Mechanical Engineering Chapter 3 Homework We can express each of the forces shown in Fig

215

3–55.

SOLUTION

Force Vectors: We can express each of the forces shown in Fig. ain Cartesian vector

form as

Equations of Equilibrium: Equilibrium requires

Equating the i,j,and kcomponents yields

Assuming that cable AD achieves maximum tension first, substituting

F

AD =250 lb

gF=0;

FAB +FAC +FAD +W=0

Determine the maximum weight of the crate that can be

suspended from cables AB,AC,and AD so that the tension

developed in any one of the cables does not exceed 250 lb.

y

A

B

C

D

x

z

6 ft

3 ft

2 ft 2 ft

3 ft

4 ft

216

*3–56.

The 25-kg flowerpot is supported at Aby the three cords.

Determine the force acting in each cord for equilibrium.

SOLUTION

Thus,

[1]

©F

x=0; 0.5F

AD –0.5F

AC =0

FAD =FAD (sin 30°i–cos 30° sin 60°j+cos 30° cos 60°k)

30fi

60fi

45fi

A

z

B

y

D

C

217

3–57.

SOLUTION

©F

x=0; 0.5F

AD –0.5F

AC =0

If each cord can sustain a maximum tension of 50 N before

it

fails, determine the greatest weight of the flowerpot the

cords can support.

30fi

60fi

45fi

z

B

D

C

218

3–58.

Determine the tension developed in the three cables

required to support the traffic light, which has a mass of

15 kg. Take h = 4 m.

SOLUTION

D

A

hB

C

4 m

6 m

3 m

z

Ans:

219

3–59.

Determine the tension developed in the three cables

required to support the traffic light, which has a mass of

20 kg. Take h = 3.5 m.

Ans:

SOLUTION

D

A

hB

C

4 m

6 m

3 m

4 m

z

220

*3–60.

SOLUTION

T

h

e 800-

lb

cy

li

n

d

er

i

ssupporte

db

yt

h

reec

h

a

i

ns as s

h

own.

Determinethe forcein eachchain for equilibrium. Take

d=1ft.

90

135

1ft

D

B

C

z

y

Ans:

221

Ans:

SOLUTION

Equations of Equilibrium. Referring to the FBD shown in Fig. a,

Solving Eqs (1), (2) and (3)

3–61.

Determine the tension in each cable for equilibrium.

5 m

y

O

C

B

D

A

5 m

4 m

3 m

800 N

4 m

2 m

x

z

222

Ans:

SOLUTION

Equations of Equilibrium. Referring to the FBD shown in Fig. a,

Solving Eqs (1), (2) and (3),

3–62.

If the maximum force in each rod can not exceed 1500 N,

determine the greatest mass of the crate that can be

supported.

3 m

2 m

1 m

2 m

1 m

3 m

A

O

B

C

y

z

2 m

223

Ans:

SOLUTION

Equations of Equilibrium. Referring to the FBD shown in Fig. a,

Solving Eqs (1), (2) and (3)

3–63.

The crate has a mass of 130 kg. Determine the tension

developed in each cable for equilibrium.

3 m

4 m

y

C

2 m

1 m

AB

D

x

z

224

*3–64.

SOLUTION

Force Vectors: We can express each of the forces on the free-body diagram shown in

Fig. ain Cartesian vector form as

Equations of Equilibrium: Equilibrium requires

Equating the i,j,and kcomponents yields

Solving Eqs. (1) through (3) yields

If cable AD is tightened by a turnbuckle and develops a

tension of 1300 lb,determine the tension developed in

cables AB and AC and the force developed along the

antenna tower AE at point A.

15 ft 15 ft

10 ft

z

x

BE

D

C

A

y

30 ft

12.5 ft

225

3–65.

SOLUTION

Force Vectors: We can express each of the forces on the free-body diagram shown in

Fig. ain Cartesian vector form as

Equations of Equilibrium: Equilibrium requires

Equating the i,j,and kcomponents yields

Let us assume that cable AB achieves maximum tension first. Substituting

gF=0;

FAB +FAC +FAD +FAE =0

If the tension developed in either cable AB or AC cannot

exceed 1000 lb,determine the maximum tension that can

be developed in cable AD when it is tightened by the

turnbuckle.Also, what is the force developed along the

antenna tower at point A?

15 ft 15 ft

10 ft

z

x

BE

D

C

A

y

30 ft

12.5 ft

Ans:

226

3–66.

Determine the tension developed in cables ,,and

required for equilibrium of the 300-lb crate.

ADACAB

A

D

C

x

1 ft

3 ft

2 ft 1 ft 2 ft

2 ft

y

z

2 ft

B

SOLUTION

Force Vectors: We can express each of the forces on the free-body diagram shown in

Fig. (a) in Cartesian vector form as

Equations of Equilibrium: Equilibrium requires

Equating the i, j, and kcomponents yields

Solving Eqs. (1) through (3) yields

Ans:

227

3–67.

SOLUTION

F

orce Vectors: We can express each of the forces on the free-body diagram shown in

F

ig.(a) in Cartesian vector form as

Determine the maximum weight of the crate so that the

tension developed in any cable does not exceed 450 lb

.

A

D

C

x

1ft

3ft

2ft1ft2ft

2ft

y

z

2ft

B

Equating the

i, j, and kcomponents yields

Let us assume that cable

AB achieves maximum tension first. Substituting

into Eqs. (1) through (3) and solving, yields

FAB =450 lb

Equations of Equilibrium:

Equilibrium requires