1. An experimental device

imparts a force of magnitude

F = 225 N to the front edge

of the rim at A to simulate the

effect of a slam dunk.

Determine the moments of

the force F about point O and

about point B. Finally, locate,

from the base at O, a point C

on the ground where the force

imparts zero moment.

(2/35)

F = 225 N, MO = ?, MB = ?, locate, from the base at O, a point C on the ground where the force imparts zero moment.

)(75.12328875.411

6.154

22505.353

225

180135

ccwmNM

M

O

NFNF

O

yx

xF

yF

+

)(5.1661265.40

7.01803.0135

cwmNM

M

B

B

+

F = 225 N, MO = ?, MB = ?, locate, from the base at O, a point C on the ground where the force imparts zero moment.

mmd

md

d

dMC

5.687

6875.0

18028875.411

06.118005.3135

xF

yF

+

C

mm1600d

2. A prybar is used

to remove a nail as

shown. Determine

the moment of the

240 N force about

the point O of

contact between

the prybar and the

small support block.

N35.23610cos240

+

65

15

10

N68.4110sin240

?OM

)(

97.8303.068.41

35.035.236

directionclockwise

mN

MO

3. Calculate the moment of the 250 N force on the

handle of the monkey wrench about the center of the

bolt. (2/35)

O

?OM

N70.6415sin250

N48.24115cos250

)(36.46

2.048.24103.070.64

cwmNM

M

O

O

+

4. Calculate the moment Mo of the 250 N

force about the base point O of the robot.

)(55.189353.110197.79

50sin3.060sin4.050sin250

50cos3.060cos4.05.050cos250

576.0

493.0

ccwmNM

M

O

O

?OM

50cos250

+

dy

dx

60° 30°

50° 40°

50°

50sin250

5. The 120 N force is applied as shown to one end of

the curved wrench. If a = 30°, calculate the moment

of F about the

center O of the

bolt. Determine

the value of a

which would

maximize the

moment about O;

state the value

of this maximum

moment. (2/54)

+

F = 120 N, a = 30°, MO =? a =? for MOmax. Compute MOmax.

yF

a=40°

xF

)(60.41

22.33

655.08.348.22

tancossin

0sin8.34cos8.22

cos8.34sin8.22

19.0sin12029.0cos120

)(54.41

025.0070.0070.0025.030sin120070.015.0070.030cos120

max

19.029.0

cwmNM

d

dM

M

M

cwmNM

M

O

O

O

O

O

O

a

aaa

aaa

aa

aa

asin120

acos120

6. The spring loaded

follower A bears against

the circular portion of the

cam until the lobe of the

cam lifts the plunger. The force required to lift the

plunger is proportional to its vertical movement h

from its lowest position.

For design purposes, determine the angle q for which the moment of the

contact force on the cam

about the bearing at O is a maximum. (2/53)

In the exploded view of the contact, neglect the small distance between the actual

contact point B and the end C of

the lobe.

The force required to lift the plunger is proportional to its vertical movement h from its lowest position. Determine the angle q for which the moment of the contact force on the cam about the bearing at O is a maximum.

7. The small crane is mounted along the side of a pickup bed

and facilitates the handling of heavy loads. When the boom

elevation angle is q = 40o , the force in the hydraulic cylinder BC is 4.5

kN, and this

force applied at

point C is in the

direction from B

to C (the cylinder

is in compression).

Determine the

moment of this

4.5 kN force

about the boom

pivot point O.

(2/57)

when q = 40o , FBC =4.5 kN (directed from B to C)

?OM

8. Assume that the hydraulic cylinder AB exerts a force of

constant magnitude 2.5 kN as the bin is elevated. Determine

the moment of about

the point O as a

function of q for the

range 0≤ q ≤90o. At what

angle q is this moment a

maximum and what is

the maximum moment?

F

F

FAB=2.5 kN, MO f(q) = ? (0≤ q ≤90o).

q ? for MOmax. Compute MOmax.

9. The pipe assembly is

subjected to an 80 N

force. Determine the

moment of this force

about point A.

Fx

Fy Fz

?AM

mNkjiM

ijikjkM

kjikjiM

mmC

A

FrM

A

A

A

ACA

38.1109.1339.5

61.1091.81681.172219.29

4007.5353.442.04.055.0

200,400,550

0,0,0

/

NkjiF

zNF

NF

NF

z

y

x

4007.5353.44

)(4030sin80

07.5340cos30cos80

53.4440sin30cos80

mNMA 16.18

10. A 300 N force is applied to the handle of the winch as

shown. The force lies in a plane which is parallel to the y-z

plane and is perpendicular to the line AB of the handle.

Determine

the moments

of this force

about point O

and about the

x-axis.

(2/133)

The force lies in a plane which is parallel to the y-z plane and is perpendicular to the line AB of the handle. Determine the moments of this force about point O and about the x-axis.

Fy

Fz

FrM

mmA

A

O

OAO

/

98.224,12.268,115

40sin350,40cos350,115

0,0,0

mNkjiM

iijkM

kjkjiM

O

O

O

87.2925.1766.98

46.582.4025.1787.29

15081.259225.0268.0115.0

mNiMmNiMM xOx

66.9866.98

NkjkjF

15081.25960cos30060sin300

OAr /

11. A 5 N vertical force is applied to the knob of the

window-opener mechanism when the crank BC is

horizontal. Determine the moment of the force about

point A and about line AB. (2/144)

Determine the moment of the 5 N force about point A and about line AB.

mmB

mmDmA

25,0,3.4330sin50,0,30cos50

5.37,75,6530sin2530sin50,75,30cos2530cos50,0,0,0

)(38.16223.281

5.0866.075.324

)(75.324)866.0)(375(

5.0866.030sin30cos

5.0866.0253.43

253.43

)(375325

55.377565

)(5.377565,5

50

22

/

/

mmNkiM

kinMM

mmNnMM

kikinor

kiki

n

mmNijM

kkjiFrM

mmkjirkF

AB

ABABAB

ABAAB

AB

AB

A

ADA

AD

12. In opening a door which is equipped with a heavy-duty return mechanism, a person exerts a force of magnitude 32 N as shown. Force and the normal n to the face of the door lie in a vertical plane. Compute the moment of about the z axis.

(2/129)

P

P

P

P=32 N, compute the moment of P about the z axis.

Direction CD is parallel to the z-axis

and lies in a parallel plane to the

horizontal plane.

mmBCmmAB 325,450

N8

13. The arms AB and BC of a desk lamp lie in a vertical plane that forms an angle

of 30o with xy plane. To reposition the light, a force of magnitude 8 N is applied

as shown. Determine,

a) the moment of the force about point A,

b) the moment of the force about the axis of arm AB,

c) The angle between AB and the force,

d) The perpendicular distance between

AB and the line of action of the force.

mmBC

mmAB

325

450

N8

FandABbetweencedisdd

FandABbetweenc

MbMa ABA

tan,)

,)

))

q

14. Concentrated force is acting perpendicular to the

crank arm BC at point C. For the position q =70°, what is

Mx , the moment of about the x axis? At this instant,

My =-20 N·m and Mz =-37.5 N·m.

150 mm z

x

200 mm

A q

100 mm

B f

O

y

C

P

P

150 mm z

x

200 mm

A q

100 mm

B f

O

y

C

P

q=70°, Mx =?, when My =-20 N·m and Mz =-37.5 N·m.