estÁtica 12va. edición - hibbeler - capítulo 8 (solucionario)

132
683 •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 . m s = 0.25 © 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. P 30 8 Solutions 44918 1/27/09 1:51 PM Page 683

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Page 1: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

683

•8–1. Determine the minimum horizontal force Prequired to hold the crate from sliding down the plane. Thecrate has a mass of 50 kg and the coefficient of static frictionbetween the crate and the plane is .ms = 0.25

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

P

30�

8 Solutions 44918 1/27/09 1:51 PM Page 683

Page 2: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

684

8–2. Determine the minimum force P required to pushthe crate up the plane.The crate has a mass of 50 kg and thecoefficient of static friction between the crate and the planeis .ms = 0.25

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

P

30�

8 Solutions 44918 1/27/09 1:51 PM Page 684

Page 3: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

685

8–3. A horizontal force of is just sufficient tohold the crate from sliding down the plane, and a horizontalforce of is required to just push the crate up theplane. Determine the coefficient of static friction betweenthe plane and the crate, and find the mass of the crate.

P = 350 N

P = 100 N

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

P

30�

8 Solutions 44918 1/27/09 1:51 PM Page 685

Page 4: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

686

*8–4. If the coefficient of static friction at A is and the collar at B is smooth so it only exerts a horizontalforce on the pipe, determine the minimum distance sothat the bracket can support the cylinder of any masswithout slipping. Neglect the mass of the bracket.

x

ms = 0.4

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

200 mm

x100 mm

B

A

C

8 Solutions 44918 1/27/09 1:51 PM Page 686

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687

•8–5. The 180-lb man climbs up the ladder and stops at theposition shown after he senses that the ladder is on the vergeof slipping. Determine the inclination of the ladder if thecoefficient of static friction between the friction pad A and theground is .Assume the wall at B is smooth.The centerof gravity for the man is at G. Neglect the weight of the ladder.

ms = 0.4

u

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

G

A

B

10 ft

3 ft

u

8 Solutions 44918 1/27/09 1:51 PM Page 687

Page 6: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

688

8–6. The 180-lb man climbs up the ladder and stops at theposition shown after he senses that the ladder is on the vergeof slipping. Determine the coefficient of static friction betweenthe friction pad at A and ground if the inclination of the ladderis and the wall at B is smooth.The center of gravity forthe man is at G. Neglect the weight of the ladder.u = 60°

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

G

A

B

10 ft

3 ft

u

8 Solutions 44918 1/27/09 1:51 PM Page 688

Page 7: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

689

8–7. The uniform thin pole has a weight of 30 lb and alength of 26 ft. If it is placed against the smooth wall and onthe rough floor in the position , will it remain inthis position when it is released? The coefficient of staticfriction is .ms = 0.3

d = 10 ft

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

A

d

B

26 ft

8 Solutions 44918 1/27/09 1:51 PM Page 689

Page 8: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

690

*8–8. The uniform pole has a weight of 30 lb and a lengthof 26 ft. Determine the maximum distance d it can be placedfrom the smooth wall and not slip. The coefficient of staticfriction between the floor and the pole is .ms = 0.3

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

A

d

B

26 ft

8 Solutions 44918 1/27/09 1:52 PM Page 690

Page 9: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

691

•8–9. If the coefficient of static friction at all contactingsurfaces is , determine the inclination at which theidentical blocks, each of weight W, begin to slide.

ums

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

A

B

u

8 Solutions 44918 1/27/09 1:52 PM Page 691

Page 10: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

692

8–10. The uniform 20-lb ladder rests on the rough floorfor which the coefficient of static friction is andagainst the smooth wall at B. Determine the horizontalforce P the man must exert on the ladder in order to causeit to move.

ms = 0.8

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

A

B

8 ft

5 ft

5 ft

6 ft

P

8 Solutions 44918 1/27/09 1:52 PM Page 692

Page 11: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

693

8–11. The uniform 20-lb ladder rests on the rough floorfor which the coefficient of static friction is andagainst the smooth wall at B. Determine the horizontalforce P the man must exert on the ladder in order to causeit to move.

ms = 0.4

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

A

B

8 ft

5 ft

5 ft

6 ft

P

8 Solutions 44918 1/27/09 1:52 PM Page 693

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694

*8–12. The coefficients of static and kinetic frictionbetween the drum and brake bar are and ,respectively. If and determine thehorizontal and vertical components of reaction at the pin O.Neglect the weight and thickness of the brake.The drum hasa mass of 25 kg.

P = 85 NM = 50 N # mmk = 0.3ms = 0.4

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

A

M

P

BO 125 mm

700 mm

500 mm

300 mm

8 Solutions 44918 1/27/09 1:52 PM Page 694

Page 13: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

695

•8–13. The coefficient of static friction between the drumand brake bar is . If the moment ,determine the smallest force P that needs to be applied tothe brake bar in order to prevent the drum from rotating.Also determine the corresponding horizontal and verticalcomponents of reaction at pin O. Neglect the weight andthickness of the brake bar. The drum has a mass of 25 kg.

M = 35 N # mms = 0.4

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

A

M

P

BO 125 mm

700 mm

500 mm

300 mm

8 Solutions 44918 1/27/09 1:52 PM Page 695

Page 14: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

696

8–14. Determine the minimum coefficient of staticfriction between the uniform 50-kg spool and the wall sothat the spool does not slip.

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

A

B

0.6 m

0.3 m

60�

8 Solutions 44918 1/27/09 1:52 PM Page 696

Page 15: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

697

8–15. The spool has a mass of 200 kg and rests against thewall and on the floor. If the coefficient of static friction at Bis , the coefficient of kinetic friction is

, and the wall is smooth, determine the frictionforce developed at B when the vertical force applied to thecable is .P = 800 N

(mk)B = 0.2(ms)B = 0.3

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

0.1 m

G A

B

0.4 m

P

8 Solutions 44918 1/27/09 1:52 PM Page 697

Page 16: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

698

*8–16. The 80-lb boy stands on the beam and pulls on thecord with a force large enough to just cause him to slip. Ifthe coefficient of static friction between his shoes and thebeam is , determine the reactions at A and B.The beam is uniform and has a weight of 100 lb. Neglect thesize of the pulleys and the thickness of the beam.

(ms)D = 0.4

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

D A

C

B

5 ft

60�

3 ft

12

135

4 ft1 ft

8 Solutions 44918 1/27/09 1:52 PM Page 698

Page 17: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

699

•8–17. The 80-lb boy stands on the beam and pulls with aforce of 40 lb. If , determine the frictional forcebetween his shoes and the beam and the reactions at A andB. The beam is uniform and has a weight of 100 lb. Neglectthe size of the pulleys and the thickness of the beam.

(ms)D = 0.4

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

D A

C

B

5 ft

60�

3 ft

12

135

4 ft1 ft

8 Solutions 44918 1/27/09 1:52 PM Page 699

Page 18: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

700

8–18. The tongs are used to lift the 150-kg crate, whosecenter of mass is at G. Determine the least coefficient ofstatic friction at the pivot blocks so that the crate can belifted.

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

275 mm

300 mm

30�

500 mm

500 mm

A

C D

F

H

E

B

P

G

8 Solutions 44918 1/27/09 1:52 PM Page 700

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701

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 thecoefficients of static friction are and .Determine the incline angle for which both blocks beginto slide.Also find the required stretch or compression in theconnecting spring for this to occur.The spring has a stiffnessof .k = 2 lb>ft

u

mB = 0.25mA = 0.15

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

A

u

Bk � 2 lb/ft

8 Solutions 44918 1/27/09 1:52 PM Page 701

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702

*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 thecoefficients of static friction are and .Determine the angle which will cause motion of one ofthe blocks. What is the friction force under each of theblocks when this occurs? The spring has a stiffness of

and is originally unstretched.k = 2 lb>ft

u

mB = 0.25mA = 0.15

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

A

u

Bk � 2 lb/ft

8 Solutions 44918 1/27/09 1:52 PM Page 702

Page 21: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

703

•8–21. Crates A and B weigh 200 lb and 150 lb,respectively. They are connected together with a cable andplaced on the inclined plane. If the angle is graduallyincreased, determine when the crates begin to slide. Thecoefficients of static friction between the crates and theplane are and .mB = 0.35mA = 0.25

u

u

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

B

A C

D

u

8 Solutions 44918 1/27/09 1:52 PM Page 703

Page 22: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

704

8–22. A man attempts to support a stack of bookshorizontally by applying a compressive force of to the ends of the stack with his hands. If each book has amass of 0.95 kg, determine the greatest number of booksthat can be supported in the stack. The coefficient of staticfriction between the man’s hands and a book is and between any two books .(ms)b = 0.4

(ms)h = 0.6

F = 120 N

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

F � 120 NF � 120 N

8 Solutions 44918 1/27/09 1:52 PM Page 704

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705

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 thefresh roll B. They weigh 2 lb and 5 lb, respectively. If thecoefficients of static friction at the points of contact C and Dare and , determine the initialvertical force P that must be applied to the paper on the stubroll in order to pull down a sheet.The stub roll is pinned in thecenter, whereas the fresh roll is not. Neglect friction at the pin.

(ms)D = 0.5(ms)C = 0.2

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

P

60�

3 in.

4 in.

45�

A

B

C D

8 Solutions 44918 1/27/09 1:52 PM Page 705

Page 24: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

706

*8–24. The drum has a weight of 100 lb and rests on thefloor for which the coefficient of static friction is . If

ft and ft, determine the smallest magnitude ofthe force P that will cause impending motion of the drum.

b = 3a = 2ms = 0.6

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

b

aP

34

5

•8–25. The drum has a weight of 100 lb and rests on thefloor for which the coefficient of static friction is . If

ft and ft, determine the smallest magnitude ofthe force P that will cause impending motion of the drum.

b = 4a = 3ms = 0.5

b

aP

34

5

8 Solutions 44918 1/27/09 1:52 PM Page 706

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707

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 atile floor for which . If the man pusheshorizontally on the refrigerator in the direction shown,determine the smallest magnitude of horizontal forceneeded to move it. Also, if the man has a weight of 150 lb,determine the smallest coefficient of friction between hisshoes and the floor so that he does not slip.

ms = 0.25

3 ft

3 ft

1.5 ft

G

A

4 ft

8 Solutions 44918 1/27/09 1:52 PM Page 707

Page 26: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

708

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 atile floor for which . Also, the man has a weight of150 lb and the coefficient of static friction between the floorand his shoes is . If he pushes horizontally on therefrigerator, determine if he can move it. If so, does therefrigerator slip or tip?

ms = 0.6

ms = 0.25

3 ft

3 ft

1.5 ft

G

A

4 ft

8 Solutions 44918 1/27/09 1:52 PM Page 708

Page 27: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

709

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 pushthe two 75-kg cylinders up the incline. The force actsparallel to the plane and the coefficients of static friction ofthe contacting surfaces are , , and

. Each cylinder has a radius of 150 mm.mC = 0.4mB = 0.25mA = 0.3

P

A

B

C 30�

8 Solutions 44918 1/27/09 1:52 PM Page 709

Page 28: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

710

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 Pthe boy must push on the stack in order to cause movement.The coefficient of static friction at A and B is . Thetables are locked together.

ms = 0.3

G

A B

30�

3.5 ft3 ft

2 ft

P

2 ft

8 Solutions 44918 1/27/09 1:52 PM Page 710

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711

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 ofgravity at G. Determine if it can push the 550-lb log up theincline.The coefficient of static friction between the log andthe ground is , and between the rear wheels of thetractor and the ground . The front wheels are freeto roll. Assume the engine can develop enough torque tocause the rear wheels to slip.

s = 0.8ms = 0.5

7 ft 3 ft

1.25 ft

2.5 ft10�

A

B

G C

8 Solutions 44918 1/27/09 1:52 PM Page 711

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712

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 ofgravity at G. Determine the greatest weight of the log thatcan be pushed up the incline. The coefficient of staticfriction between the log and the ground is , andbetween the rear wheels of the tractor and the ground

. The front wheels are free to roll. Assume theengine can develop enough torque to cause the rear wheelsto slip.

msœ

= 0.7

ms = 0.5

7 ft 3 ft

1.25 ft

2.5 ft10�

A

B

G C

8 Solutions 44918 1/27/09 1:52 PM Page 712

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713

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 slippingat A when . Determine the coefficient of staticfriction at A.

u = 45°

A

B

C

8 m

5 mu

8 Solutions 44918 1/27/09 1:52 PM Page 713

Page 32: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

714

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 is applied perpendicular tothe handle of the gooseneck wrecking bar as shown. If thecoefficient of static friction between the bar and the wood is

, determine the normal force of the tines at A onthe upper board. Assume the surface at C is smooth.ms = 0.5

P = 20 lb

20 in.

3 in.3 in.

1 in.

A

C

P

30�

8 Solutions 44918 1/27/09 1:52 PM Page 714

Page 33: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

715

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 thefloor and wall for which the coefficients of static friction are

and , respectively. Determine the smallest value of for which the rod will not move.

umBmA

L

A

B

u

8–35. A roll of paper has a uniform weight of 0.75 lb andis suspended from the wire hanger so that it rests againstthe wall. If the hanger has a negligible weight and thebearing at O can be considered frictionless, determine theforce P needed to start turning the roll if . Thecoefficient of static friction between the wall and the paperis .ms = 0.25

u = 30°30�

P

A

3 in.

O

u

8 Solutions 44918 1/27/09 1:52 PM Page 715

Page 34: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

716

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 andis suspended from the wire hanger so that it rests againstthe wall. If the hanger has a negligible weight and thebearing at O can be considered frictionless, determine theminimum force P and the associated angle needed to startturning the roll. The coefficient of static friction betweenthe wall and the paper is ms = 0.25.

u

30�

P

A

3 in.

O

u

8 Solutions 44918 1/27/09 1:52 PM Page 716

Page 35: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

717

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 thechain and the inclined plane is , determine theoverhang length b so that the chain is on the verge ofslipping up the plane. The chain weighs w per unit length.

ms = tan u

b

a

u

8 Solutions 44918 1/27/09 1:52 PM Page 717

Page 36: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

718

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 towhich the girl can walk up the slide without supportingherself by the rails or by her left leg.The coefficient of staticfriction between the girl’s shoes and the slide is .ms = 0.8

y

h

x

y � x21––3

8 Solutions 44918 1/27/09 1:52 PM Page 718

Page 37: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

719

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8–39. If the coefficient of static friction at B is ,determine the largest angle and the minimum coefficientof 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 frictionbetween the belt and the vertical surface.

u

ms = 0.3

P

AB

30 mm

u

8 Solutions 44918 1/27/09 1:52 PM Page 719

Page 38: ESTÁTICA 12va. Edición - Hibbeler - Capítulo 8 (Solucionario)

720

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 , determine the minimum coefficient ofstatic friction at A and B so that the roller remains self-locking, regardless of the magnitude of force P applied tothe belt. Neglect the weight of the roller and neglect frictionbetween the belt and the vertical surface.

u = 30°

P

AB

30 mm

u

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•8–41. The clamp is used to tighten the connectionbetween two concrete drain pipes. Determine the leastcoefficient of static friction at A or B so that the clamp doesnot slip regardless of the force in the shaft CD.

B

C D

A

100 mm

250 mm

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722

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8–42. The coefficient of static friction between the 150-kgcrate and the ground is , while the coefficient ofstatic friction between the 80-kg man’s shoes and theground is . Determine if the man can move thecrate.

msœ

= 0.4

ms = 0.3

30�

8 Solutions 44918 1/27/09 1:52 PM Page 722

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723

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 crateand the ground is , determine the minimumcoefficient of static friction between the man’s shoes andthe ground so that the man can move the crate.

ms = 0.3

30�

8 Solutions 44918 1/27/09 1:52 PM Page 723

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724

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 centerof mass at G. Determine the largest number of crates thatcan be pushed by the loader if each crate has a mass of 500 kg. The coefficient of static friction between a crate andthe ground is , and the coefficient of static frictionbetween the rear wheels of the loader and the ground is

. The front wheels are free to roll. Assume that theengine of the loader is powerful enough to generate atorque that will cause the rear wheels to slip.

msœ

= 0.5

ms = 0.3

0.75 m0.25 m

G

0.3 mBA

8 Solutions 44918 1/27/09 1:52 PM Page 724

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725

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•8–45. The 45-kg disk rests on the surface for which thecoefficient of static friction is Determine thelargest couple moment M that can be applied to the barwithout causing motion.

mA = 0.2.

400 mm

125 mm

300 mm

B

A

C

M

8–46. The 45-kg disk rests on the surface for which thecoefficient of static friction is If determine the friction force at A.

M = 50 N # m,mA = 0.15.

400 mm

125 mm

300 mm

B

A

C

M

8 Solutions 44918 1/27/09 1:52 PM Page 725

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8–47. Block C has a mass of 50 kg and is confined betweentwo walls by smooth rollers. If the block rests on top of the40-kg spool, determine the minimum cable force P neededto move the spool. The cable is wrapped around the spool’sinner core. The coefficients of static friction at A and B are

and .mB = 0.6mA = 0.3

CA

B

O

0.4 m

0.2 mP

*8–48. Block C has a mass of 50 kg and is confinedbetween two walls by smooth rollers. If the block rests ontop of the 40-kg spool, determine the required coefficientsof static friction at A and B so that the spool slips at A andB when the magnitude of the applied force is increased to

.P = 300 N

CA

B

O

0.4 m

0.2 mP

8 Solutions 44918 1/27/09 1:52 PM Page 726

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727

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•8–49. The 3-Mg four-wheel-drive truck (SUV) has acenter of mass at G. Determine the maximum mass of thelog that can be towed by the truck. The coefficient of staticfriction between the log and the ground is , and thecoefficient of static friction between the wheels of the truckand the ground is . Assume that the engine of thetruck is powerful enough to generate a torque that willcause all the wheels to slip.

msœ

= 0.4

ms = 0.81.2 m1.6 m0.5 m

G

AB

8 Solutions 44918 1/27/09 1:52 PM Page 727

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728

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8–50. A 3-Mg front-wheel-drive truck (SUV) has a centerof mass at G. Determine the maximum mass of the log thatcan be towed by the truck. The coefficient of static frictionbetween the log and the ground is , and thecoefficient of static friction between the front wheels of thetruck and the ground is .The rear wheels are free toroll. Assume that the engine of the truck is powerful enoughto generate a torque that will cause the front wheels to slip.

msœ

= 0.4

ms = 0.81.2 m1.6 m0.5 m

G

AB

8 Solutions 44918 1/27/09 1:52 PM Page 728

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729

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8–51. If the coefficients of static friction at contact pointsA and B are and respectively, determinethe smallest force P that will cause the 150-kg spool to haveimpending motion.

msœ

= 0.4ms = 0.3P

400 mm

200 mm

150 mm

B

A

8 Solutions 44918 1/27/09 1:52 PM Page 729

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730

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*8–52. If the coefficients of static friction at contact pointsA and B are and respectively, determinethe smallest force P that will cause the 150-kg spool to haveimpending motion.

msœ

= 0.2ms = 0.4P

400 mm

200 mm

150 mm

B

A

8 Solutions 44918 1/27/09 1:52 PM Page 730

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731

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•8–53. The carpenter slowly pushes the uniform boardhorizontally over the top of the saw horse. The board has auniform weight of and the saw horse has a weightof 15 lb and a center of gravity at G. Determine if the sawhorse will stay in position, slip, or tip if the board is pushedforward when The coefficients of static frictionare shown in the figure.

d = 10 ft.

3 lb>ft,d

G

18 ft

1 ft1 ft

3 ftm � 0.5

m¿ � 0.3 m¿ � 0.3

8 Solutions 44918 1/27/09 1:52 PM Page 731

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732

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8–54. The carpenter slowly pushes the uniform boardhorizontally over the top of the saw horse. The board has auniform weight of and the saw horse has a weight of15 lb and a center of gravity at G. Determine if the sawhorse will stay in position, slip, or tip if the board is pushedforward when The coefficients of static frictionare shown in the figure.

d = 14 ft.

3 lb>ft,d

G

18 ft

1 ft1 ft

3 ftm � 0.5

m¿ � 0.3 m¿ � 0.3

8 Solutions 44918 1/27/09 1:52 PM Page 732

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733

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8–55. If the 75-lb girl is at position d = 4 ft, determine theminimum coefficient of static friction at contact points Aand B so that the plank does not slip. Neglect the weight ofthe plank.

ms

A

G

d

B

12 ft

45�60�

8 Solutions 44918 1/27/09 1:52 PM Page 733

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734

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 contactpoints A and B is , determine the minimum distanced where a 75-lb girl can stand on the plank without causing itto slip. Neglect the weight of the plank.

ms = 0.4

A

G

d

B

12 ft

45�60�

8 Solutions 44918 1/27/09 1:52 PM Page 734

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•8–57. If each box weighs 150 lb, determine the leasthorizontal force P that the man must exert on the top box inorder to cause motion. The coefficient of static frictionbetween the boxes is , and the coefficient of staticfriction between the box and the floor is .ms

œ

= 0.2ms = 0.5

3 ft

4.5 ft

5 ft

P

4.5 ft

A B

8 Solutions 44918 1/27/09 1:52 PM Page 735

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736

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 leasthorizontal force P that the man must exert on the top box inorder to cause motion. The coefficient of static frictionbetween the boxes is , and the coefficient of staticfriction between the box and the floor is .ms

œ

= 0.35ms = 0.65

3 ft

4.5 ft

5 ft

P

4.5 ft

A B

8 Solutions 44918 1/27/09 1:52 PM Page 736

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© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 collarsA and B and the rod is , determine the maximumangle for the system to remain in equilibrium, regardless ofthe weight of cylinder D. Links AC and BC have negligibleweight and are connected together at C by a pin.

u

ms = 0.6

D

C

A B

u u

15�15�

8 Solutions 44918 1/27/09 1:52 PM Page 737

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738

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 , determine the minimum coefficient ofstatic friction between the collars A and B and the rodrequired for the system to remain in equilibrium, regardlessof the weight of cylinder D. Links AC and BC havenegligible weight and are connected together at C by a pin.

u = 15°

D

C

A B

u u

15�15�

8 Solutions 44918 1/27/09 1:52 PM Page 738

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739

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 thecoefficients of static friction at the points of contact are

, , , and , determine thesmallest couple moment M needed to rotate cylinder E.

mD = 0.6mC = 0.5mB = 0.5mA = 0.5

300 mm

A D

300 mm

EM

B C

8 Solutions 44918 1/27/09 1:52 PM Page 739

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740

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8–62. Blocks A, B, and C have weights of 50 lb, 25 lb, and15 lb, respectively. Determine the smallest horizontal force Pthat will cause impending motion. The coefficient of staticfriction between A and B is , between B and C, , and between block C and the ground,

.m¿œ

s = 0.35ms

œ

= 0.4ms = 0.3

P

A

B

C

D

8 Solutions 44918 1/27/09 1:52 PM Page 740

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741

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 causeimpending motion. The crate and wheel have a mass of 50 kg and 25 kg, respectively. The coefficient of staticfriction between the crate and the ground is , andbetween the wheel and the ground .ms

œ

= 0.5ms = 0.2

300 mm

P

B

C A

8 Solutions 44918 1/27/09 1:52 PM Page 741

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742

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 causeimpending motion. The crate and wheel have a mass of 50 kg and 25 kg, respectively. The coefficient of staticfriction between the crate and the ground is , andbetween the wheel and the ground .ms

œ

= 0.3ms = 0.5

300 mm

P

B

C A

8 Solutions 44918 1/27/09 1:52 PM Page 742

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743

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 requiredto pull out wedge A.The crate has a weight of 300 lb and thecoefficient of static friction at all contacting surfaces is

. Neglect the weight of the wedge.ms = 0.3

AP

BB

15�

8 Solutions 44918 1/27/09 1:52 PM Page 743

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744

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 requiredto lift the 200-kg crate. The coefficient of static friction atall contacting surfaces is . Neglect the mass of the wedge.

ms = 0.3

P

A

B15�

8 Solutions 44918 1/27/09 1:52 PM Page 744

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745

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 requiredto lift the 100-kg cylinder. The coefficients of static frictionat the contact points A and B are and

, respectively; and the coefficient of staticfriction between the wedge and the ground is .ms = 0.3(ms)B = 0.2

(ms)A = 0.6

P

10�

A

C

B

0.5 m

8 Solutions 44918 1/27/09 1:52 PM Page 745

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746

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 coefficientof static friction with all contacting surfaces.Determine the largest angle so that it is “self-locking.”This requires no slipping for any magnitude of the force Papplied to the joint.

u

ms = 0.35 ––2

––2

P

uu

P

8 Solutions 44918 1/27/09 1:52 PM Page 746

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747

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 Prequired to just move block A to the right if the spring forceis and the coefficient of static friction at all contactingsurfaces on A is .The sleeve at C is smooth. Neglectthe mass of A and B.

ms = 0.3600 N

AP

B C

45�45�

8 Solutions 44918 1/27/09 1:52 PM Page 747

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748

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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, and Determine

the smallest horizontal force P that must be applied toblock C in order to move this block.The coefficient of staticfriction between the blocks is and between thefloor and each block ms

œ

= 0.5.ms = 0.3,

WC = 500 lb.WB = 150 lb,WA = 600 lb A B C45�

P

8 Solutions 44918 1/27/09 1:52 PM Page 748

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749

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 requiredto move the wedge to the right. The coefficient of staticfriction at all contacting surfaces is . Set and . Neglect the weight of the wedge.F = 400 N

u = 15°ms = 0.3

P

300 mm

450 mm

20 mm

A

BC

F

u

8 Solutions 44918 1/27/09 1:52 PM Page 749

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750

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*8–72. If the horizontal force P is removed, determine thelargest angle that will cause the wedge to be self-lockingregardless of the magnitude of force F applied to thehandle. The coefficient of static friction at all contactingsurfaces is .ms = 0.3

u

P

300 mm

450 mm

20 mm

A

BC

F

u

8 Solutions 44918 1/27/09 1:52 PM Page 750

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751

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 tohold the wedge between the two identical cylinders, eachhaving a weight of W. The coefficient of static friction at allcontacting surfaces is .ms = 0.1

P

30�30�

15�

8 Solutions 44918 1/27/09 1:52 PM Page 751

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752

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 topush the wedge between the two identical cylinders, eachhaving a weight of W. The coefficient of static friction at allcontacting surfaces is .ms = 0.3

P

30�30�

15�

8 Solutions 44918 1/27/09 1:52 PM Page 752

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753

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 movethe wedge to the left. The coefficient of static frictionbetween the wedge and the concrete and the wedge and thefloor is . The coefficient of static friction betweenthe concrete and floor is .ms

œ

= 0.5ms = 0.3

A

3 m

P150 mm

B

7.5�

8 Solutions 44918 1/27/09 1:52 PM Page 753

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754

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 specimenin a tension testing machine. Determine the largest designangle of the wedges so that the specimen will not slipregardless of the applied load. The coefficients of staticfriction are at A and at B. Neglect theweight of the blocks.

mB = 0.6mA = 0.1

u

P

A B

u u

•8–77. The square threaded screw of the clamp has amean diameter of 14 mm and a lead of 6 mm. If forthe threads, and the torque applied to the handle is

, determine the compressive force F on the block.1.5 N # m

ms = 0.21.5 N � m

�F

F

8 Solutions 44918 1/27/09 1:52 PM Page 754

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755

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 terminalC from the post of a battery. If the required pulling force is85 lb, determine the torque M that must be applied to thehandle on the screw to tighten it. The screw has squarethreads, a mean diameter of 0.2 in., a lead of 0.08 in., and thecoefficient of static friction is .ms = 0.5

C

A

B

M

8–79. The jacking mechanism consists of a link that has asquare-threaded screw with a mean diameter of 0.5 in. and alead of 0.20 in., and the coefficient of static friction is

. Determine the torque M that should be applied tothe screw to start lifting the 6000-lb load acting at the end ofmember ABC.

ms = 0.4

D

B

C

A

7.5 in.

10 in.

15 in.20 in. 10 in.

6000 lb

M

8 Solutions 44918 1/27/09 1:52 PM Page 755

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756

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 Pthat must be applied to the handle of the bench vise in orderto produce a clamping force of 600 N on the block. Thesingle square-threaded screw has a mean diameter of 25 mm and a lead of 7.5 mm. The coefficient of staticfriction is .ms = 0.25

•8–81. Determine the clamping force exerted on theblock if a force of P = 30 N is applied to the lever of thebench vise. The single square-threaded screw has a meandiameter of 25 mm and a lead of 7.5 mm. The coefficient ofstatic friction is .ms = 0.25

100 mm

P

100 mm

P

8 Solutions 44918 1/27/09 1:52 PM Page 756

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757

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. 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 mustbe applied perpendicular to the handle in order to developa 900-N clamping force on the pipe. The single square-threaded screw has a mean diameter of 25 mm and a lead of5 mm.The coefficient of static friction is . Note: Thescrew is a two-force member since it is contained withinpinned collars at A and B.

ms = 0.4

B

D

E

C

A

150 mm

200 mm

200 mm

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758

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8–83. If the clamping force on the pipe is 900 N,determine the horizontal force that must be appliedperpendicular to the handle in order to loosen the screw.The single square-threaded screw has a mean diameter of25 mm and a lead of 5 mm. The coefficient of static frictionis . Note: The screw is a two-force member since itis contained within pinned collars at A and B.ms = 0.4

B

D

E

C

A

150 mm

200 mm

200 mm

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*8–84. The clamp provides pressure from several directionson the edges of the board. If the square-threaded screw has alead of 3 mm, mean radius of 10 mm, and the coefficient ofstatic friction is determine the horizontal forcedeveloped on the board at A and the vertical forcesdeveloped at B and C if a torque of is appliedto the handle to tighten it further. The blocks at B and C arepin connected to the board.

M = 1.5 N # m

ms = 0.4, 45�

A

B

C

D

45�

M

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•8–85. If the jack supports the 200-kg crate, determine thehorizontal force that must be applied perpendicular to thehandle at E to lower the crate. Each single square-threadedscrew 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 B

D

E

100 mm45�

45�

45�

45�

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8–86. If the jack is required to lift the 200-kg crate,determine the horizontal force that must be appliedperpendicular to the handle at E. Each single square-threaded screw has a mean diameter of 25 mm and a lead of7.5 mm. The coefficient of static friction is .ms = 0.25

C

A B

D

E

100 mm45�

45�

45�

45�

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8–87. The machine part is held in place using thedouble-end clamp. The bolt at B has square threads with amean radius of 4 mm and a lead of 2 mm, and thecoefficient of static friction with the nut is If atorque of is applied to the nut to tighten it,determine the normal force of the clamp at the smoothcontacts A and C.

M = 0.4 N # mms = 0.5.

260 mm

A C

B

90 mm

*8–88. Blocks A and B weigh 50 lb and 30 lb, respectively.Using the coefficients of static friction indicated, determinethe greatest weight of block D without causing motion.

A

B

CD

m � 0.5

mBA � 0.6

mAC � 0.4

20�

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•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 andbetween block A and the floor C. A

B

CD

m � 0.5

mBA � 0.6

mAC � 0.4

20�

8–90. A cylinder having a mass of 250 kg is to besupported by the cord which wraps over the pipe.Determine the smallest vertical force F needed to supportthe load if the cord passes (a) once over the pipe, ,and (b) two times over the pipe, . Take .ms = 0.2b = 540°

b = 180°

F

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8–91. A cylinder having a mass of 250 kg is to besupported 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, , and (b) two times over thepipe, . Take .ms = 0.2b = 540°

b = 180°

F

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*8–92. The boat has a weight of 500 lb and is held inposition off the side of a ship by the spars at A and B.A manhaving a weight of 130 lb gets in the boat, wraps a ropearound an overhead boom at C, and ties it to the end of theboat as shown. If the boat is disconnected from the spars,determine the minimum number of half turns the rope mustmake around the boom so that the boat can be safelylowered into the water at constant velocity. Also, what is thenormal force between the boat and the man? The coefficientof kinetic friction between the rope and the boom is

. Hint: The problem requires that the normal forcebetween the man’s feet and the boat be as small as possible.ms = 0.15

A

C

B

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•8–93. The 100-lb boy at A is suspended from the cablethat passes over the quarter circular cliff rock. Determine ifit is possible for the 185-lb woman to hoist him up; and ifthis is possible, what smallest force must she exert on thehorizontal cable? The coefficient of static friction betweenthe cable and the rock is , and between the shoes ofthe woman and the ground .ms

œ

= 0.8ms = 0.2

A

8–94. The 100-lb boy at A is suspended from the cablethat passes over the quarter circular cliff rock. Whathorizontal force must the woman at A exert on the cable inorder to let the boy descend at constant velocity? Thecoefficients of static and kinetic friction between the cableand the rock are and , respectively.mk = 0.35ms = 0.4

A

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8–95. A 10-kg cylinder D, which is attached to a smallpulley B, is placed on the cord as shown. Determine thesmallest angle so that the cord does not slip over the peg atC. The cylinder at E has a mass of 10 kg, and the coefficientof static friction between the cord and the peg is .ms = 0.1

u A

B

D

E

Cu u

*8–96. A 10-kg cylinder D, which is attached to a smallpulley B, is placed on the cord as shown. Determine thelargest angle so that the cord does not slip over the peg atC. The cylinder at E has a mass of 10 kg, and the coefficientof static friction between the cord and the peg is .ms = 0.1

u A

B

D

E

Cu u

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•8–97. Determine the smallest lever force P needed toprevent the wheel from rotating if it is subjected to a torqueof The coefficient of static friction betweenthe belt and the wheel is The wheel is pinconnected at its center, B.

ms = 0.3.M = 250 N # m.

400 mm

200 mm

750 mm

P

MB

A

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8–98. If a force of is applied to the handle ofthe bell crank, determine the maximum torque M that canbe resisted so that the flywheel is not on the verge ofrotating clockwise. The coefficient of static friction betweenthe brake band and the rim of the wheel is .ms = 0.3

P = 200 N

P

900 mm

400 mm

100 mm

300 mm

MO

AB

C

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8–99. Show that the frictional relationship between thebelt tensions, the coefficient of friction , and the angularcontacts and for the V-belt is .T2 = T1e

mb>sin(a>2)ba

m

T2 T1

Impendingmotion

b

a

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*8–100. Determine the force developed in spring AB inorder to hold the wheel from rotating when it is subjectedto a couple moment of . The coefficient ofstatic friction between the belt and the rim of the wheel is

, and between the belt and peg C, . Thepulley at B is free to rotate.

msœ

= 0.4ms = 0.2

M = 200 N # m

C

A

200 mm

BM

45�

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•8–101. If the tension in the spring is ,determine the largest couple moment that can be applied tothe wheel without causing it to rotate. The coefficient ofstatic friction between the belt and the wheel is ,and between the belt the peg . The pulley B free torotate.

msœ

= 0.4ms = 0.2

FAB = 2.5 kN

C

A

200 mm

BM

45�

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8–102. The simple band brake is constructed so that theends of the friction strap are connected to the pin at A andthe lever arm at B. If the wheel is subjected to a torque of

determine the smallest force P applied to thelever that is required to hold the wheel stationary. Thecoefficient of static friction between the strap and wheel isms = 0.5.

M = 80 lb # ft,

1.5 ft 3 ft

45�

M � 80 lb � ft

20�

1.25 ft

A B

P

O

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8–103. A 180-lb farmer tries to restrain the cow fromescaping by wrapping the rope two turns around the treetrunk as shown. If the cow exerts a force of 250 lb on therope, determine if the farmer can successfully restrain thecow. The coefficient of static friction between the rope andthe tree trunk is , and between the farmer’s shoesand the ground .ms

œ

= 0.3ms = 0.15

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*8–104. The uniform 50-lb beam is supported by the ropewhich is attached to the end of the beam, wraps over therough peg, and is then connected to the 100-lb block. If the coefficient of static friction between the beam and theblock, and between the rope and the peg, is determine the maximum distance that the block can beplaced from A and still remain in equilibrium. Assume theblock will not tip.

ms = 0.4,

10 ft

1 ft

d

A

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•8–105. The 80-kg man tries to lower the 150-kg crateusing a rope that passes over the rough peg. Determine theleast number of full turns in addition to the basic wrap(165°) around the peg to do the job. The coefficients ofstatic friction between the rope and the peg and betweenthe man’s shoes and the ground are and ,respectively.

msœ

= 0.4ms = 0.115�

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8–106. If the rope wraps three full turns plus the basicwrap (165°) around the peg, determine if the 80-kg man cankeep the 300-kg crate from moving. The coefficients ofstatic friction between the rope and the peg and betweenthe man’s shoes and the ground are and ,respectively.

msœ

= 0.4ms = 0.1 15�

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8–107. The drive pulley B in a video tape recorder is onthe verge of slipping when it is subjected to a torque of

. If the coefficient of static friction betweenthe tape and the drive wheel and between the tape and thefixed shafts A and C is , determine the tensions and developed in the tape for equilibrium.T2

T1ms = 0.1

M = 0.005 N # m T1

T2

A

C

B

M � 5 mN � m10 mm

10 mm

10 mm

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*8–108. Determine the maximum number of 50-lb packagesthat can be placed on the belt without causing the belt toslip at the drive wheel A which is rotating with a constantangular velocity. Wheel B is free to rotate. Also, find thecorresponding torsional moment M that must be suppliedto wheel A. The conveyor belt is pre-tensioned with the 300-lb horizontal force. The coefficient of kinetic frictionbetween the belt and platform P is , and thecoefficient of static friction between the belt and the rim ofeach wheel is .ms = 0.35

mk = 0.2

P � 300 lbA P B

M

0.5 ft 0.5 ft

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•8–109. Blocks A and B have a mass of 7 kg and 10 kg,respectively. Using the coefficients of static frictionindicated, determine the largest vertical force P which canbe applied to the cord without causing motion.

P

300 mm

400 mm

AC

D

B

mD � 0.1

mC � 0.4

mB � 0.4

mA � 0.3

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8–110. Blocks A and B have a mass of 100 kg and 150 kg,respectively. If the coefficient of static friction between Aand B and between B and C is and between theropes and the pegs D and E , determine thesmallest force F needed to cause motion of block B ifP = 30 N.

msœ

= 0.5ms = 0.25,

P

F

DA

B

E

C

45�

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8–111. Block A has a weight of 100 lb and rests on asurface for which . If the coefficient of staticfriction between the cord and the fixed peg at C is ,determine the greatest weight of the suspended cylinder Bwithout causing motion.

ms = 0.3ms = 0.25

B

4 ft

2 ft

C

30�A

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*8–112. Block A has a mass of 50 kg and rests on surfaceB for which . If the coefficient of static frictionbetween the cord and the fixed peg at C is ,determine the greatest mass of the suspended cylinder Dwithout causing motion.

msœ

= 0.3ms = 0.25

C

D

A0.3 m

0.25 m

34

5

0.4 m

B

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•8–113. Block A has a mass of 50 kg and rests on surfaceB for which . If the mass of the suspended cylinderD is 4 kg, determine the frictional force acting on A andcheck if motion occurs. The coefficient of static frictionbetween the cord and the fixed peg at C is .ms

œ

= 0.3

ms = 0.25C

D

A0.3 m

0.25 m

34

5

0.4 m

B

8–114. The collar bearing uniformly supports an axialforce of If the coefficient of static friction is

determine the torque M required to overcomefriction.ms = 0.3,

P = 800 lb.

3 in. 2 in. P

M

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8–115. The collar bearing uniformly supports an axialforce of If a torque of is applied tothe shaft and causes it to rotate at constant velocity,determine the coefficient of kinetic friction at the surface ofcontact.

M = 3 lb # ftP = 500 lb.

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. Thecoefficient of static friction at all contacting surfaces is

.ms = 0.3

6 in.

2 in.

M

•8–117. The disk clutch is used in standard transmissionsof automobiles. If four springs are used to force the twoplates A and B together, determine the force in each springrequired to transmit a moment of across theplates. The coefficient of static friction between A and B is

.ms = 0.3

M = 600 lb # ft

Fs

M5 in.

B

2 in.

A

M

Fs

Fs

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8–118. If is applied to the handle of the bellcrank, determine the maximum torque M the cone clutchcan transmit. The coefficient of static friction at thecontacting surface is .ms = 0.3

P = 900 N

375 mm

200 mm

300 mm250 mm

P

M

AB

C

15�

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8–119. Because of wearing at the edges, the pivot bearingis subjected to a conical pressure distribution at its surfaceof contact. Determine the torque M required to overcomefriction and turn the shaft, which supports an axial force P.The coefficient of static friction is . For the solution, it isnecessary to determine the peak pressure in terms of Pand the bearing radius R.

p0

ms

P

M

R

p0

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*8–120. The pivot bearing is subjected to a parabolicpressure distribution at its surface of contact. If thecoefficient of static friction is , determine the torque Mrequired to overcome friction and turn the shaft if itsupports an axial force P.

ms

P

p0p � p0 (1� ) r2

––R2

R

r

M

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•8–121. The shaft is subjected to an axial force P. If thereactive pressure on the conical bearing is uniform,determine the torque M that is just sufficient to rotate theshaft. The coefficient of static friction at the contactingsurface is .ms

P

M

d1

d2

uu

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8–122. The tractor is used to push the 1500-lb pipe. To dothis it must overcome the frictional forces at the ground,caused by sand.Assuming that the sand exerts a pressure onthe bottom of the pipe as shown, and the coefficient of staticfriction between the pipe and the sand is determine the horizontal force required to push the pipeforward. Also, determine the peak pressure p0.

ms = 0.3,

15 in.

12 ft

p � p0 cos up0

u

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8–123. The conical bearing is subjected to a constantpressure distribution at its surface of contact. If thecoefficient of static friction is determine the torque Mrequired to overcome friction if the shaft supports an axialforce P.

ms,

P

M

R

u

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*8–124. Assuming that the variation of pressure at thebottom of the pivot bearing is defined as ,determine the torque M needed to overcome friction if theshaft is subjected to an axial force P.The coefficient of staticfriction is . For the solution, it is necessary to determine

in terms of P and the bearing dimensions and .R2R1p0

ms

p = p01R2>r2P

M

R2R1

p0

p � p0R2r

r

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793

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•8–125. The shaft of radius r fits loosely on the journalbearing. If the shaft transmits a vertical force P to thebearing and the coefficient of kinetic friction between theshaft and the bearing is , determine the torque Mrequired to turn the shaft with constant velocity.

mk r

P

M

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794

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8–126. The pulley is supported by a 25-mm-diameter pin.If the pulley fits loosely on the pin, determine the smallestforce P required to raise the bucket. The bucket has a massof 20 kg and the coefficient of static friction between thepulley and the pin is . Neglect the mass of thepulley and assume that the cable does not slip on the pulley.

ms = 0.3

75 mm

P

z 60�

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795

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8–127. The pulley is supported by a 25-mm-diameter pin.If the pulley fits loosely on the pin, determine the largestforce P that can be applied to the rope and yet lower thebucket. The bucket has a mass of 20 kg and the coefficientof static friction between the pulley and the pin is .Neglect the mass of the pulley and assume that the cabledoes not slip on the pulley.

ms = 0.3

75 mm

P

z 60�

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796

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*8–128. The cylinders are suspended from the end of thebar which fits loosely into a 40-mm-diameter pin. If A has amass of 10 kg, determine the required mass of B which isjust sufficient to keep the bar from rotating clockwise. Thecoefficient of static friction between the bar and the pin is

. Neglect the mass of the bar.ms = 0.3

AB

800 mm 600 mm

•8–129. The cylinders are suspended from the end of thebar which fits loosely into a 40-mm-diameter pin. If A has amass of 10 kg, determine the required mass of B which is justsufficient to keep the bar from rotating counterclockwise.The coefficient of static friction between the bar and the pinis . Neglect the mass of the bar.ms = 0.3

AB

800 mm 600 mm

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 movingdownwards, and the coefficient of static friction at thecontact points is , determine the radius of thefriction circle at each connection.

ms = 0.2

A

B

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797

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8–131. The connecting rod is attached to the piston by a20-mm-diameter pin at B and to the crank shaft by a 50-mm-diameter bearing A. If the piston is movingupwards, and the coefficient of static friction at the contactpoints is , determine the radius of the friction circleat each connection.

ms = 0.3

A

B

*8–132. The 5-kg pulley has a diameter of 240 mm and theaxle has a diameter of 40 mm. If the coefficient of kineticfriction between the axle and the pulley is determine the vertical force P on the rope required to liftthe 80-kg block at constant velocity.

mk = 0.15,

120 mm

P

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798

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•8–133. Solve Prob. 8–132 if the force P is appliedhorizontally to the right.

120 mm

P

8–134. The bell crank fits loosely into a 0.5-in-diameterpin. Determine the required force P which is just sufficientto rotate the bell crank clockwise. The coefficient of staticfriction between the pin and the bell crank is .ms = 0.3

P

10 in.

12 in.50 lb

45�

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799

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8–135. The bell crank fits loosely into a 0.5-in-diameterpin. If P = 41 lb, the bell crank is then on the verge ofrotating counterclockwise. Determine the coefficient ofstatic friction between the pin and the bell crank.

P

10 in.

12 in.50 lb

45�

8 Solutions 44918 1/27/09 1:53 PM Page 799

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800

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*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 withconstant velocity.

P

3 in.3 in.

45�

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801

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•8–137. The lawn roller has a mass of 80 kg. If the arm BAis held at an angle of 30° from the horizontal and thecoefficient of rolling resistance for the roller is 25 mm,determine the force P needed to push the roller at constantspeed. Neglect friction developed at the axle, A, and assumethat the resultant force P acting on the handle is appliedalong arm BA.

P

250 mm

B

A30�

8 Solutions 44918 1/27/09 1:53 PM Page 801

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802

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8–138. Determine the force P required to overcomerolling resistance and pull the 50-kg roller up the inclinedplane with constant velocity. The coefficient of rollingresistance is .a = 15 mm

300 mm

P

30�

30�

8 Solutions 44918 1/27/09 1:53 PM Page 802

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803

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8–139. Determine the force P required to overcomerolling resistance and support the 50-kg roller if it rollsdown the inclined plane with constant velocity. Thecoefficient of rolling resistance is .a = 15 mm

300 mm

P

30�

30�

8 Solutions 44918 1/27/09 1:53 PM Page 803

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804

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*8–140. The cylinder is subjected to a load that has aweight W. If the coefficients of rolling resistance for thecylinder’s top and bottom surfaces are and ,respectively, show that a horizontal force having amagnitude of is required to move theload and thereby roll the cylinder forward. Neglect theweight of the cylinder.

P = [W(aA + aB)]>2r

aBaA

W

P

r

A

B

•8–141. The 1.2-Mg steel beam is moved over a levelsurface using a series of 30-mm-diameter rollers for whichthe coefficient of rolling resistance is 0.4 mm at the groundand 0.2 mm at the bottom surface of the beam. Determinethe horizontal force P needed to push the beam forward ata constant speed. Hint: Use the result of Prob. 8–140.

P

8 Solutions 44918 1/27/09 1:53 PM Page 804

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805

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8–142. Determine the smallest horizontal force P thatmust be exerted on the 200-lb block to move it forward.Therollers each weigh 50 lb, and the coefficient of rollingresistance at the top and bottom surfaces is .a = 0.2 in

1.25 ft

P

1.25 ft

8–143. A single force P is applied to the handle of thedrawer. If friction is neglected at the bottom and thecoefficient of static friction along the sides is ,determine the largest spacing s between the symmetricallyplaced handles so that the drawer does not bind at thecorners A and B when the force P is applied to one of the handles.

ms = 0.4

P

s

B

Drawer

1.25 m

0.3 mChest

A

8 Solutions 44918 1/27/09 1:53 PM Page 805

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806

*8–144. The semicircular thin hoop of weight W andcenter of gravity at G is suspended by the small peg at A. Ahorizontal force P is slowly applied at B. If the hoop beginsto slip at A when , determine the coefficient of staticfriction between the hoop and the peg.

u = 30°

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P

RA

B

G

2R––

u

p

8 Solutions 44918 1/27/09 1:53 PM Page 806

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807

•8–145. The truck has a mass of 1.25 Mg and a center ofmass at G. Determine the greatest load it can pull if (a) thetruck has rear-wheel drive while the front wheels are free toroll, and (b) the truck has four-wheel drive.The coefficient ofstatic friction between the wheels and the ground is ,and between the crate and the ground, it is .ms

œ

= 0.4ms = 0.5

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1.5 m 1 m

G

A B600 mm

800 mm

8 Solutions 44918 1/27/09 1:53 PM Page 807

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808

8–146. Solve Prob. 8–145 if the truck and crate aretraveling up a 10° incline.

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1.5 m 1 m

G

A B600 mm

800 mm

8 Solutions 44918 1/27/09 1:53 PM Page 808

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809

8–147. If block A has a mass of 1.5 kg, determine thelargest mass of block B without causing motion of thesystem. The coefficient of static friction between the blocksand inclined planes is .ms = 0.2

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45�60�

AB

8 Solutions 44918 1/27/09 1:53 PM Page 809

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810

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*8–148. The cone has a weight W and center of gravity atG. If a horizontal force P is gradually applied to the stringattached to its vertex, determine the maximum coefficientof static friction for slipping to occur.

G

P

h34

h14

h14 h1

4

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811

•8–149. The tractor pulls on the fixed tree stump.Determine the torque that must be applied by the engine tothe rear wheels to cause them to slip. The front wheels arefree to roll. The tractor weighs 3500 lb and has a center ofgravity at G. The coefficient of static friction between therear wheels and the ground is .ms = 0.5

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2 ft

5 ft 3 ftBA

G

2 ftO

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812

8–150. The tractor pulls on the fixed tree stump. If thecoefficient of static friction between the rear wheels andthe ground is , determine if the rear wheels slip orthe front wheels lift off the ground as the engine providestorque to the rear wheels. What is the torque needed tocause this motion? The front wheels are free to roll. Thetractor weighs 2500 lb and has a center of gravity at G.

ms = 0.6

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2 ft

5 ft 3 ftBA

G

2 ftO

8 Solutions 44918 1/27/09 1:53 PM Page 812

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813

8–151. A roofer, having a mass of 70 kg, walks slowly in anupright position down along the surface of a dome that hasa radius of curvature of If the coefficient of staticfriction between his shoes and the dome is determine the angle at which he first begins to slip.u

ms = 0.7,r = 20 m.

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60�

20 mu

*8–152. Column D is subjected to a vertical load of8000 lb. It is supported on two identical wedges A and B forwhich the coefficient of static friction at the contactingsurfaces between A and B and between B and C is Determine the force P needed to raise the column and theequilibrium force needed to hold wedge A stationary.The contacting surface between A and D is smooth.

P¿

ms = 0.4.

D

10�10�

C

BAP P¿

8000 lb

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814

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D

10�10�

C

BAP P¿

8000 lb•8–153. Column D is subjected to a vertical load of 8000 lb.It is supported on two identical wedges A and B for whichthe coefficient of static friction at the contacting surfacesbetween A and B and between B and C is If theforces P and are removed, are the wedges self-locking?The contacting surface between A and D is smooth.

P¿

ms = 0.4.

8 Solutions 44918 1/27/09 1:53 PM Page 814