MOMENT - DEUkisi.deu.edu.tr/emine.cinar/STATICS/SPRING18... · where the force imparts zero moment....
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Transcript of MOMENT - DEUkisi.deu.edu.tr/emine.cinar/STATICS/SPRING18... · where the force imparts zero moment....
1. 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
+
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. 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
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
d
d
O
x
y
?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
O
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
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.
