Mechanical Engineering Chapter 4 Homework It can act at any point on the beam

288

Ans:

SOLUTION

4–61.

Determine the magnitude of the moment of the force

F = {50i – 20j – 80k} N

about the base line AB of the tripod.

CA

D

F

z

1.5 m

2 m

4 m

SOLUTION

CA

D

F

z

1.5 m

2 m

4 m

4–62.

Determine the magnitude of the moment of the force

F = {50i – 20j – 80k} N

about the base line BC of the tripod.

SOLUTION

4–63.

Determine the magnitude of the moment of the force

F = {50i – 20j – 80k} N

about the base line CA of the tripod.

CA

D

F

z

1.5 m

2 m

4 m

291

SOLUTION

Ans:

*4–64.

A horizontal force of

F = {–50i} N

is applied perpendicular

to the handle of the pipe wrench. Determine the moment

that this force exerts along the axis OA (z axis) of the pipe

assembly. Both the wrench and pipe assembly, OABC, lie in

the y-z plane. Suggestion: Use a scalar analysis.

z

O

A

135°

0.6 m

0.8 m

B

C

F

0.2 m

292

Ans:

SOLUTION

4–65.

Determine the magnitude of the horizontal force

F=–Fi

acting on the handle of the wrench so that this force

produces a component of the moment along the OA axis

(z axis) of the pipe assembly of Mz

={4k}

N

#

m. Both the

wrench and the pipe assembly, OABC, lie in they-z plane.

Suggestion: Use a scalar analysis.

z

O

A

135°

0.6 m

0.8 m

B

C

F

0.2 m

293

Ans:

4–66.

SOLUTION

Fmust be perpendicular to uand r.

The force of acts on the bracket as shown.

Determine the moment of the force about the axis of

the pipe if a = 60°, b = 60°, and g = 45°. Also, determine

the coordinate direction angles of Fin order to produce the

maximum moment about the a–a axis.What is this moment?

a–a

F=30 N

60••

45••

60••

y

x

z

100 mm

50 mm

F=30N

100 mm

294

SOLUTION

4–67.

A clockwise couple M

=

5 N #m

is resisted by the shaft of

the electric motor. Determine the magnitude of the reactive

forces

–R

and R which act at supports A and B so that the

resultant of the two couples is zero.

AB

M

RR

150 mm

6060

295

Ans:

*4–68.

Atwist of is applied to the handle of the screwdriver.

Resolve this couple moment into a pair of couple forces F

exerted on the handle and Pexerted on the blade.

4N

#

m

SOLUTION

For the handle

30 mm

5mm

4N·m

F

P

–F

–P

296

Ans:

4–69.

If the resultant couple of the three couples acting on the

triangular block is to be zero,determine the magnitude of

forces Fand P.

SOLUTION

F

y

z

DP

F

C

B

150N

297

Ans:

4–70.

Two couples act on the beam. If F= 125 lb , determine the result-

ant couple moment.

SOLUTION

200 lb

1.5 ft 1.25 ft

30



F

298

Ans:

4–71.

Two couples act on the beam. Determine the magnitude of

Fso that the resultant couple moment is

counterclockwise.Where on the beam does the resultant

couple moment act?

450 lb #ft,

SOLUTION

200 lb

2ft

1.5 ft 1.25 ft

30

F

F

299

*4–72.

Determine the magnitude of the couple force

F

so that the

resultant couple moment on the crank is zero.

SOLUTION

By resolving F and the 150-lb couple into components parallel and perpendicular to

the lever arm of the crank, Fig. a, and summing the moment of these two force

150 lb

30 30

45

30

F

–F

5 in.

4 in.

300

4–73.

SOLUTION

The ends of the triangular plate are subjected to three

couples. Determine the magnitude of the force Fso that the

resultant couple moment is clockwise.400 N #m

600 N

F

40 40

301

4–74.

The man tries to open the valve by applying the couple forces

of F= 75 N to the wheel. Determine the couple moment

produced.

SOLUTION

150 mm 150 mm

F

302

4–75.

If the valve can be opened with a couple moment of ,determine

the required magnitude of each couple force which must be applied

to the wheel.

SOLUTION

25 N

#

m150 mm 150 mm

F

Ans:

SOLUTION

*4–76.

Determine the magnitude of F so that the resultant couple

moment is 12 kN

#

m, counterclockwise. Where on the beam

does the resultant couple moment act?

F



F

8 kN

1.2 m

0.3 m

0.4 m

3030

304

Ans:

4–77.

Two couples act on the beam as shown. If F= 150 lb,determine

the resultant couple moment.

SOLUTION

150 lb couple is resolved into their horizontal and vertical components as shown in

Fig.a

200 lb

1.5 ft

–

F

4

3

5

F4

3

5

4 ft

305

Ans:

4–78.

200 lb

1.5 ft

–F

4

3

5

F4

3

5

Two couples act on the beam as shown. Determine the

magnitude of Fso that the resultant couple moment is

counterclockwise.Where on the beam does the

resultant couple act?

300 lb #ft

SOLUTION

306

Ans:

4–79.

Two couples act on the frame.If the resultant couple moment

is to be zero,determine the distance dbetween the 80-lb

couple forces.

SOLUTION

2ft

B

y

1ft

3ft

50 lb

80 lb

50 lb

30

5

4

3

d

*4–80.

SOLUTION

Two coup

l

es act on t

h

e frame.If

d

eterm

i

ne t

h

e

resultant couple moment. Compute the result by resolving

each force into xand ycomponents and (a) finding the

moment of each couple (Eq. 4–13) and (b) summing the

moments of all the force components about point A.

d=4ft,

2ft

B

y

1ft

3ft

50 lb

80 lb

50 lb

30

5

4

3

d