978-0073380292 Chapter 3 Part 2

Problem 3.17

Guy wire

AB

is used to help support the utility pole

AC

. If the guy wire

AB

can support a maximum tensile force of

500 lb

, and if the pole

AC

can support

a maximum compressive force of

800 lb

before buckling, determine the largest

force Pthat can be supported.

Problem 3.18

A component of a machine has a frictionless roller

A

that rests in a slot. The

roller is supported by bar

AB

where point

B

is a pin. For the values of

P

and

given below, determine the force supported by bar AB.

PD200 N and D15ı.

Problem 3.19

A component of a machine has a frictionless roller

A

that rests in a slot. The

roller is supported by bar

AB

where point

B

is a pin. For the values of

P

and

given below, determine the force supported by bar AB.

PD400 N and D35ı.

Problem 3.20

A bead

A

weighing

2lb

slides on a quarter-circular frictionless bar

BC

with

radius

r

. The bead is supported by a cable

AC

. For the value of



given below,

determine the force supported by cable AC .

D20ı.

Problem 3.21

A bead

A

weighing

2lb

slides on a quarter-circular frictionless bar

BC

with

radius

r

. The bead is supported by a cable

AC

. For the value of



given below,

determine the force supported by cable AC .

General values of where 0ı<  < 90ı.

Solution

y

x

A

C

TAC

2 lb

R

r r sin

r sin

r cos

The FBD for bead

A

is shown at the right. The reaction between

the bead and bar is constructed as follows. The bead may not move

perpendicular to the bar, therefore there is a reaction force

R

perpen-

dicular to the bar. The bead is free to move parallel to the frictionless

bar, therefore there is no reaction force in that direction. To determine

the orientation for

TAC

we consider the triangle shown below. The

hypotenuse hof this triangle is

h2D.r cos /2CŒr.1 sin /2(1)

Dr2cos2C12sin Csin2:(2)

A

C

hr(1 sin )

r cos

Since cos2Csin2D1, Eq. (2) becomes

h2Dr22.1 sin  /: (3)

Hence,

hDrp2.1 sin  /: (4)

Summing forces in the xand ydirections provides

XFxD0W Rcos CTAC

rcos 

rp2.1 sin  / D0; (5)

XFyD0WRsin CTAC

r.1 sin /

rp2.1 sin  / 2lb D0: (6)

Equation (5) provides

TAC DRp2.1 sin  /: (7)

Substituting Eq. (7) into Eq. (6) provides

288 Solutions Manual

Problem 3.22

Two schemes are shown for hanging a large number of ﬂowerpots side by side

on an outdoor porch. The ﬂowerpots are to have

60 cm

spacing. Each ﬂowerpot

weighs 175 N.

(a) Determine the force in wire AB.

(b) Determine the forces in wires CD and CE.

(c)

Compared to the scheme using one wire, the scheme using two wires

may be more resistant to adjacent ﬂowerpots hitting one another in high

winds. Do you believe this statement is valid? Explain. Hint: Consider

the application of a horizontal wind force

P

to points

A

and

C

and

speculate on the ability of each system to resist horizontal motion. To

do this, compare the values of

P

needed to produce the same horizontal

displacement of points Aand Cof, say, 10 cm.

Problem 3.23

A hydraulic cylinder

AB

on a backhoe produces a

4500 lb

compressive force. Deter–

mine the forces in members BD and BC .

Problem 3.24

A worker inside a truck at point

A

applies a force to rope

ABC

to slowly

lower a box

C

down a ramp

DE

. The box has

400

N weight and slides without

friction on the ramp, and the pulley at Bis frictionless. For the position of the

box given below, determine the force the worker must apply to the rope and the

reaction between the box and ramp. Neglect the size of the box and pulley.

The box is 1/4 the distance from point Dto point E.

Solution

y

x

TABC

C

1.2

3.53.7

1.2

3.5

3.7

400 N

R

The FBD for box

C

is shown at the right. If the box is

1=4

the distance from

Dto E, then

ErCB D1

4.3:5 m/0:8 mO{C1

4.1:2 m/C2:5 mO|(1)

D.1:675 O{C2:8 O|/ m;(2)

E

TABC DTABC

1:675 O{C2:8 O|

3:263 :(3)

Summing forces in the xand ydirections provides

XFxD0W TABC

1:675

3:263 CR1:2

3:7 D0; (4)

XFyD0WTABC

2:8

3:263 CR3:5

3:7 400 ND0: (5)

Solving these equations provides

TABC D169:8 N and RD268:8 N:(6)

Problem 3.25

A worker inside a truck at point

A

applies a force to rope

ABC

to slowly

lower a box

C

down a ramp

DE

. The box has

400

N weight and slides without

friction on the ramp, and the pulley at Bis frictionless. For the position of the

box given below, determine the force the worker must apply to the rope and the

reaction between the box and ramp. Neglect the size of the box and pulley.

The box is 3/4 the distance from point Dto point E.

Solution

y

x

TABC

C

1.2

3.53.7

1.2

3.5

3.7

400 N

R

The FBD for box

C

is shown at the right. If the box is

3=4

the distance from

Dto E, then

ErCB D3

4.3:5 m/0:8 mO{C3

4.1:2 m/C2:5 mO|(1)

D.3:425 O{C3:4 O|/ m;(2)

E

TABC DTABC

3:425 O{C3:4 O|

4:826 :(3)

Summing forces in the xand ydirections provides

XFxD0W TABC

3:425

4:826 CR1:2

3:7 D0; (4)

XFyD0WTABC

3:4

4:826 CR3:5

3:7 400 ND0: (5)

Solving these equations provides

TABC D144:2 N and RD315:5 N:(6)

Problem 3.26

The pulley shown is frictionless and all weights are negligible.

(a) Show that D˛.

(b)

By drawing an FBD of the pulley and writing and solving equilibrium

equations, determine the force

F

in terms of the force

T

and angle



.

Plot the ratio F=T versus for 090ı.

(c)

Imagine a structure has this pulley and cable arrangement, and you

carefully measure



and

˛

and find they are not equal. Explain possible

circumstances that might cause this to occur.

Solution

Problem 3.27

Due to settlement of soil, a recently planted tree has started to lean. To straighten

it, the cable system shown is used, where a turnbuckle on cable AB is periodi-

cally tightened to keep the cable taut as the tree gradually straightens. If the

force in cable AB is 450 N, determine the force in cable CBD.

Solution

Problem 3.28

The symmetric cable and pulley arrangement shown is used to lift a fragile

architectural stone beam. If the only significant mass in the system is the

800 kg

mass mof the beam, determine the forces in cables ACB and CDE.

Problem 3.29

The symmetric cable and pulley arrangement shown is used to lift a fragile

architectural stone beam. If the only significant mass in the system is the

800 kg

mass mof the beam, determine the forces in cables ACB and CDE.

Problem 3.30

In Fig. P3.29, cables

ACB

and

FEG

each can support a maximum force of

3kN

. Cable

CDE

can support

a maximum force of 9 kN. The spreader bar

CE

can support a maximum compressive force of

5kN

.

Determine the largest mass

m

of the stone beam that may be lifted, assuming this is the only significant

mass in the system.

Problem 3.31

Bars

AB

and

BC

have the tensile and compressive strengths listed below. If

QD0

and P0, determine the largest value of Pthat may be supported.

Member Strength

AB 4000 lb tension & 2500 lb compression

BC 4500 lb tension & 3000 lb compression

Problem 3.32

Bars

AB

and

BC

have the tensile and compressive strengths listed in Prob. 3.31.

If PD0and Q0, determine the largest value of Qthat may be supported.

Problem 3.33

Blocks

A

and

B

each weigh

100 lb

and rest on frictionless surfaces. They are

connected to one another by cable

AB

. Determine the force

P

required to hold

the blocks in the equilibrium position shown and the reactions between the

blocks and surfaces.

Problem 3.34

Two weights are supported by cable

ABCD

. With the geometry shown, if one

of the weights is

2000

N, determine the other weight

W

and the cable tensions.