94 CH A P T E R 3 EQ U I L I B R I U M O F A PA RT I C L E

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FUNDAMENTAL PROBLEMS

All problem solutions must include an FBD.

F3–1. The crate has a weight of 550 lb. Determine theforce in each supporting cable.

F3–2. The beam has a weight of 700 lb. Determine theshortest cable ABC that can be used to lift it if themaximum force the cable can sustain is 1500 lb.

F3–3. If the 5-kg block is suspended from the pulley B andthe sag of the cord is d = 0.15 m, determine the force in cordABC. Neglect the size of the pulley.

F3–4. The block has a mass of 5 kg and rests on the smoothplane. Determine the unstretched length of the spring.

F3–5. If the mass of cylinder C is 40 kg, determine themass of cylinder A in order to hold the assembly in theposition shown.

F3–6. Determine the tension in cables AB, BC, and CD,necessary to support the 10-kg and 15-kg traffic lights at Band C, respectively. Also, find the angle .u

30�

435

A

BC

D

10 ft

A C

B

u u

d � 0.15m

D

A C

B

0.4 m

45�

0.4 m

0.3 m

k � 200 N/m

40 kg

D

A

C

E

B

30�

B

A

C

D

u15�

F3–4F3–1

F3–2

F3–3 F3–6

F3–5

3.3 COPLANAR FORCE SYSTEMS 95

3

All problem solutions must include an FBD.

•3–1. Determine the force in each cord for equilibrium ofthe 200-kg crate. Cord remains horizontal due to theroller at , and has a length of . Set .

3–2. If the 1.5-m-long cord can withstand a maximumforce of , determine the force in cord and thedistance y so that the 200-kg crate can be supported.

BC3500 NAB

y = 0.75 m1.5 mABCBC

•3–5. The members of a truss are connected to the gussetplate. If the forces are concurrent at point O, determine themagnitudes of F and T for equilibrium. Take .

3–6. The gusset plate is subjected to the forces of fourmembers. Determine the force in member B and its properorientation for equilibrium. The forces are concurrent atpoint O. Take .F = 12 kN

u

u = 30°

3–7. The towing pendant AB is subjected to the force of50 kN exerted by a tugboat. Determine the force in each ofthe bridles, BC and BD, if the ship is moving forward withconstant velocity.

PROBLEMS

CB

A

2 m

y

Probs. 3–1/2

FAB

A

B

C D

G

30�45�

Probs. 3–3/4

5 kN

A

B

C

D

T

O

45�

u

F

8 kN

Probs. 3–5/6

30�

A

B

CD

50 kN

20�

Prob. 3–7

3–3. If the mass of the girder is and its center of massis located at point G, determine the tension developed incables , , and for equilibrium.

*3–4. If cables and can withstand a maximumtensile force of , determine the maximum mass of thegirder that can be suspended from cable so that neithercable will fail. The center of mass of the girder is located atpoint .G

AB20 kN

BCBD

BDBCAB

3 Mg

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*3–8. Members and support the 300-lb crate.Determine the tensile force developed in each member.

•3–9. If members and can support a maximumtension of and , respectively, determine thelargest weight of the crate that can be safely supported.

250 lb300 lbABAC

ABAC

3–10. The members of a truss are connected to the gussetplate. If the forces are concurrent at point O, determine themagnitudes of F and T for equilibrium. Take .

3–11. The gusset plate is subjected to the forces of threemembers. Determine the tension force in member C and itsangle for equilibrium.The forces are concurrent at point O.Take .F = 8 kN

u

u = 90°

*3–12. If block weighs and block weighs ,determine the required weight of block and the angle for equilibrium.

•3–13. If block weighs 300 lb and block weighs 275 lb,determine the required weight of block and the angle for equilibrium.

uCBD

uD100 lbC200 lbB

A

BC

4 ft

4 ft

3 ft

Probs. 3–8/9

x

y

A

O

F

T

B

9 kN

C

45 3

u

Probs. 3–10/11

A

BD

C

u 30�

Probs. 3–12/13

3 m

3 m 4 m

kAC � 20 N/m

kAB � 30 N/m

C B

A

D

Probs. 3–14/15

3–14. Determine the stretch in springs AC and AB forequilibrium of the 2-kg block. The springs are shown in the equilibrium position.

3–15. The unstretched length of spring AB is 3 m. If theblock is held in the equilibrium position shown, determinethe mass of the block at D.

3.3 COPLANAR FORCE SYSTEMS 97

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*3–16. Determine the tension developed in wires andrequired for equilibrium of the 10-kg cylinder. Take

.

•3–17. If cable is subjected to a tension that is twicethat of cable , determine the angle for equilibrium ofthe 10-kg cylinder. Also, what are the tensions in wires and ?CB

CAuCA

CB

u = 40°CB

CA

3–18. Determine the forces in cables AC and AB neededto hold the 20-kg ball D in equilibrium. Take and .

3–19. The ball D has a mass of 20 kg. If a force of is applied horizontally to the ring at A, determine thedimension d so that the force in cable AC is zero.

F = 100 N

d = 1 mF = 300 N

*3–20. Determine the tension developed in each wireused to support the 50-kg chandelier.

•3–21. If the tension developed in each of the four wires isnot allowed to exceed , determine the maximum massof the chandelier that can be supported.

600 N

�3–22. A vertical force is applied to the ends ofthe 2-ft cord AB and spring AC. If the spring has anunstretched length of 2 ft, determine the angle forequilibrium. Take

3–23. Determine the unstretched length of spring AC if aforce causes the angle for equilibrium.Cord AB is 2 ft long. Take k = 50 lb>ft.

u = 60°P = 80 lb

k = 15 lb>ft.u

P = 10 lb

30°

A B

Cu

Probs. 3–16/17

A

C

B

F

D

2 m

1.5 m

d

Probs. 3–18/19

A

B

D

C

30�

30�

45�

Prob. 3–20/21

2 ft

k

2 ft

A

B C

P

u

Probs. 3–22/23

98 CH A P T E R 3 EQ U I L I B R I U M O F A PA RT I C L E

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*3–24. If the bucket weighs 50 lb, determine the tensiondeveloped in each of the wires.

•3–25. Determine the maximum weight of the bucket thatthe wire system can support so that no single wire developsa tension exceeding 100 lb.

3–26. Determine the tensions developed in wires , ,and and the angle required for equilibrium of the 30-lb cylinder and the 60-lb cylinder .

3–27. If cylinder weighs 30 lb and , determinethe weight of cylinder .F

u = 15°E

FEuBA

CBCD

*3–28. Two spheres A and B have an equal mass and areelectrostatically charged such that the repulsive force actingbetween them has a magnitude of 20 mN and is directedalong line AB. Determine the angle the tension in cordsAC and BC, and the mass m of each sphere.

u,

A

B

E

C

D4

3

5

30�

30�

Probs. 3–24/25

D A

C

FE

B

u30�

45�

Probs. 3–26/27

C

30�

20 mN

20 mN

30�

B

u

A

Prob. 3–28

12

5

13

B

A

C

D

u

Prob. 3–29

•3–29. The cords BCA and CD can each support amaximum load of 100 lb. Determine the maximum weightof the crate that can be hoisted at constant velocity and theangle for equilibrium. Neglect the size of the smoothpulley at C.

u