978-0073380292 Chapter 2 Part 3

Statics 2e 73

Problem 2.29

For the following problems, use an

xy

Cartesian coordinate system where

x

is horizontal, positive to the

right, and

y

is vertical, positive upward. For problems where the answers require vector expressions, report

the vectors using Cartesian representations.

Repeat Prob. 2.2 on p. 43.

Problem 2.30

For the following problems, use an

xy

Cartesian coordinate system where

x

is horizontal, positive to the

right, and

y

is vertical, positive upward. For problems where the answers require vector expressions, report

the vectors using Cartesian representations.

Repeat Prob. 2.3 on p. 43.

Solution

y

x

R

18 kN

35 kN

Part (a)

The

18 kN

and

35 kN

force vectors are shown to the right with an

xy

Cartesian coordinate system, and the sum of these vectors is given by

E

RD.18 O{C35 O|/kN:(1)

1.23 ft 1.89 ft

R

60◦

45◦x

y

The

1:23 ft

and

1:89 ft

position vectors are shown at the right with an

xy

Cartesian

coordinate system, and the sum of these vectors is given by

E

RD1:23.cos 45ıO{sin 45ıO|/ ft C1:89.cos 60ıO{Csin 60ıO|/ ft

D.1:81 O{C0:767 O|/ft:

(2)

(3)

Problem 2.31

For the following problems, use an

xy

Cartesian coordinate system where

x

is horizontal, positive to the

right, and

y

is vertical, positive upward. For problems where the answers require vector expressions, report

the vectors using Cartesian representations.

Repeat Prob. 2.13 on p. 45.

Problem 2.32

For the following problems, use an

xy

Cartesian coordinate system where

x

is horizontal, positive to the

right, and

y

is vertical, positive upward. For problems where the answers require vector expressions, report

the vectors using Cartesian representations.

Repeat Prob. 2.16 on p. 45.

Problem 2.33

For the following problems, use an

xy

Cartesian coordinate system where

x

is horizontal, positive to the

right, and

y

is vertical, positive upward. For problems where the answers require vector expressions, report

the vectors using Cartesian representations.

Repeat Prob. 2.17 on p. 45.

Problem 2.34

For the following problems, use an

xy

Cartesian coordinate system where

x

is horizontal, positive to the

right, and

y

is vertical, positive upward. For problems where the answers require vector expressions, report

the vectors using Cartesian representations.

Repeat Prob. 2.18 on p. 45.

Solution

Problem 2.35

For the following problems, use an

xy

Cartesian coordinate system where

x

is horizontal, positive to the

right, and

y

is vertical, positive upward. For problems where the answers require vector expressions, report

the vectors using Cartesian representations.

Repeat Prob. 2.21 on p. 46.

Problem 2.36

For the following problems, use an

xy

Cartesian coordinate system where

x

is horizontal, positive to the

right, and

y

is vertical, positive upward. For problems where the answers require vector expressions, report

the vectors using Cartesian representations.

Repeat Prob. 2.22 on p. 46.

Solution

400 N

200 N

F1

60◦

a

x

y

30◦

60◦

The dashed line in the figure to the right represents the direction along which

the resultant force vector

E

R

is required to act. The horizontal and vertical

components of E

Rare given by

RxD400 NF1cos 30ı;and RyD200 NCF1sin 30ı:(1)

It follows that

tan 60ıDRy

Rx

D200 NCF1sin 30ı

400 NF1cos 30ı)F1D246 N:(2)

Note that ˛equals 60ısince F1is perpendicular to line a. Using Cartesian representation, E

F1is given by

E

F1D.246 N/.cos 30ıO{Csin 30ıO|/ D.213 O{C123 O|/ N:(3)

May 11, 2012

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Problem 2.37

Let

E

AD.150 O{200 O|/ lb

and

E

BD.200 O{C480 O|/ lb

. Evaluate the following, and for Parts (a) and (b)

state the magnitude of E

R.

(a) E

RDE

ACE

B.

(b) E

RD2E

A.1=2/ E

B.

(c) Find a scalar ssuch that E

RDsE

ACE

Bhas an xcomponent only.

(d) Determine a dimensionless unit vector in the direction E

BE

A.

Solution

Problem 2.38

Let

E

AD.6O{C8O|/ kN

and

E

BD.9O{12 O|/ kN

. Evaluate the following, and for Parts (a) and (b)

state the magnitude of E

R.

(a) E

RDE

ACE

B.

(b) E

RD 2E

ACE

B.

(c) Find a scalar ssuch that E

RD  E

ACsE

Bhas a ycomponent only.

(d) Determine a dimensionless unit vector in the direction E

AE

B.

Solution

Part (a)

84 Solutions Manual

Problem 2.39

Let

E

AD.150 O{C200 O|/ mm

,

E

BD.300 O{450 O|/ mm

, and

E

CD.100 O{250 O|/ mm

. Evaluate the

following, and for Parts (a) and (b) state the magnitude of E

R.

(a) E

RDE

ACE

BCE

C.

(b) E

RD3E

A2E

BCE

C.

(c) Find scalars rand s, if possible, such that E

RDrE

ACsE

BCE

Chas zero xand ycomponents.

(d) Determine a dimensionless unit vector in the direction E

ACE

BCE

C.

Solution

Part (a)

86 Solutions Manual

Problem 2.40

A rope connecting points

A

and

B

supports the force

F

shown in the figure.

Write expressions using Cartesian vector representation for the following:

(a) ErAB : the position vector from Ato B.

(b) ErBA: the position vector from Bto A.

(c) OuAB : the unit vector in the direction from Ato B.

(d) OuBA: the unit vector in the direction from Bto A.

(e) E

FAB : the force vector the rope applies to A.

(f) E

FBA: the force vector the rope applies to B.

Solution

Problem 2.41

A rope connecting points

A

and

B

supports the force

F

shown in the figure.

Write expressions using Cartesian vector representation for the following:

(a) ErAB : the position vector from Ato B.

(b) ErBA: the position vector from Bto A.

(c) OuAB : the unit vector in the direction from Ato B.

(d) OuBA: the unit vector in the direction from Bto A.

(e) E

FAB : the force vector the rope applies to A.

(f) E

FBA: the force vector the rope applies to B.

Solution

Problem 2.42

A cleat on a boat is used to support forces from three ropes as shown. Determine

the resultant force vector

E

R

, using Cartesian representation, and determine the

magnitude R. Also express E

Rin polar vector representation.

Solution

Problem 2.43

A control arm in a machine supports the three forces shown. Determine the

resultant force vector

E

R

, using Cartesian representation, and determine the

magnitude R. Also express E

Rin polar vector representation.

Problem 2.44

A cantilevered bracket supports forces from two bars and two cables, as shown.

Determine the resultant force vector

E

R

, using Cartesian representation, and

determine the magnitude R. Also express E

Rin polar vector representation.

Problem 2.45

A model of a person’s arm is used for ergonomics studies. Distances are

rAB D

35 cm, rBC D28 cm, and rCD D19 cm.

(a) Determine the position vector ErAD and its magnitude rAD .

(b)

Express

ErAD

using polar vector representation, measuring orientation posi-

tive counterclockwise from the right-hand horizontal direction.

(c) Determine a unit vector OuAD in the direction from Ato D.