Mechanical Engineering Chapter 3 Homework Assuming that the tension in cable BD reaches the limit

161

3–1.

SOLUTION

The members of a truss are pin connected at joint O.

Determine the magnitudes of and for equilibrium.

Set .u=60°

F2

F1

u

F2

70fi

30fi

5 kN

y

x

O

3

5

Ans:

162

3–2.

SOLUTION

The members of a truss are pin connected at joint O.

Determine the magnitude of and its angle for

equilibrium. Set .F

2=6kN

uF1

u

F2

70fi

30fi

5 kN

y

x

O

3

5

Ans:

163

Ans:

3–3.

Determine the magnitude and direction

u

of F so that the

particle is in equilibrium.

y

5 kN

8 kN

4 kN

x

60fi

30fi

u

SOLUTION

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

Divide Eq (1) by (2),

164

*3–4.

The bearing consists of rollers, symmetrically confined

within the housing.The bottom one is subjected to a 125-N

force at its contact Adue to the load on the shaft.

Determine the normal reactions NBand NCon the bearing

at its contact points Band Cfor equilibrium.

SOLUTION

40°

N

C

Ans:

165

3–5.

SOLUTION

The members of a truss are connected to the gusset plate.If

the forces are concurrent at point O, determine the

magnitudes of Fand Tfor equilibrium. Take .u=90°

y

A

F

B

9kN

4

53

Ans:

166

3–6.

SOLUTION

Rearrange then divide Eq. (1) into Eq. (2):

The gusset plate is subjected to the forces of three members.

Determine the tension force in member Cand its angle for

equilibrium. The forces are concurrent at point O.Take

.F=8kN

u

y

A

F

T

B

9kN

4

53

Ans:

167

3–7.

SOLUTION

Thus,

The man attempts to pull down the tree using the cable and

small pulley arrangement shown. If the tension in AB is

60 lb, determine the tension in cable CAD and the angle

which the cable makes at the pulley.

u

20°

θ

B

A

C

D

30°

Ans:

168

SOLUTION

Equations of Equilibrium. Assume that for equilibrium, the tension along the

length of rope ABC is constant. Assuming that the tension in cable BD reaches the

Divide Eq. (2) by (1),

*3–8.

The cords ABC and BD can each support a maximum load

of 100 lb. Determine the maximum weight of the crate, and

the angle

u

for equilibrium.

12

5

13

B

A

D

u

169

3–9.

Determine the maximum force F that can be supported in

the position shown if each chain can support a maximum

tension of 600 lb before it fails.

C

A

B

45

3

30fi

F

SOLUTION

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

170

3–10.

The block has a weight of 20 lb and is being hoisted at

uniform velocity. Determine the angle

u

for equilibrium and

the force in cord AB.B

F

20fiA

C

D

u

SOLUTION

Substitute Eq (1) into (2),

171

Ans:

SOLUTION

3–11.

Determine the maximum weight W of the block that can be

suspended in the position shown if cords AB and CAD can

each support a maximum tension of 80 lb. Also, what is the

angle

u

for equilibrium?

B

F

20fiA

C

D

u

172

*3–12.

SOLUTION

Free-Body Diagram: By observation, the force has to support the entire weight

Equations of Equilibrium:

If the maximum allowable tension in the cable is 5 kN,then

F1

The lift sling is used to hoist a container having a mass of

500 kg.Determine the force in each of the cables AB and

AC as a function of If the maximum tension allowed in

each cable is 5 kN,determine the shortest lengths of cables

AB and AC that can be used for the lift. The center of

gravity of the container is located at G.

u.A

CB

F

θθ

Ans:

173

3–13.

A nuclear-reactor vessel has a weight of 500

(

10

3

)

lb.

Determine the horizontal compressive force that the

spreader bar AB exerts on point A and the force that each

cable segment CA and AD exert on this point while the

vessel is hoisted upward at constant velocity.

SOLUTION

At point C :

AB

C

DE

30fi30fi

174

3–14.

Determine the stretch in each spring for equlibrium of the

2-kg block. The springs are shown in the equilibrium

position.

SOLUTION

3 m

3

m4

m

kAB fi 30 N/m

kAC fi 20 N/m

CB

Ans:

175

3–15.

The unstretched length of spring AB is 3 m. If the block is

held in the equilibrium position shown, determine the mass

of the block at D.

3m

3m 4 m

k

AC

20 N/m

k

AB

30 N/m

CB

SOLUTION

Ans:

176

*3–16.

Determine the mass of each of the two cylinders if they

cause a sag of when suspended from the rings at

Aand B.Note that when the cylinders are removed.s=0

s=0.5 m

1m 2 m2m

1.5m

s

BA

CD

k100 N/mk100 N/m

SOLUTION

Ans:

177

3–17.

Determine the stiffness kT of the single spring such that the

force F will stretch it by the same amount s as the force F

stretches the two springs. Express kT in terms of stiffness k1

and k2 of the two springs.

SOLUTION

s

Unstretched

position

k1

s

k2

kT

F

Ans:

178

Ans:

SOLUTION

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

Solving Eqs (1) and (2)

The stretched length of the spring is

3–18.

If the spring DB has an unstretched length of 2 m, determine

the stiffness of the spring to hold the 40-kg crate in the

position shown.

2 m

2

m3

m

k

CB

A

D

179

Ans:

SOLUTION

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

Solving Eqs (1) and (2)

The stretched length of the spring is

3–19.

Determine the unstretched length of DB to hold the 40-kg

crate in the position shown. Take k = 180 N

>

m.

2 m

2

m3

m

k

CB

A

D

*3–20.

Avertical force is applied to the ends of the 2-ft

cord AB and spring AC.If the spring has an unstretched

length of 2 ft,determine the angle for equilibrium. Take

k=15 lb>ft.

u

P=10 lb

SOLUTION

From Eq.(2):

2 ft

k

2 ft

A

BC

u

Ans: