolt and its direction measured clockwise from the positive x axis y T u x 45Њ kN Solutions 44918 1/21/09 12:01 PM Page © 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 2–2 If u = 60° and T = kN, determine the magnitude of the resultant force acting on the eyebolt and its direction measured clockwise from the positive x axis y T u x 45Њ kN Solutions 44918 1/21/09 12:01 PM Page © 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 2–3 If the magnitude of the resultant force is to be kN directed along the positive x axis, determine the magnitude of force T acting on the eyebolt and its angle u y T u x 45Њ kN Solutions 44918 1/21/09 12:01 PM Page 10 © 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 *2–4 Determine the magnitude of the resultant force acting on the bracket and its direction measured counterclockwise from the positive u axis F2 ϭ 150 lb v 30Њ u 30Њ 45Њ F1 ϭ 200 lb 10 Solutions 44918 1/21/09 12:01 PM Page 11 © 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 •2–5 Resolve F1 into components along the u and v axes, and determine the magnitudes of these components F2 ϭ 150 lb v 30Њ u 30Њ 45Њ F1 ϭ 200 lb 11 Solutions 44918 1/21/09 12:01 PM Page 12 © 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 2–6 Resolve F2 into components along the u and v axes, and determine the magnitudes of these components F2 ϭ 150 lb v 30Њ u 30Њ 45Њ F1 ϭ 200 lb 12 Solutions 44918 1/21/09 12:01 PM Page 13 © 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 2–7 If FB = kN and the resultant force acts along the positive u axis, determine the magnitude of the resultant force and the angle u y FA ϭ kN u 30Њ B u FB 13 x A Solutions 44918 1/21/09 12:01 PM Page 14 © 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 *2–8 If the resultant force is required to act along the positive u axis and have a magnitude of kN, determine the required magnitude of FB and its direction u y FA ϭ kN u 30Њ B u FB 14 x A Solutions 44918 1/21/09 12:01 PM Page 15 © 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 •2–9 The plate is subjected to the two forces at A and B as shown If u = 60°, determine the magnitude of the resultant of these two forces and its direction measured clockwise from the horizontal FA ϭ kN u A 40Њ B FB ϭ kN 15 Solutions 44918 1/21/09 12:01 PM Page 16 © 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 FA ϭ kN 2–10 Determine the angle of u for connecting member A to the plate so that the resultant force of FA and FB is directed horizontally to the right.Also, what is the magnitude of the resultant force? u A 40Њ B FB ϭ kN 2–11 If the tension in the cable is 400 N, determine the magnitude and direction of the resultant force acting on the pulley This angle is the same angle u of line AB on the tailboard block y 400 N 30Њ u B x 400 N A 16 Solutions 44918 1/21/09 12:02 PM Page 106 © 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 z 2–122 Determine the projection of force F = 400 N acting along line AC of the pipe assembly Express the result as a Cartesian vector F ϭ 400 N B 45Њ C 30Њ A 3m x 4m y 106 Solutions 44918 1/21/09 12:02 PM Page 107 © 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 z 2–123 Determine the magnitudes of the components of force F = 400 N acting parallel and perpendicular to segment BC of the pipe assembly F ϭ 400 N B 45Њ C 30Њ A 3m x 4m y 107 Solutions 44918 1/21/09 12:02 PM Page 108 © 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 z *2–124 Cable OA is used to support column OB Determine the angle u it makes with beam OC D 30Њ O f C y 4m u 8m x 8m B A z •2–125 Cable OA is used to support column OB Determine the angle f it makes with beam OD D 30Њ O f C 4m u 8m x 8m B 108 A y Solutions 44918 1/21/09 12:02 PM Page 109 © 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 z 2–126 The cables each exert a force of 400 N on the post Determine the magnitude of the projected component of F1 along the line of action of F2 F1 ϭ 400 N 35Њ 120Њ 20Њ u 45Њ y 60Њ x F2 ϭ 400 N z 2–127 Determine the angle u between the two cables attached to the post F1 ϭ 400 N 35Њ 120Њ 20Њ x 109 u 45Њ y 60Њ F2 ϭ 400 N Solutions 44918 1/21/09 12:02 PM Page 110 © 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 z *2–128 A force of F = 80 N is applied to the handle of the wrench Determine the angle u between the tail of the force and the handle AB F ϭ 80 N u B 30Њ 45Њ A 300 mm x y 500 mm z •2–129 Determine the angle u between cables AB and AC ft ft C B 12 ft ft y u F 15 ft A x 110 Solutions 44918 1/21/09 12:02 PM Page 111 © 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 z 2–130 If F has a magnitude of 55 lb, determine the magnitude of its projected components acting along the x axis and along cable AC ft ft C B 12 ft ft y u F 15 ft A x 2–131 Determine the magnitudes of the projected components of the force F = 300 N acting along the x and y axes z 30Њ F ϭ 300 N A 30Њ 300 mm O 300 mm x 111 300 mm y Solutions 44918 1/21/09 12:02 PM Page 112 © 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 *2–132 Determine the magnitude of the projected component of the force F = 300 N acting along line OA 30Њ F ϭ 300 N z A 30Њ 300 mm O 300 mm x 112 300 mm y Solutions 44918 1/21/09 12:02 PM Page 113 © 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 •2–133 Two cables exert forces on the pipe Determine the magnitude of the projected component of F1 along the line of action of F2 z F2 ϭ 25 lb 60Њ u 60Њ x 30Њ 30Њ y F1 ϭ 30 lb z 2–134 Determine the angle u between the two cables attached to the pipe F2 ϭ 25 lb 60Њ u 60Њ x 30Њ 30Њ F1 ϭ 30 lb 113 y Solutions 44918 1/21/09 12:02 PM Page 114 © 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 2–135 force Determine the x and y components of the 700-lb 700 lb y 60Њ 30Њ x 114 Solutions 44918 1/21/09 12:02 PM Page 115 © 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 z *2–136 Determine the magnitude of the projected component of the 100-lb force acting along the axis BC of the pipe A B ft u ft x ft ft ft D F ϭ 100 lb C y z •2–137 Determine the angle u between pipe segments BA and BC A B ft u ft x ft 115 ft ft C F ϭ 100 lb D y Solutions 44918 1/21/09 12:02 PM Page 116 © 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 2–138 Determine the magnitude and direction of the resultant FR = F1 + F2 + F3 of the three forces by first finding the resultant F¿ = F1 + F3 and then forming FR = F¿ + F2 Specify its direction measured counterclockwise from the positive x axis y F2 ϭ 75 N F1 ϭ 80 N F3 ϭ 50 N 30Њ 30Њ 45Њ x 116 Solutions 44918 1/21/09 12:02 PM Page 117 © 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 2–139 Determine the design angle u (u < 90°) between the two struts so that the 500-lb horizontal force has a component of 600 lb directed from A toward C What is the component of force acting along member BA? B C 20Њ u 500 lb A 117 Solutions 44918 1/21/09 12:02 PM Page 118 © 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 F2 ϭ 10 lb *2–140 Determine the magnitude and direction of the smallest force F3 so that the resultant force of all three forces has a magnitude of 20 lb F3 u F1 ϭ lb 118 Solutions 44918 1/21/09 12:02 PM Page 119 © 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 •2–141 Resolve the 250-N force into components acting along the u and v axes and determine the magnitudes of these components u 20Њ 250 N 40Њ v z 2–142 Cable AB exerts a force of 80 N on the end of the 3-m-long boom OA Determine the magnitude of the projection of this force along the boom B 4m O y 60Њ 80 N 3m A x 119 Solutions 44918 1/21/09 12:02 PM Page 120 © 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 z 2–143 The three supporting cables exert the forces shown on the sign Represent each force as a Cartesian vector C 2m E 2m B FE ϭ 350 N FC ϭ 400 N FB ϭ 400 N D A x 120 3m 2m 3m y