Mechanical Engineering Chapter 5 Homework Fa Fb And Then The Rest The

417

SOLUTION

Equations of Equilibrium. P will be minimum if its orientation produces the greatest

moment about point B. This happens when it acts perpendicular to AB as shown in

5–30.

Determine the magnitude and direction

u

of the minimum

force P needed to pull the 50-kg roller over the smooth step.

A

B

P

300 mm

50 mm

u

418

5–31.

The operation of the fuel pump for an automobile depends

on the reciprocating action of the rocker arm ABC, which

is pinned at Band is spring loaded at Aand D.When the

smooth cam Cis in the position shown, determine the

horizontal and vertical components of force at the pin and

the force along the spring DF for equilibrium.The vertical

force acting on the rocker arm at Ais , and at C

it is .FC=125 N

FA=60 N

30°

F

A

= 60 N

C

D

B

A

F

E

F

C

= 125 N

SOLUTION

Ans:

419

*5–32.

Determine the magnitude of force at the pin and in the

cable needed to support the 500-lb load. Neglect the

weight of the boom .

SOLUTION

Equations of Equilibrium:The force in cable can be obtained directly by

summing moments about point .

A

BC

AB

BC

A

35

22

8 ft

C

B

A

Ans:

420

5–33.

SOLUTION

The dimensions of a jib crane,which is manufactured by the

Basick Co., are given in the figure. If the crane has a mass of

800 kg and a center of mass at G,and the maximum rated

force at its end is F15 kN,determine the reactions at its

bearings. The bearing at Ais a journal bearing and supports

only a horizontal force,whereas the bearing at Bisathrust

bearing that supports both horizontal and vertical components.

F

G

A

3m

2m

0.75 m

Ans:

5–34.

The dimensions of a jib crane,which is manufactured by the

Basick Co., are given in the figure. The crane has a mass of

800 kg and a center of mass at G.The bearing at Ais a journal

bearing and can support a horizontal force,whereas the

bearing at Bis a thrust bearing that supports both horizontal

andvertical components.Determine the maximum load Fthat

can be suspended from its end if the selected bearings at A

and Bcan sustain a maximum resultant load of 24 kN and

34 kN,respectively.

SOLUTION

F

G

A

3m

2m

B

0.75 m

Ans:

422

Ans:

SOLUTION

5–35.

The smooth pipe rests against the opening at the points of

contact A, B, and C. Determine the reactions at these points

needed to support the force of 300 N. Neglect the pipe’s

thickness in the calculation.

30

300 N

B

A

C

0.5 m 0.5 m

0.26 m

0.15 m

Ans:

SOLUTION

From the geometry shown in Fig. b

The assumption of small

u

is conrmed.

*5–36.

The beam of negligible weight is supported horizontally by

two springs. If the beam is horizontal and the springs are

unstretched when the load is removed, determine the angle

of tilt of the beam when the load is applied.

3 m3 m

A

kAkB

B

CD

600 N/m

= 1 kN/m = 1.5 kN/m

424

5–37.

The cantilevered jib crane is used to support the load of

780 lb.If ,determine the reactions at the supports.

Note that the supports are collars that allow the crane to

rotate freely about the vertical axis.The collar at Bsupports a

force in the vertical direction, whereas the one at Adoes not.

x=5 ft

8 ft

4 ft

780 lb

x

T

B

A

SOLUTION

Equations of Equilibrium:Referring to the of the jib crane shown in Fig. a,we

FBD

Ans:

425

5–38.

T

h

e cant

il

evere

d

jib

crane

i

s use

d

to support t

h

e

l

oa

d

of

780 lb.If the trolley Tcan be placed anywhere between

determine the maximum magnitude of

reaction

at the supports Aand B.Note that the supports

are collars that allow the crane to rotate freely about the

vertical axis.The collar at Bsupports a force in the vertical

direction, whereas the one at Adoes not.

1.5 ft …x…7.5 ft,

SOLUTION

Require

x=7.5 ft

8ft

4ft

780 lb

x

T

B

A

Ans:

SOLUTION

Equations of Equilibrium. FA and FB can be determined directly by writing the

moment equation of equilibrium about points B and A respectively by referring to

the FBD of the bar shown in Fig. a.

Note: The moment equations are set up assuming small

u

, but even with non-small

u

the reactions come out with the same

FA

,

FB

, and then the rest of the solution goes

through as before.

5–39.

The bar of negligible weight is supported by two springs,

each having a stiffness k

=

100 N

>

m. If the springs are

originally unstretched, and the force is vertical as shown,

determine the angle

u

the bar makes with the horizontal,

when the 30-N force is applied to the bar. 2 m

1 m

B

C

30 N

k

Ans:

SOLUTION

Equations of Equilibrium. FA and FB can be determined directly by writing the

moment equation of equilibrium about points B and A respectively by referring to

the FBD of the bar shown in Fig. a.

From the geometry shown in Fig. b

u

*5–40.

Determine the stiffness k of each spring so that the30-N

force causes the bar to tip

u

= 15° when the force is applied.

Originally the bar is horizontal and the springs are

unstretched. Neglect the weight of the bar.

2 m

1 m

B

C

30 N

k

428

5–41.

The bulk head AD is subjected to both water and soil–

backfill pressures.Assuming AD is “pinned” to the

ground at A,determine the horizontal and vertical

reactions there and also the required tension in the

ground anchor BC necessary for equilibrium. The bulk

head has a mass of 800 kg.

6m

4m

310 kN/m118 kN/m

0.5 m

CF

A

B

D

SOLUTION

Equations of Equilibrium: The force in ground anchor BC can be obtained directly

by summing moments about point A.

Ans:

429

5–42.

SOLUTION

Theboom supports the two vertical loads.Neglect the size

of

the collars at Dand Band the thickness of the boom,

and

compute the horizontal and vertical components of

force

at the pin Aand the force in cable CB.Set

and F

2=350 N.

F

1=800 N

3

C

4

5

Ans:

430

5–43.

The boom is intended to support two vertical loads,and

If the cable CB can sustain a maximum load of 1500 N before

it fails, determine the critical loads if Also, what is

the magnitude of the maximum reaction at pin A?

F

1=2F

2.

F

2.

F

1

SOLUTION

3

C

4

5

Ans:

431

Ans:

*5–44.

The 10-kg uniform rod is pinned at end A. If it is also

subjected to a couple moment of 50 N

#

m, determine the

smallest angle

u

for equilibrium. The spring is unstretched

when

u

= 0, and has a stiffness of k = 60 N

>

m.

0.5 m

2 m

50 N  m

k  60 N/m

B

A

u

SOLUTION

432

SOLUTION

Equations of Equilibriums.

P

y can be determined directly by writing the force

and the angle is

5–45.

The man uses the hand truck to move material up the step.

If the truck and its contents have a mass of 50 kg with center

of gravity at G, determine the normal reaction on both

wheels and the magnitude and direction of the minimum

force required at the grip B needed to lift the load.

A

B

60

0.4 m

0.5 m

0.4 m

0.1 m

0.2 m G

433

5–46.

Three uniform books, each having a weight Wand length a,

are stacked as shown. Determine the maximum distance d

that the top book can extend out from the bottom one so

the stack does not topple over.

SOLUTION

ad

434

5–47.

Determine the reactions at the pin A and the tension in cord

BC. Set F = 40 kN. Neglect the thickness of the beam.

SOLUTION

C

A

F

26 kN

13 12

5

53

4

B

4 m

2 m

Ans:

435

*5–48.

If rope BC will fail when the tension becomes 50 kN,

determine the greatest vertical load F that can be applied to

the beam at B. What is the magnitude of the reaction at A

for this loading? Neglect the thickness of thebeam.

SOLUTION

C

A

F

26 kN

13 12

5

53

4

B

4 m

2 m

436

5–49.

The rigid metal strip of negligible weight is used as part of an

electromagnetic switch. If the stiffness of the springs at A

and Bis and the strip is originally horizontal

when the springs are unstretched, determine the smallest

force needed to close the contact gap at C.

k=5N>m,

SOLUTION

Substituting into Eq. (1):

50 mm 50 mm

10 mm

A

B

C

k