Solucionario Estatica Bedford Cap. 3

Problem 3.1 In Active Example 3.1, suppose that the angle between the ramp supporting the car is increased from 20° to 30° . Draw the free-body diagram of the car showing the new geometry. Suppose that the cable from A to B must exert a 1900-lb horizontal force on the car to hold it in place. Determine the car’s weight in pounds.
20

A

B

Solution: The free-body diagram is shown to theright.
Applying the equilibrium equations Fx : T N sin 30° D 0, mg D 0

Fy : N cos 30°

Setting T D 1900 lb and solving yields N D 3800 lb, mg D 3290 lb

Problem 3.2 The ring weighs 5 lb and is in equilibrium. The force F1 D 4.5 lb. Determine the force F2 and the angle ˛.

F2

y

a 30

F1

x

Solution: The free-body diagram is shown below the drawing. The
equilibrium equationsare Fx : F1 cos 30° F2 cos ˛ D 0 5 lb D 0

Fy : F1 sin 30° C F2 sin ˛ We can write these equations as F2 sin ˛ D 5 lb F1 sin 30°

F2 cos ˛ D F1 cos 30° Dividing these equations and using the known value for F1 we have. tan ˛ D 5 lb 4.5 lb sin 30° D 0.706 ) ˛ D 35.2° 4.5 lb cos 30°

F2 D

4.5 lb cos 30° D 4.77 lb cos ˛

F2 D 4.77 lb, ˛ D 35.2°

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Problem 3.3 In Example 3.2, suppose that the attachment point C is moved to the right and cable AC is extended so that the angle between cable AC and theceiling decreases from 45° to 35° . The angle between cable AB and the ceiling remains 60° . What are the tensions in cables AB and AC?

B

60 A

45

C

Solution: The free-body diagram is shown below the picture. The equilibrium equations are:
Fx : TAC cos 35° TAB cos 60° D 0 1962 N D 0

Fy : TAC sin 35° C TAB sin 60° Solving we find

TAB D 1610 N, TAC D 985 N

Problem 3.4 The200-kg engine block is suspended by the cables AB and AC. The angle ˛ D 40° . The freebody diagram obtained by isolating the part of the system within the dashed line is shown. Determine the forces TAB and TAC .

y B C

TAB a
A A

TAC a
x

(200 kg) (9.81 m/s2)

Solution:
˛ D 40° Fx : TAC cos ˛ TAB cos ˛ D 0 1962 N D 0

TAB

TAC

α

α

Fy : TAC sin ˛ C TAB sin ˛ Solving:

TAB DTAC D 1.526 kN

1962 Ν

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Problem 3.5 A heavy rope used as a mooring line for a cruise ship sags as shown.If the mass of the rope is 90 kg, what are the tensions in the rope at A and B?

55

A B 40

Solution: The free-body diagram is shown.
The equilibrium equations are Fx : TB cos 40° TA cos 55° D 0 90 9.81 N D 0

Fy : TB sin 40° C TA sin 55°

Solving: TA D 679 N, TB D 508 N

Problem 3.6 A physiologist estimates that the masseter muscle of a predator, Martes, is capable of exerting aforce M as large as 900 N. Assume that the jaw is in equilibrium and determine the necessary force T that the temporalis muscle exerts and the force P exerted on the object being bitten. Solution: The equilibrium equations are
Fx : T cos 22° M cos 36° D 0 PD0

22 T P

M

36

Fy : T sin 22° C M sin 36°

Setting M D 900 N, and solving, we find T D 785 N, P D 823 N

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c 2008 PearsonEducation, 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.

Problem 3.7 The two springs are identical, with unstretched lengths 250 mm and spring constants k D 1200 N/m. (a) Draw the free-body...