Chapter

8 Solutions 44918 1/27/09 1:51 PM Page 683 © 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. •8–1. Determine the minimum horizontal force P required to hold the crate from sliding down the plane. The crate has a mass of 50 kg and the coefficient of static friction between the crate and the plane is ms = 0.25. P 30⬚ 683 8 Solutions 44918 1/27/09 1:51 PM Page 684 © 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. 8–2. Determine the minimum force P required to push the crate up the plane. The crate has a mass of 50 kg and the coefficient of static friction between the crate and the plane is ms = 0.25. P 30⬚ 684 8 Solutions 44918 1/27/09 1:51 PM Page 685 © 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. 8–3. A horizontal force of P = 100 N is just sufficient to hold the crate from sliding down the plane, and a horizontal force of P = 350 N is required to just push the crate up the plane. Determine the coefficient of static friction between the plane and the crate, and find the mass of the crate. P 30⬚ 685 8 Solutions 44918 1/27/09 1:51 PM Page 686 © 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. *8–4. If the coefficient of static friction at A is ms = 0.4 and the collar at B is smooth so it only exerts a horizontal force on the pipe, determine the minimum distance x so that the bracket can support the cylinder of any mass without slipping. Neglect the mass of the bracket. 100 mm x B C 200 mm A 686 8 Solutions 44918 1/27/09 1:51 PM Page 687 © 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. •8–5. The 180-lb man climbs up the ladder and stops at the position shown after he senses that the ladder is on the verge of slipping. Determine the inclination u of the ladder if the coefficient of static friction between the friction pad A and the ground is ms = 0.4.Assume the wall at B is smooth.The center of gravity for the man is at G. Neglect the weight of the ladder. B G 10 ft u 3 ft 687 A 8 Solutions 44918 1/27/09 1:51 PM Page 688 © 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. 8–6. The 180-lb man climbs up the ladder and stops at the position shown after he senses that the ladder is on the verge of slipping. Determine the coefficient of static friction between the friction pad at A and ground if the inclination of the ladder is u = 60° and the wall at B is smooth.The center of gravity for the man is at G. Neglect the weight of the ladder. B G 10 ft u 3 ft 688 A 8 Solutions 44918 1/27/09 1:51 PM Page 689 © 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. 8–7. The uniform thin pole has a weight of 30 lb and a length of 26 ft. If it is placed against the smooth wall and on the rough floor in the position d = 10 ft, will it remain in this position when it is released? The coefficient of static friction is ms = 0.3. B 26 ft A d 689 8 Solutions 44918 1/27/09 1:52 PM Page 690 © 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. *8–8. The uniform pole has a weight of 30 lb and a length of 26 ft. Determine the maximum distance d it can be placed from the smooth wall and not slip. The coefficient of static friction between the floor and the pole is ms = 0.3. B 26 ft A d 690 8 Solutions 44918 1/27/09 1:52 PM Page 691 © 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. •8–9. If the coefficient of static friction at all contacting surfaces is ms, determine the inclination u at which the identical blocks, each of weight W, begin to slide. A B u 691 8 Solutions 44918 1/27/09 1:52 PM Page 692 © 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. 8–10. The uniform 20-lb ladder rests on the rough floor for which the coefficient of static friction is ms = 0.8 and against the smooth wall at B. Determine the horizontal force P the man must exert on the ladder in order to cause it to move. B 5 ft 8 ft P 5 ft A 6 ft 692 8 Solutions 44918 1/27/09 1:52 PM Page 693 © 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. 8–11. The uniform 20-lb ladder rests on the rough floor for which the coefficient of static friction is ms = 0.4 and against the smooth wall at B. Determine the horizontal force P the man must exert on the ladder in order to cause it to move. B 5 ft 8 ft P 5 ft A 6 ft 693 8 Solutions 44918 1/27/09 1:52 PM Page 694 © 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. *8–12. The coefficients of static and kinetic friction between the drum and brake bar are ms = 0.4 and mk = 0.3, respectively. If M = 50 N # m and P = 85 N determine the horizontal and vertical components of reaction at the pin O. Neglect the weight and thickness of the brake. The drum has a mass of 25 kg. 300 mm 700 mm B O 125 mm 500 mm M P 694 A 8 Solutions 44918 1/27/09 1:52 PM Page 695 © 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. •8–13. The coefficient of static friction between the drum and brake bar is ms = 0.4. If the moment M = 35 N # m, determine the smallest force P that needs to be applied to the brake bar in order to prevent the drum from rotating. Also determine the corresponding horizontal and vertical components of reaction at pin O. Neglect the weight and thickness of the brake bar. The drum has a mass of 25 kg. 300 mm 700 mm B O 125 mm 500 mm M P 695 A 8 Solutions 44918 1/27/09 1:52 PM Page 696 © 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. 8–14. Determine the minimum coefficient of static friction between the uniform 50-kg spool and the wall so that the spool does not slip. 60⬚ B A 0.6 m 0.3 m 696 8 Solutions 44918 1/27/09 1:52 PM Page 697 © 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. 8–15. The spool has a mass of 200 kg and rests against the wall and on the floor. If the coefficient of static friction at B is (ms)B = 0.3, the coefficient of kinetic friction is (mk)B = 0.2, and the wall is smooth, determine the friction force developed at B when the vertical force applied to the cable is P = 800 N. P 0.4 m G 0.1 m B 697 A 8 Solutions 44918 1/27/09 1:52 PM Page 698 © 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. *8–16. The 80-lb boy stands on the beam and pulls on the cord with a force large enough to just cause him to slip. If the coefficient of static friction between his shoes and the beam is (ms)D = 0.4, determine the reactions at A and B. The beam is uniform and has a weight of 100 lb. Neglect the size of the pulleys and the thickness of the beam. 13 12 5 D A B C 60⬚ 5 ft 3 ft 1 ft 698 4 ft 8 Solutions 44918 1/27/09 1:52 PM Page 699 © 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. •8–17. The 80-lb boy stands on the beam and pulls with a force of 40 lb. If (ms)D = 0.4, determine the frictional force between his shoes and the beam and the reactions at A and B. The beam is uniform and has a weight of 100 lb. Neglect the size of the pulleys and the thickness of the beam. 13 12 5 D A B C 60⬚ 5 ft 3 ft 1 ft 699 4 ft 8 Solutions 44918 1/27/09 1:52 PM Page 700 © 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. 8–18. The tongs are used to lift the 150-kg crate, whose center of mass is at G. Determine the least coefficient of static friction at the pivot blocks so that the crate can be lifted. P 275 mm E 500 mm 30⬚ F H C D 500 mm A 300 mm 700 G B 8 Solutions 44918 1/27/09 1:52 PM Page 701 © 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. 8–19. Two blocks A and B have a weight of 10 lb and 6 lb, respectively. They are resting on the incline for which the coefficients of static friction are mA = 0.15 and mB = 0.25. Determine the incline angle u for which both blocks begin to slide. Also find the required stretch or compression in the connecting spring for this to occur. The spring has a stiffness of k = 2 lb>ft. k ⫽ 2 lb/ft A u 701 B 8 Solutions 44918 1/27/09 1:52 PM Page 702 © 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. *8–20. Two blocks A and B have a weight of 10 lb and 6 lb, respectively. They are resting on the incline for which the coefficients of static friction are mA = 0.15 and mB = 0.25. Determine the angle u which will cause motion of one of the blocks. What is the friction force under each of the blocks when this occurs? The spring has a stiffness of k = 2 lb>ft and is originally unstretched. k ⫽ 2 lb/ft A u 702 B 8 Solutions 44918 1/27/09 1:52 PM Page 703 © 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. •8–21. Crates A and B weigh 200 lb and 150 lb, respectively. They are connected together with a cable and placed on the inclined plane. If the angle u is gradually increased, determine u when the crates begin to slide. The coefficients of static friction between the crates and the plane are mA = 0.25 and mB = 0.35. B D A C u 703 8 Solutions 44918 1/27/09 1:52 PM Page 704 © 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. 8–22. A man attempts to support a stack of books horizontally by applying a compressive force of F = 120 N to the ends of the stack with his hands. If each book has a mass of 0.95 kg, determine the greatest number of books that can be supported in the stack. The coefficient of static friction between the man’s hands and a book is (ms)h = 0.6 and between any two books (ms)b = 0.4. F ⫽ 120 N 704 F ⫽ 120 N 8 Solutions 44918 1/27/09 1:52 PM Page 705 © 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. 8–23. The paper towel dispenser carries two rolls of paper. The one in use is called the stub roll A and the other is the fresh roll B. They weigh 2 lb and 5 lb, respectively. If the coefficients of static friction at the points of contact C and D are (ms)C = 0.2 and (ms)D = 0.5, determine the initial vertical force P that must be applied to the paper on the stub roll in order to pull down a sheet.The stub roll is pinned in the center, whereas the fresh roll is not. Neglect friction at the pin. B C 4 in. D 45⬚ 3 in. 60⬚ P 705 A 8 Solutions 44918 1/27/09 1:52 PM Page 706 © 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. *8–24. The drum has a weight of 100 lb and rests on the floor for which the coefficient of static friction is ms = 0.6. If a = 2 ft and b = 3 ft, determine the smallest magnitude of the force P that will cause impending motion of the drum. P 3 5 a 4 b •8–25. The drum has a weight of 100 lb and rests on the floor for which the coefficient of static friction is ms = 0.5. If a = 3 ft and b = 4 ft, determine the smallest magnitude of the force P that will cause impending motion of the drum. P 3 5 a 4 b 706 8 Solutions 44918 1/27/09 1:52 PM Page 707 © 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. 8–26. The refrigerator has a weight of 180 lb and rests on a tile floor for which ms = 0.25. If the man pushes horizontally on the refrigerator in the direction shown, determine the smallest magnitude of horizontal force needed to move it. Also, if the man has a weight of 150 lb, determine the smallest coefficient of friction between his shoes and the floor so that he does not slip. 3 ft G 1.5 ft 4 ft 3 ft A 707 8 Solutions 44918 1/27/09 1:52 PM Page 708 © 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. 8–27. The refrigerator has a weight of 180 lb and rests on a tile floor for which ms = 0.25. Also, the man has a weight of 150 lb and the coefficient of static friction between the floor and his shoes is ms = 0.6. If he pushes horizontally on the refrigerator, determine if he can move it. If so, does the refrigerator slip or tip? 3 ft G 1.5 ft 4 ft 3 ft A 708 8 Solutions 44918 1/27/09 1:52 PM Page 709 © 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. *8–28. Determine the minimum force P needed to push the two 75-kg cylinders up the incline. The force acts parallel to the plane and the coefficients of static friction of the contacting surfaces are mA = 0.3, mB = 0.25, and mC = 0.4. Each cylinder has a radius of 150 mm. A P 709 C B 30⬚ 8 Solutions 44918 1/27/09 1:52 PM Page 710 © 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. •8–29. If the center of gravity of the stacked tables is at G, and the stack weighs 100 lb, determine the smallest force P the boy must push on the stack in order to cause movement. The coefficient of static friction at A and B is ms = 0.3. The tables are locked together. 30⬚ 3.5 ft G P 3 ft A B 2 ft 710 2 ft 8 Solutions 44918 1/27/09 1:52 PM Page 711 © 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. 8–30. The tractor has a weight of 8000 lb with center of gravity at G. Determine if it can push the 550-lb log up the incline. The coefficient of static friction between the log and the ground is ms = 0.5, and between the rear wheels of the tractor and the ground msœ = 0.8. The front wheels are free to roll. Assume the engine can develop enough torque to cause the rear wheels to slip. C G B 10⬚ 711 A 2.5 ft 7 ft 3 ft 1.25 ft 8 Solutions 44918 1/27/09 1:52 PM Page 712 © 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. 8–31. The tractor has a weight of 8000 lb with center of gravity at G. Determine the greatest weight of the log that can be pushed up the incline. The coefficient of static friction between the log and the ground is ms = 0.5, and between the rear wheels of the tractor and the ground msœ = 0.7. The front wheels are free to roll. Assume the engine can develop enough torque to cause the rear wheels to slip. C G B 10⬚ 712 A 2.5 ft 7 ft 3 ft 1.25 ft 8 Solutions 44918 1/27/09 1:52 PM Page 713 © 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. *8–32. The 50-kg uniform pole is on the verge of slipping at A when u = 45°. Determine the coefficient of static friction at A. C B 8m u 5m A 713 8 Solutions 44918 1/27/09 1:52 PM Page 714 © 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. •8–33. A force of P = 20 lb is applied perpendicular to the handle of the gooseneck wrecking bar as shown. If the coefficient of static friction between the bar and the wood is ms = 0.5, determine the normal force of the tines at A on the upper board. Assume the surface at C is smooth. P 30⬚ 20 in. 1 in. A C 3 in. 714 3 in. 8 Solutions 44918 1/27/09 1:52 PM Page 715 © 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. 8–34. The thin rod has a weight W and rests against the floor and wall for which the coefficients of static friction are mA and mB, respectively. Determine the smallest value of u for which the rod will not move. B L A 8–35. A roll of paper has a uniform weight of 0.75 lb and is suspended from the wire hanger so that it rests against the wall. If the hanger has a negligible weight and the bearing at O can be considered frictionless, determine the force P needed to start turning the roll if u = 30°. The coefficient of static friction between the wall and the paper is ms = 0.25. u 30⬚ 3 in. A O u P 715 8 Solutions 44918 1/27/09 1:52 PM Page 716 © 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. *8–36. A roll of paper has a uniform weight of 0.75 lb and is suspended from the wire hanger so that it rests against the wall. If the hanger has a negligible weight and the bearing at O can be considered frictionless, determine the minimum force P and the associated angle u needed to start turning the roll. The coefficient of static friction between the wall and the paper is ms = 0.25. 30⬚ 3 in. A O u P 716 8 Solutions 44918 1/27/09 1:52 PM Page 717 © 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. •8–37. If the coefficient of static friction between the chain and the inclined plane is ms = tan u, determine the overhang length b so that the chain is on the verge of slipping up the plane. The chain weighs w per unit length. a b u 717 8 Solutions 44918 1/27/09 1:52 PM Page 718 © 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. 8–38. Determine the maximum height h in meters to which the girl can walk up the slide without supporting herself by the rails or by her left leg. The coefficient of static friction between the girl’s shoes and the slide is ms = 0.8. y 1 x2 y ⫽ –– 3 h x 718 8 Solutions 44918 1/27/09 1:52 PM Page 719 © 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. 8–39. If the coefficient of static friction at B is ms = 0.3, determine the largest angle u and the minimum coefficient of static friction at A so that the roller remains self-locking, regardless of the magnitude of force P applied to the belt. Neglect the weight of the roller and neglect friction between the belt and the vertical surface. 30 mm u A B P 719 8 Solutions 44918 1/27/09 1:52 PM Page 720 © 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. *8–40. If u = 30°, determine the minimum coefficient of static friction at A and B so that the roller remains selflocking, regardless of the magnitude of force P applied to the belt. Neglect the weight of the roller and neglect friction between the belt and the vertical surface. 30 mm u A B P 720 8 Solutions 44918 1/27/09 1:52 PM Page 721 © 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. •8–41. The clamp is used to tighten the connection between two concrete drain pipes. Determine the least coefficient of static friction at A or B so that the clamp does not slip regardless of the force in the shaft CD. 100 mm A 250 mm C D B 721 8 Solutions 44918 1/27/09 1:52 PM Page 722 © 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. 8–42. The coefficient of static friction between the 150-kg crate and the ground is ms = 0.3, while the coefficient of static friction between the 80-kg man’s shoes and the ground is msœ = 0.4. Determine if the man can move the crate. 30⬚ 722 8 Solutions 44918 1/27/09 1:52 PM Page 723 © 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. 8–43. If the coefficient of static friction between the crate and the ground is ms = 0.3, determine the minimum coefficient of static friction between the man’s shoes and the ground so that the man can move the crate. 30⬚ 723 8 Solutions 44918 1/27/09 1:52 PM Page 724 © 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. *8–44. The 3-Mg rear-wheel-drive skid loader has a center of mass at G. Determine the largest number of crates that can be pushed by the loader if each crate has a mass of 500 kg. The coefficient of static friction between a crate and the ground is ms = 0.3, and the coefficient of static friction between the rear wheels of the loader and the ground is msœ = 0.5. The front wheels are free to roll. Assume that the engine of the loader is powerful enough to generate a torque that will cause the rear wheels to slip. G 0.3 m A 0.75 m 0.25 m 724 B 8 Solutions 44918 1/27/09 1:52 PM Page 725 © 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. •8–45. The 45-kg disk rests on the surface for which the coefficient of static friction is mA = 0.2. Determine the largest couple moment M that can be applied to the bar without causing motion. 300 mm C M 400 mm B 125 mm A 8–46. The 45-kg disk rests on the surface for which the coefficient of static friction is mA = 0.15. If M = 50 N # m, determine the friction force at A. 300 mm C M 400 mm B 125 mm A 725 8 Solutions 44918 1/27/09 1:52 PM Page 726 © 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. 8–47. Block C has a mass of 50 kg and is confined between two walls by smooth rollers. If the block rests on top of the 40-kg spool, determine the minimum cable force P needed to move the spool. The cable is wrapped around the spool’s inner core. The coefficients of static friction at A and B are mA = 0.3 and mB = 0.6. C A 0.4 m O 0.2 m P B *8–48. Block C has a mass of 50 kg and is confined between two walls by smooth rollers. If the block rests on top of the 40-kg spool, determine the required coefficients of static friction at A and B so that the spool slips at A and B when the magnitude of the applied force is increased to P = 300 N. C A 0.4 m O 0.2 m P B 726 8 Solutions 44918 1/27/09 1:52 PM Page 727 © 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. •8–49. The 3-Mg four-wheel-drive truck (SUV) has a center of mass at G. Determine the maximum mass of the log that can be towed by the truck. The coefficient of static friction between the log and the ground is ms = 0.8, and the coefficient of static friction between the wheels of the truck and the ground is msœ = 0.4. Assume that the engine of the truck is powerful enough to generate a torque that will cause all the wheels to slip. G B 0.5 m 727 A 1.6 m 1.2 m 8 Solutions 44918 1/27/09 1:52 PM Page 728 © 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. 8–50. A 3-Mg front-wheel-drive truck (SUV) has a center of mass at G. Determine the maximum mass of the log that can be towed by the truck. The coefficient of static friction between the log and the ground is ms = 0.8, and the coefficient of static friction between the front wheels of the truck and the ground is msœ = 0.4. The rear wheels are free to roll. Assume that the engine of the truck is powerful enough to generate a torque that will cause the front wheels to slip. G B 0.5 m 728 A 1.6 m 1.2 m 8 Solutions 44918 1/27/09 1:52 PM Page 729 © 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. 8–51. If the coefficients of static friction at contact points A and B are ms = 0.3 and msœ = 0.4 respectively, determine the smallest force P that will cause the 150-kg spool to have impending motion. 200 mm P 400 mm B 150 mm A 729 8 Solutions 44918 1/27/09 1:52 PM Page 730 © 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. *8–52. If the coefficients of static friction at contact points A and B are ms = 0.4 and msœ = 0.2 respectively, determine the smallest force P that will cause the 150-kg spool to have impending motion. 200 mm P 400 mm B 150 mm A 730 8 Solutions 44918 1/27/09 1:52 PM Page 731 © 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. •8–53. The carpenter slowly pushes the uniform board horizontally over the top of the saw horse. The board has a uniform weight of 3 lb>ft, and the saw horse has a weight of 15 lb and a center of gravity at G. Determine if the saw horse will stay in position, slip, or tip if the board is pushed forward when d = 10 ft. The coefficients of static friction are shown in the figure. 18 ft d 3 ft G m¿ ⫽ 0.3 1 ft 731 m ⫽ 0.5 m¿ ⫽ 0.3 1 ft 8 Solutions 44918 1/27/09 1:52 PM Page 732 © 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. 8–54. The carpenter slowly pushes the uniform board horizontally over the top of the saw horse. The board has a uniform weight of 3 lb>ft, and the saw horse has a weight of 15 lb and a center of gravity at G. Determine if the saw horse will stay in position, slip, or tip if the board is pushed forward when d = 14 ft. The coefficients of static friction are shown in the figure. 18 ft d 3 ft G m¿ ⫽ 0.3 1 ft 732 m ⫽ 0.5 m¿ ⫽ 0.3 1 ft 8 Solutions 44918 1/27/09 1:52 PM Page 733 © 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. 8–55. If the 75-lb girl is at position d = 4 ft, determine the minimum coefficient of static friction ms at contact points A and B so that the plank does not slip. Neglect the weight of the plank. d G A B 60⬚ 45⬚ 12 ft 733 8 Solutions 44918 1/27/09 1:52 PM Page 734 © 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. *8–56. If the coefficient of static friction at the contact points A and B is ms = 0.4 , determine the minimum distance d where a 75-lb girl can stand on the plank without causing it to slip. Neglect the weight of the plank. d G A B 60⬚ 45⬚ 12 ft 734 8 Solutions 44918 1/27/09 1:52 PM Page 735 © 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. •8–57. If each box weighs 150 lb, determine the least horizontal force P that the man must exert on the top box in order to cause motion. The coefficient of static friction between the boxes is ms = 0.5, and the coefficient of static friction between the box and the floor is msœ = 0.2. 3 ft 4.5 ft P 5 ft 4.5 ft A 735 B 8 Solutions 44918 1/27/09 1:52 PM Page 736 © 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. 8–58. If each box weighs 150 lb, determine the least horizontal force P that the man must exert on the top box in order to cause motion. The coefficient of static friction between the boxes is ms = 0.65, and the coefficient of static friction between the box and the floor is msœ = 0.35. 3 ft 4.5 ft P 5 ft 4.5 ft A 736 B 8 Solutions 44918 1/27/09 1:52 PM Page 737 © 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. 8–59. If the coefficient of static friction between the collars A and B and the rod is ms = 0.6, determine the maximum angle u for the system to remain in equilibrium, regardless of the weight of cylinder D. Links AC and BC have negligible weight and are connected together at C by a pin. A B 15⬚ 15⬚ u u C D 737 8 Solutions 44918 1/27/09 1:52 PM Page 738 © 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. *8–60. If u = 15°, determine the minimum coefficient of static friction between the collars A and B and the rod required for the system to remain in equilibrium, regardless of the weight of cylinder D. Links AC and BC have negligible weight and are connected together at C by a pin. A B 15⬚ 15⬚ u u C D 738 8 Solutions 44918 1/27/09 1:52 PM Page 739 © 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. •8–61. Each of the cylinders has a mass of 50 kg. If the coefficients of static friction at the points of contact are mA = 0.5, mB = 0.5, mC = 0.5, and mD = 0.6, determine the smallest couple moment M needed to rotate cylinder E. D A 300 mm B 739 M E 300 mm C 8 Solutions 44918 1/27/09 1:52 PM Page 740 © 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. 8–62. Blocks A, B, and C have weights of 50 lb, 25 lb, and 15 lb, respectively. Determine the smallest horizontal force P that will cause impending motion. The coefficient of static friction between A and B is ms = 0.3, between B and C, msœ = 0.4, and between block C and the ground, m¿ sœ = 0.35. A P B C D 740 8 Solutions 44918 1/27/09 1:52 PM Page 741 © 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. 8–63. Determine the smallest force P that will cause impending motion. The crate and wheel have a mass of 50 kg and 25 kg, respectively. The coefficient of static friction between the crate and the ground is ms = 0.2, and between the wheel and the ground msœ = 0.5. P B C 741 A 300 mm 8 Solutions 44918 1/27/09 1:52 PM Page 742 © 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. *8–64. Determine the smallest force P that will cause impending motion. The crate and wheel have a mass of 50 kg and 25 kg, respectively. The coefficient of static friction between the crate and the ground is ms = 0.5, and between the wheel and the ground msœ = 0.3. P B C 742 A 300 mm 8 Solutions 44918 1/27/09 1:52 PM Page 743 © 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. •8–65. Determine the smallest horizontal force P required to pull out wedge A. The crate has a weight of 300 lb and the coefficient of static friction at all contacting surfaces is ms = 0.3. Neglect the weight of the wedge. P A B 15⬚ 743 B 8 Solutions 44918 1/27/09 1:52 PM Page 744 © 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. 8–66. Determine the smallest horizontal force P required to lift the 200-kg crate. The coefficient of static friction at all contacting surfaces is ms = 0.3. Neglect the mass of the wedge. A P B 15⬚ 744 8 Solutions 44918 1/27/09 1:52 PM Page 745 © 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. 8–67. Determine the smallest horizontal force P required to lift the 100-kg cylinder. The coefficients of static friction at the contact points A and B are (ms)A = 0.6 and (ms)B = 0.2, respectively; and the coefficient of static friction between the wedge and the ground is ms = 0.3. 0.5 m A 10⬚ B P C 745 8 Solutions 44918 1/27/09 1:52 PM Page 746 © 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. *8–68. The wedge has a negligible weight and a coefficient of static friction ms = 0.35 with all contacting surfaces. Determine the largest angle u so that it is “self-locking.” This requires no slipping for any magnitude of the force P applied to the joint. u –– 2 P 746 u –– 2 P 8 Solutions 44918 1/27/09 1:52 PM Page 747 © 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. •8–69. Determine the smallest horizontal force P required to just move block A to the right if the spring force is 600 N and the coefficient of static friction at all contacting surfaces on A is ms = 0.3. The sleeve at C is smooth. Neglect the mass of A and B. B P 747 A 45⬚ C 45⬚ 8 Solutions 44918 1/27/09 1:52 PM Page 748 © 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. 8–70. The three stone blocks have weights of WA = 600 lb, WB = 150 lb, and WC = 500 lb. Determine the smallest horizontal force P that must be applied to block C in order to move this block. The coefficient of static friction between the blocks is ms = 0.3, and between the floor and each block msœ = 0.5. 45⬚ A 748 B C P 8 Solutions 44918 1/27/09 1:52 PM Page 749 © 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. 8–71. Determine the smallest horizontal force P required to move the wedge to the right. The coefficient of static friction at all contacting surfaces is ms = 0.3. Set u = 15° and F = 400 N. Neglect the weight of the wedge. F A 450 mm 20 mm P C u 300 mm 749 B 8 Solutions 44918 1/27/09 1:52 PM Page 750 © 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. *8–72. If the horizontal force P is removed, determine the largest angle u that will cause the wedge to be self-locking regardless of the magnitude of force F applied to the handle. The coefficient of static friction at all contacting surfaces is ms = 0.3. F A 450 mm 20 mm P C u 300 mm 750 B 8 Solutions 44918 1/27/09 1:52 PM Page 751 © 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. •8–73. Determine the smallest vertical force P required to hold the wedge between the two identical cylinders, each having a weight of W. The coefficient of static friction at all contacting surfaces is ms = 0.1. P 15⬚ 30⬚ 751 30⬚ 8 Solutions 44918 1/27/09 1:52 PM Page 752 © 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. 8–74. Determine the smallest vertical force P required to push the wedge between the two identical cylinders, each having a weight of W. The coefficient of static friction at all contacting surfaces is ms = 0.3. P 15⬚ 30⬚ 752 30⬚ 8 Solutions 44918 1/27/09 1:52 PM Page 753 © 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. 8–75. If the uniform concrete block has a mass of 500 kg, determine the smallest horizontal force P needed to move the wedge to the left. The coefficient of static friction between the wedge and the concrete and the wedge and the floor is ms = 0.3. The coefficient of static friction between the concrete and floor is msœ = 0.5. 3m B 150 mm A 753 P 7.5⬚ 8 Solutions 44918 1/27/09 1:52 PM Page 754 © 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. *8–76. The wedge blocks are used to hold the specimen in a tension testing machine. Determine the largest design angle u of the wedges so that the specimen will not slip regardless of the applied load. The coefficients of static friction are mA = 0.1 at A and mB = 0.6 at B. Neglect the weight of the blocks. u u A B P •8–77. The square threaded screw of the clamp has a mean diameter of 14 mm and a lead of 6 mm. If ms = 0.2 for the threads, and the torque applied to the handle is 1.5 N # m, determine the compressive force F on the block. 1.5 N ⭈ m ⫺F F 754 8 Solutions 44918 1/27/09 1:52 PM Page 755 © 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. 8–78. The device is used to pull the battery cable terminal C from the post of a battery. If the required pulling force is 85 lb, determine the torque M that must be applied to the handle on the screw to tighten it. The screw has square threads, a mean diameter of 0.2 in., a lead of 0.08 in., and the coefficient of static friction is ms = 0.5. M A C B 8–79. The jacking mechanism consists of a link that has a square-threaded screw with a mean diameter of 0.5 in. and a lead of 0.20 in., and the coefficient of static friction is ms = 0.4. Determine the torque M that should be applied to the screw to start lifting the 6000-lb load acting at the end of member ABC. 6000 lb C 7.5 in. B M 10 in. D A 20 in. 755 15 in. 10 in. 8 Solutions 44918 1/27/09 1:52 PM Page 756 © 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. *8–80. Determine the magnitude of the horizontal force P that must be applied to the handle of the bench vise in order to produce a clamping force of 600 N on the block. The single square-threaded screw has a mean diameter of 25 mm and a lead of 7.5 mm. The coefficient of static friction is ms = 0.25. 100 mm P •8–81. Determine the clamping force exerted on the block if a force of P = 30 N is applied to the lever of the bench vise. The single square-threaded screw has a mean diameter of 25 mm and a lead of 7.5 mm. The coefficient of static friction is ms = 0.25. 100 mm P 756 8 Solutions 44918 1/27/09 1:52 PM Page 757 © 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. 8–82. Determine the required horizontal force that must be applied perpendicular to the handle in order to develop a 900-N clamping force on the pipe. The single squarethreaded screw has a mean diameter of 25 mm and a lead of 5 mm. The coefficient of static friction is ms = 0.4. Note: The screw is a two-force member since it is contained within pinned collars at A and B. E C 200 mm 150 mm A B 200 mm D 757 8 Solutions 44918 1/27/09 1:52 PM Page 758 © 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. 8–83. If the clamping force on the pipe is 900 N, determine the horizontal force that must be applied perpendicular to the handle in order to loosen the screw. The single square-threaded screw has a mean diameter of 25 mm and a lead of 5 mm. The coefficient of static friction is ms = 0.4. Note: The screw is a two-force member since it is contained within pinned collars at A and B. E C 200 mm 150 mm A B 200 mm D 758 8 Solutions 44918 1/27/09 1:52 PM Page 759 © 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. *8–84. The clamp provides pressure from several directions on the edges of the board. If the square-threaded screw has a lead of 3 mm, mean radius of 10 mm, and the coefficient of static friction is ms = 0.4, determine the horizontal force developed on the board at A and the vertical forces developed at B and C if a torque of M = 1.5 N # m is applied to the handle to tighten it further. The blocks at B and C are pin connected to the board. B 45⬚ D A 45⬚ C 759 M 8 Solutions 44918 1/27/09 1:52 PM Page 760 © 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. •8–85. If the jack supports the 200-kg crate, determine the horizontal force that must be applied perpendicular to the handle at E to lower the crate. Each single square-threaded screw has a mean diameter of 25 mm and a lead of 7.5 mm. The coefficient of static friction is ms = 0.25. C A 45⬚ 45⬚ 45⬚ 45⬚ D 760 E 100 mm B 8 Solutions 44918 1/27/09 1:52 PM Page 761 © 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. 8–86. If the jack is required to lift the 200-kg crate, determine the horizontal force that must be applied perpendicular to the handle at E. Each single squarethreaded screw has a mean diameter of 25 mm and a lead of 7.5 mm. The coefficient of static friction is ms = 0.25. C A 45⬚ 45⬚ 45⬚ 45⬚ D 761 E 100 mm B 8 Solutions 44918 1/27/09 1:52 PM Page 762 © 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. 8–87. The machine part is held in place using the double-end clamp. The bolt at B has square threads with a mean radius of 4 mm and a lead of 2 mm, and the coefficient of static friction with the nut is ms = 0.5. If a torque of M = 0.4 N # m is applied to the nut to tighten it, determine the normal force of the clamp at the smooth contacts A and C. 260 mm 90 mm B A *8–88. Blocks A and B weigh 50 lb and 30 lb, respectively. Using the coefficients of static friction indicated, determine the greatest weight of block D without causing motion. C B m ⫽ 0.5 mBA ⫽ 0.6 20⬚ A C D 762 mAC ⫽ 0.4 8 Solutions 44918 1/27/09 1:52 PM Page 763 © 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. •8–89. Blocks A and B weigh 75 lb each, and D weighs 30 lb. Using the coefficients of static friction indicated, determine the frictional force between blocks A and B and between block A and the floor C. B m ⫽ 0.5 mBA ⫽ 0.6 20⬚ A C D 8–90. A cylinder having a mass of 250 kg is to be supported by the cord which wraps over the pipe. Determine the smallest vertical force F needed to support the load if the cord passes (a) once over the pipe, b = 180°, and (b) two times over the pipe, b = 540°. Take ms = 0.2. F 763 mAC ⫽ 0.4 8 Solutions 44918 1/27/09 1:52 PM Page 764 © 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. 8–91. A cylinder having a mass of 250 kg is to be supported by the cord which wraps over the pipe. Determine the largest vertical force F that can be applied to the cord without moving the cylinder. The cord passes (a) once over the pipe, b = 180°, and (b) two times over the pipe, b = 540°. Take ms = 0.2. F 764 8 Solutions 44918 1/27/09 1:52 PM Page 765 © 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. *8–92. The boat has a weight of 500 lb and is held in position off the side of a ship by the spars at A and B. A man having a weight of 130 lb gets in the boat, wraps a rope around an overhead boom at C, and ties it to the end of the boat as shown. If the boat is disconnected from the spars, determine the minimum number of half turns the rope must make around the boom so that the boat can be safely lowered into the water at constant velocity. Also, what is the normal force between the boat and the man? The coefficient of kinetic friction between the rope and the boom is ms = 0.15. Hint: The problem requires that the normal force between the man’s feet and the boat be as small as possible. C A B 765 8 Solutions 44918 1/27/09 1:52 PM Page 766 © 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. •8–93. The 100-lb boy at A is suspended from the cable that passes over the quarter circular cliff rock. Determine if it is possible for the 185-lb woman to hoist him up; and if this is possible, what smallest force must she exert on the horizontal cable? The coefficient of static friction between the cable and the rock is ms = 0.2, and between the shoes of the woman and the ground msœ = 0.8. A 8–94. The 100-lb boy at A is suspended from the cable that passes over the quarter circular cliff rock. What horizontal force must the woman at A exert on the cable in order to let the boy descend at constant velocity? The coefficients of static and kinetic friction between the cable and the rock are ms = 0.4 and mk = 0.35, respectively. A 766 8 Solutions 44918 1/27/09 1:52 PM Page 767 © 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. 8–95. A 10-kg cylinder D, which is attached to a small pulley B, is placed on the cord as shown. Determine the smallest angle u so that the cord does not slip over the peg at C. The cylinder at E has a mass of 10 kg, and the coefficient of static friction between the cord and the peg is ms = 0.1. A u u C B E D *8–96. A 10-kg cylinder D, which is attached to a small pulley B, is placed on the cord as shown. Determine the largest angle u so that the cord does not slip over the peg at C. The cylinder at E has a mass of 10 kg, and the coefficient of static friction between the cord and the peg is ms = 0.1. A u u C B E D 767 8 Solutions 44918 1/27/09 1:52 PM Page 768 © 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. •8–97. Determine the smallest lever force P needed to prevent the wheel from rotating if it is subjected to a torque of M = 250 N # m. The coefficient of static friction between the belt and the wheel is ms = 0.3. The wheel is pin connected at its center, B. 400 mm B M A 200 mm 750 mm P 768 8 Solutions 44918 1/27/09 1:52 PM Page 769 © 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. 8–98. If a force of P = 200 N is applied to the handle of the bell crank, determine the maximum torque M that can be resisted so that the flywheel is not on the verge of rotating clockwise. The coefficient of static friction between the brake band and the rim of the wheel is ms = 0.3. P 900 mm 400 mm C 100 mm A B O M 300 mm 769 8 Solutions 44918 1/27/09 1:52 PM Page 770 © 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. 8–99. Show that the frictional relationship between the belt tensions, the coefficient of friction m, and the angular contacts a and b for the V-belt is T2 = T1emb>sin(a>2). Impending motion a b T2 770 T1 8 Solutions 44918 1/27/09 1:53 PM Page 771 © 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. *8–100. Determine the force developed in spring AB in order to hold the wheel from rotating when it is subjected to a couple moment of M = 200 N # m. The coefficient of static friction between the belt and the rim of the wheel is ms = 0.2, and between the belt and peg C, msœ = 0.4. The pulley at B is free to rotate. A 200 mm C 45⬚ 771 B M 8 Solutions 44918 1/27/09 1:53 PM Page 772 © 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. •8–101. If the tension in the spring is FAB = 2.5 kN, determine the largest couple moment that can be applied to the wheel without causing it to rotate. The coefficient of static friction between the belt and the wheel is ms = 0.2, and between the belt the peg msœ = 0.4. The pulley B free to rotate. A 200 mm C 45⬚ 772 B M 8 Solutions 44918 1/27/09 1:53 PM Page 773 © 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. 8–102. The simple band brake is constructed so that the ends of the friction strap are connected to the pin at A and the lever arm at B. If the wheel is subjected to a torque of M = 80 lb # ft, determine the smallest force P applied to the lever that is required to hold the wheel stationary. The coefficient of static friction between the strap and wheel is ms = 0.5. M ⫽ 80 lb ⭈ ft O 20⬚ 45⬚ 1.25 ft B A 1.5 ft 3 ft P 773 8 Solutions 44918 1/27/09 1:53 PM Page 774 © 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. 8–103. A 180-lb farmer tries to restrain the cow from escaping by wrapping the rope two turns around the tree trunk as shown. If the cow exerts a force of 250 lb on the rope, determine if the farmer can successfully restrain the cow. The coefficient of static friction between the rope and the tree trunk is ms = 0.15, and between the farmer’s shoes and the ground msœ = 0.3. 774 8 Solutions 44918 1/27/09 1:53 PM Page 775 © 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. *8–104. The uniform 50-lb beam is supported by the rope which is attached to the end of the beam, wraps over the rough peg, and is then connected to the 100-lb block. If the coefficient of static friction between the beam and the block, and between the rope and the peg, is ms = 0.4, determine the maximum distance that the block can be placed from A and still remain in equilibrium. Assume the block will not tip. d 1 ft A 10 ft 775 8 Solutions 44918 1/27/09 1:53 PM Page 776 © 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. •8–105. The 80-kg man tries to lower the 150-kg crate using a rope that passes over the rough peg. Determine the least number of full turns in addition to the basic wrap (165°) around the peg to do the job. The coefficients of static friction between the rope and the peg and between the man’s shoes and the ground are ms = 0.1 and msœ = 0.4, respectively. 15⬚ 776 8 Solutions 44918 1/27/09 1:53 PM Page 777 © 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. 8–106. If the rope wraps three full turns plus the basic wrap (165°) around the peg, determine if the 80-kg man can keep the 300-kg crate from moving. The coefficients of static friction between the rope and the peg and between the man’s shoes and the ground are ms = 0.1 and msœ = 0.4, respectively. 15⬚ 777 8 Solutions 44918 1/27/09 1:53 PM Page 778 © 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. 8–107. The drive pulley B in a video tape recorder is on the verge of slipping when it is subjected to a torque of M = 0.005 N # m. If the coefficient of static friction between the tape and the drive wheel and between the tape and the fixed shafts A and C is ms = 0.1, determine the tensions T1 and T2 developed in the tape for equilibrium. 10 mm T1 A M ⫽ 5 mN ⭈ m 10 mm B 10 mm C T2 778 8 Solutions 44918 1/27/09 1:53 PM Page 779 © 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. *8–108. Determine the maximum number of 50-lb packages that can be placed on the belt without causing the belt to slip at the drive wheel A which is rotating with a constant angular velocity. Wheel B is free to rotate. Also, find the corresponding torsional moment M that must be supplied to wheel A. The conveyor belt is pre-tensioned with the 300-lb horizontal force. The coefficient of kinetic friction between the belt and platform P is mk = 0.2, and the coefficient of static friction between the belt and the rim of each wheel is ms = 0.35. 0.5 ft 0.5 ft A P B P ⫽ 300 lb M 779 8 Solutions 44918 1/27/09 1:53 PM Page 780 © 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. •8–109. Blocks A and B have a mass of 7 kg and 10 kg, respectively. Using the coefficients of static friction indicated, determine the largest vertical force P which can be applied to the cord without causing motion. 300 mm mD ⫽ 0.1 D B mB ⫽ 0.4 400 mm P mC ⫽ 0.4 A mA ⫽ 0.3 780 C 8 Solutions 44918 1/27/09 1:53 PM Page 781 © 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. 8–110. Blocks A and B have a mass of 100 kg and 150 kg, respectively. If the coefficient of static friction between A and B and between B and C is ms = 0.25, and between the ropes and the pegs D and E msœ = 0.5, determine the smallest force F needed to cause motion of block B if P = 30 N. E D A 45⬚ B C P 781 F 8 Solutions 44918 1/27/09 1:53 PM Page 782 © 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. 8–111. Block A has a weight of 100 lb and rests on a surface for which ms = 0.25. If the coefficient of static friction between the cord and the fixed peg at C is ms = 0.3, determine the greatest weight of the suspended cylinder B without causing motion. 2 ft 30⬚ 4 ft A C B 782 8 Solutions 44918 1/27/09 1:53 PM Page 783 © 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. *8–112. Block A has a mass of 50 kg and rests on surface B for which ms = 0.25. If the coefficient of static friction between the cord and the fixed peg at C is msœ = 0.3, determine the greatest mass of the suspended cylinder D without causing motion. C 3 5 4 0.25 m A 0.3 m 0.4 m B D 783 8 Solutions 44918 1/27/09 1:53 PM Page 784 © 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. •8–113. Block A has a mass of 50 kg and rests on surface B for which ms = 0.25. If the mass of the suspended cylinder D is 4 kg, determine the frictional force acting on A and check if motion occurs. The coefficient of static friction between the cord and the fixed peg at C is msœ = 0.3. C 3 5 4 0.25 m A 0.3 m 0.4 m B D 8–114. The collar bearing uniformly supports an axial force of P = 800 lb. If the coefficient of static friction is ms = 0.3, determine the torque M required to overcome friction. 3 in. 2 in. P M 784 8 Solutions 44918 1/27/09 1:53 PM Page 785 © 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. 8–115. The collar bearing uniformly supports an axial force of P = 500 lb. If a torque of M = 3 lb # ft is applied to the shaft and causes it to rotate at constant velocity, determine the coefficient of kinetic friction at the surface of contact. 3 in. 2 in. P M *8–116. If the spring exerts a force of 900 lb on the block, determine the torque M required to rotate the shaft. The coefficient of static friction at all contacting surfaces is ms = 0.3. M 2 in. 6 in. •8–117. The disk clutch is used in standard transmissions of automobiles. If four springs are used to force the two plates A and B together, determine the force in each spring required to transmit a moment of M = 600 lb # ft across the plates. The coefficient of static friction between A and B is ms = 0.3. A B Fs M M 2 in. Fs Fs 785 5 in. 8 Solutions 44918 1/27/09 1:53 PM Page 786 © 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. 8–118. If P = 900 N is applied to the handle of the bell crank, determine the maximum torque M the cone clutch can transmit. The coefficient of static friction at the contacting surface is ms = 0.3. 15⬚ 250 mm 300 mm C M 200 mm B A 375 mm P 786 8 Solutions 44918 1/27/09 1:53 PM Page 787 © 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. 8–119. Because of wearing at the edges, the pivot bearing is subjected to a conical pressure distribution at its surface of contact. Determine the torque M required to overcome friction and turn the shaft, which supports an axial force P. The coefficient of static friction is ms. For the solution, it is necessary to determine the peak pressure p0 in terms of P and the bearing radius R. P M R p0 787 8 Solutions 44918 1/27/09 1:53 PM Page 788 © 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. *8–120. The pivot bearing is subjected to a parabolic pressure distribution at its surface of contact. If the coefficient of static friction is ms, determine the torque M required to overcome friction and turn the shaft if it supports an axial force P. P M R r 2 p0 788 r ) p ⫽ p0 (1⫺ –– R2 8 Solutions 44918 1/27/09 1:53 PM Page 789 © 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. •8–121. The shaft is subjected to an axial force P. If the reactive pressure on the conical bearing is uniform, determine the torque M that is just sufficient to rotate the shaft. The coefficient of static friction at the contacting surface is ms. P M d2 d1 u 789 u 8 Solutions 44918 1/27/09 1:53 PM Page 790 © 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. 8–122. The tractor is used to push the 1500-lb pipe. To do this it must overcome the frictional forces at the ground, caused by sand. Assuming that the sand exerts a pressure on the bottom of the pipe as shown, and the coefficient of static friction between the pipe and the sand is ms = 0.3, determine the horizontal force required to push the pipe forward. Also, determine the peak pressure p0. 15 in. u p0 12 ft 790 p ⫽ p0 cos u 8 Solutions 44918 1/27/09 1:53 PM Page 791 © 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. 8–123. The conical bearing is subjected to a constant pressure distribution at its surface of contact. If the coefficient of static friction is ms, determine the torque M required to overcome friction if the shaft supports an axial force P. P M R u 791 8 Solutions 44918 1/27/09 1:53 PM Page 792 © 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. *8–124. Assuming that the variation of pressure at the bottom of the pivot bearing is defined as p = p01R2>r2, determine the torque M needed to overcome friction if the shaft is subjected to an axial force P. The coefficient of static friction is ms. For the solution, it is necessary to determine p0 in terms of P and the bearing dimensions R1 and R2. P M R2 R1 r p0 p ⫽ p0 R2 r 792 8 Solutions 44918 1/27/09 1:53 PM Page 793 © 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. •8–125. The shaft of radius r fits loosely on the journal bearing. If the shaft transmits a vertical force P to the bearing and the coefficient of kinetic friction between the shaft and the bearing is mk, determine the torque M required to turn the shaft with constant velocity. P r 793 M 8 Solutions 44918 1/27/09 1:53 PM Page 794 © 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. 8–126. The pulley is supported by a 25-mm-diameter pin. If the pulley fits loosely on the pin, determine the smallest force P required to raise the bucket. The bucket has a mass of 20 kg and the coefficient of static friction between the pulley and the pin is ms = 0.3. Neglect the mass of the pulley and assume that the cable does not slip on the pulley. 75 mm z 60⬚ P 794 8 Solutions 44918 1/27/09 1:53 PM Page 795 © 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. 8–127. The pulley is supported by a 25-mm-diameter pin. If the pulley fits loosely on the pin, determine the largest force P that can be applied to the rope and yet lower the bucket. The bucket has a mass of 20 kg and the coefficient of static friction between the pulley and the pin is ms = 0.3. Neglect the mass of the pulley and assume that the cable does not slip on the pulley. 75 mm z 60⬚ P 795 8 Solutions 44918 1/27/09 1:53 PM Page 796 © 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. *8–128. The cylinders are suspended from the end of the bar which fits loosely into a 40-mm-diameter pin. If A has a mass of 10 kg, determine the required mass of B which is just sufficient to keep the bar from rotating clockwise. The coefficient of static friction between the bar and the pin is ms = 0.3. Neglect the mass of the bar. 800 mm 600 mm A •8–129. The cylinders are suspended from the end of the bar which fits loosely into a 40-mm-diameter pin. If A has a mass of 10 kg, determine the required mass of B which is just sufficient to keep the bar from rotating counterclockwise. The coefficient of static friction between the bar and the pin is ms = 0.3. Neglect the mass of the bar. B 800 mm 600 mm A B 8–130. The connecting rod is attached to the piston by a 0.75-in.-diameter pin at B and to the crank shaft by a 2-in.-diameter bearing A. If the piston is moving downwards, and the coefficient of static friction at the contact points is ms = 0.2, determine the radius of the friction circle at each connection. B A 796 8 Solutions 44918 1/27/09 1:53 PM Page 797 © 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. 8–131. The connecting rod is attached to the piston by a 20-mm-diameter pin at B and to the crank shaft by a 50-mm-diameter bearing A. If the piston is moving upwards, and the coefficient of static friction at the contact points is ms = 0.3, determine the radius of the friction circle at each connection. B A *8–132. The 5-kg pulley has a diameter of 240 mm and the axle has a diameter of 40 mm. If the coefficient of kinetic friction between the axle and the pulley is mk = 0.15, determine the vertical force P on the rope required to lift the 80-kg block at constant velocity. 120 mm P 797 8 Solutions 44918 1/27/09 1:53 PM Page 798 © 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. •8–133. Solve Prob. 8–132 if the force P is applied horizontally to the right. 120 mm P 8–134. The bell crank fits loosely into a 0.5-in-diameter pin. Determine the required force P which is just sufficient to rotate the bell crank clockwise. The coefficient of static friction between the pin and the bell crank is ms = 0.3. 12 in. 50 lb 45⬚ 10 in. 798 P 8 Solutions 44918 1/27/09 1:53 PM Page 799 © 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. 8–135. The bell crank fits loosely into a 0.5-in-diameter pin. If P = 41 lb, the bell crank is then on the verge of rotating counterclockwise. Determine the coefficient of static friction between the pin and the bell crank. 12 in. 50 lb 45⬚ 10 in. 799 P 8 Solutions 44918 1/27/09 1:53 PM Page 800 © 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. *8–136. The wagon together with the load weighs 150 lb. If the coefficient of rolling resistance is a = 0.03 in., determine the force P required to pull the wagon with constant velocity. P 45⬚ 3 in. 800 3 in. 8 Solutions 44918 1/27/09 1:53 PM Page 801 © 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. •8–137. The lawn roller has a mass of 80 kg. If the arm BA is held at an angle of 30° from the horizontal and the coefficient of rolling resistance for the roller is 25 mm, determine the force P needed to push the roller at constant speed. Neglect friction developed at the axle, A, and assume that the resultant force P acting on the handle is applied along arm BA. P B 250 mm A 801 30⬚ 8 Solutions 44918 1/27/09 1:53 PM Page 802 © 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. 8–138. Determine the force P required to overcome rolling resistance and pull the 50-kg roller up the inclined plane with constant velocity. The coefficient of rolling resistance is a = 15 mm. P 300 mm 30⬚ 30⬚ 802 8 Solutions 44918 1/27/09 1:53 PM Page 803 © 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. 8–139. Determine the force P required to overcome rolling resistance and support the 50-kg roller if it rolls down the inclined plane with constant velocity. The coefficient of rolling resistance is a = 15 mm. P 300 mm 30⬚ 30⬚ 803 8 Solutions 44918 1/27/09 1:53 PM Page 804 © 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. *8–140. The cylinder is subjected to a load that has a weight W. If the coefficients of rolling resistance for the cylinder’s top and bottom surfaces are aA and aB, respectively, show that a horizontal force having a magnitude of P = [W(aA + aB)]>2r is required to move the load and thereby roll the cylinder forward. Neglect the weight of the cylinder. W P A r B •8–141. The 1.2-Mg steel beam is moved over a level surface using a series of 30-mm-diameter rollers for which the coefficient of rolling resistance is 0.4 mm at the ground and 0.2 mm at the bottom surface of the beam. Determine the horizontal force P needed to push the beam forward at a constant speed. Hint: Use the result of Prob. 8–140. P 804 8 Solutions 44918 1/27/09 1:53 PM Page 805 © 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. 8–142. Determine the smallest horizontal force P that must be exerted on the 200-lb block to move it forward. The rollers each weigh 50 lb, and the coefficient of rolling resistance at the top and bottom surfaces is a = 0.2 in. P 1.25 ft 8–143. A single force P is applied to the handle of the drawer. If friction is neglected at the bottom and the coefficient of static friction along the sides is ms = 0.4, determine the largest spacing s between the symmetrically placed handles so that the drawer does not bind at the corners A and B when the force P is applied to one of the handles. 1.25 ft 1.25 m A Chest 0.3 m Drawer B s P 805 8 Solutions 44918 1/27/09 1:53 PM Page 806 © 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. *8–144. The semicircular thin hoop of weight W and center of gravity at G is suspended by the small peg at A. A horizontal force P is slowly applied at B. If the hoop begins to slip at A when u = 30°, determine the coefficient of static friction between the hoop and the peg. A R G u 2R –– p B 806 P 8 Solutions 44918 1/27/09 1:53 PM Page 807 © 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. •8–145. The truck has a mass of 1.25 Mg and a center of mass at G. Determine the greatest load it can pull if (a) the truck has rear-wheel drive while the front wheels are free to roll, and (b) the truck has four-wheel drive. The coefficient of static friction between the wheels and the ground is ms = 0.5, and between the crate and the ground, it is msœ = 0.4. 800 mm G 600 mm A B 1.5 m 807 1m 8 Solutions 44918 1/27/09 1:53 PM Page 808 © 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. 8–146. Solve Prob. 8–145 if the truck and crate are traveling up a 10° incline. 800 mm G 600 mm A B 1.5 m 808 1m 8 Solutions 44918 1/27/09 1:53 PM Page 809 © 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. 8–147. If block A has a mass of 1.5 kg, determine the largest mass of block B without causing motion of the system. The coefficient of static friction between the blocks and inclined planes is ms = 0.2. A B 45⬚ 809 60⬚ 8 Solutions 44918 1/27/09 1:53 PM Page 810 © 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. *8–148. The cone has a weight W and center of gravity at G. If a horizontal force P is gradually applied to the string attached to its vertex, determine the maximum coefficient of static friction for slipping to occur. P 3 h 4 G 1 h 4 1 h 4 810 1 h 4 8 Solutions 44918 1/27/09 1:53 PM Page 811 © 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. •8–149. The tractor pulls on the fixed tree stump. Determine the torque that must be applied by the engine to the rear wheels to cause them to slip. The front wheels are free to roll. The tractor weighs 3500 lb and has a center of gravity at G. The coefficient of static friction between the rear wheels and the ground is ms = 0.5. G 2 ft O 2 ft A 811 5 ft 3 ft B 8 Solutions 44918 1/27/09 1:53 PM Page 812 © 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. 8–150. The tractor pulls on the fixed tree stump. If the coefficient of static friction between the rear wheels and the ground is ms = 0.6, determine if the rear wheels slip or the front wheels lift off the ground as the engine provides torque to the rear wheels. What is the torque needed to cause this motion? The front wheels are free to roll. The tractor weighs 2500 lb and has a center of gravity at G. G 2 ft O 2 ft A 812 5 ft 3 ft B 8 Solutions 44918 1/27/09 1:53 PM Page 813 © 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. 8–151. A roofer, having a mass of 70 kg, walks slowly in an upright position down along the surface of a dome that has a radius of curvature of r = 20 m. If the coefficient of static friction between his shoes and the dome is ms = 0.7, determine the angle u at which he first begins to slip. u 20 m 60⬚ *8–152. Column D is subjected to a vertical load of 8000 lb. It is supported on two identical wedges A and B for which the coefficient of static friction at the contacting surfaces between A and B and between B and C is ms = 0.4. Determine the force P needed to raise the column and the equilibrium force P¿ needed to hold wedge A stationary. The contacting surface between A and D is smooth. 8000 lb D P B 10⬚ 10⬚ C 813 A P¿ 8 Solutions 44918 1/27/09 1:53 PM Page 814 © 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. •8–153. Column D is subjected to a vertical load of 8000 lb. It is supported on two identical wedges A and B for which the coefficient of static friction at the contacting surfaces between A and B and between B and C is ms = 0.4. If the forces P and P¿ are removed, are the wedges self-locking? The contacting surface between A and D is smooth. 8000 lb D P B 10⬚ 10⬚ C 814 A P¿