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PROBLEM 1
The uniform 30-kg bar OB is secured to
the accelerating frame in the 30o
position from the horizontal by the
hinge at O and roller at A. If the
horizontal acceleration of the frame is
a=20 m/s2, compute the force FA on the
roller and the x- and y-components of
the force supported by the pin at O.
PROBLEM 2
The block A and attached rod have a combined mass
of 60 kg and are confined to move along the 60o guide
under the action of the 800 N applied force. The
uniform horizontal rod has a mass of 20 kg and is
welded to the block at B. Friction in the guide is
negligible. Compute the bending moment M exerted
by the weld on the rod at B.
SOLUTION
x
W=60(9.81) N
60o
N
FBD Kinetic Diagram
x
2/84.4
6060sin)81.9(60800
sma
amaF
x
xxx
FBD of rod
Bx
By
M
W1=20(9.81) N
KD of rod
mTax=60ax
m1ax=20ax
2/196
)60sin7.0)(94.4)(20(7.0)81.9(20
smM
MdmaM xB
The parallelogram linkage shown moves in
the vertical plane with the uniform 8 kg bar
EF attached to the plate at E by a pin which
is welded both to the plate and to the bar. A
torque (not shown) is applied to link AB
through its lower pin to drive the links in a
clockwise direction. When q reaches 60o, the
links have an angular acceleration an
angular velocity of 6 rad/s2 and 3 rad/s,
respectively. For this instant calculate the
magnitudes of the force F and torque M
supported by the pin at E.
PROBLEM 3
The uniform 100 kg log is supported by
the two cables and used as a battering
ram. If the log is released from rest in the
position shown, calculate the initial
tension induced in each cable
immediately after release and the
corresponding angular acceleration a of
the cables.
PROBLEM 4
SOLUTION
W=100(9.81) N
FBD KD
TA TB
nam
tam
+n
+t
+n
+t
When it starts to move, v=0, w=0 but a≠0 02 ran w
2
..
..
/905.430sin
57.849030cos0
smaammgamF
TTmgTTF
tttkd
t
BABAkd
n
2/45.22
905.4sradrat aa
Length of the cables
NTNT
TTTTM
BA
BABAkd
G
17.63739.212
30)5.0(60sin)5.1(60sin0..
The motion of the log is curvilinear translation.
*
*
An 18 kg triangular plate is supported by cables AB and CD. When the plate is in the
position shown, the angular velocity of the cables is 4 rad/s ccw. At this instant,
calculate the acceleration of the mass center of the plate and the tension in each of the
cables.
G 10 cm
A
B
C
D
60° 60°
24 cm
20 cm 20 cm
Answer:
NTNT
sma
CDAB 93.7811.143
/23.6 2
PROBLEM 5
PROBLEM 6
The uniform 8 kg slender bar is hinged about a horizontal axis through O and released from rest
in the horizontal position. Determine the distance b from the mass center to O which will result
in an initial angular acceleration of 16 rad/s2, and find the force R on the bar at O just after
release.
SOLUTION
FBD KD
mg Ot
On
G O
G O
aI
tam
nam
+n
+t
0
6471053601688198
0536005360
55008434878128
168162408198
24060812
1
12
1
2
222
nnn
tttt
a
to
OmaF
N.O..OmaF
m.b.
.b.b.b
bb.b.
bamIM
kgm..mlI
t
a
When it is released, w=0 (v=0, an=w2r=0) but a≠0.
PROBLEM 7
The spring is uncompressed when the uniform slender bar is in the vertical position
shown. Determine the initial angular acceleration a of the bar when it is released from
rest in a position where the bar has been rotated 30o clockwise from the position
shown. Neglect any sag of the spring, whose mass is negligible.
SOLUTION Unstrecthed length of the spring: llllo
2
5)4/2( 22
When q=30o , length of the spring: llspring2
3
When q=30o , spring force:
2
3
2
5
2
3
2
5klllkFspring
(in compression)
l
g
m
k
lamml
lF
lmg
amIM
l
tspring
tO
857.0864.0
412
1
2460cos
4
2
a
a
a
W
O
G +n
+t
On
Ot
30o
30o
l
Fspring
60o
.
lspring
G +n
+t
04
2 l
mam n w
tam
aI 60o
PROBLEM 8
In the mechanism shown, the flywheel has a mass of 50 kg and radius of gyration about
its center of 160 mm. Uniform connecting rod AB has a mass of 10 kg. Mass of the
piston B is 15 kg. Flywheel is rotating by the couple T ccw at a constant rate 50 rad/s.
When q=53o determine the angular velocity and angular acceleration of the connecting
rod AB (wAB ve aAB). What are the forces transmitted by the pins at A and B? Neglect the
friction. Take sin 53=0.8, cos 53=0.6.
PROBLEM 9
The masses of uniform bars AB and BC are mAB = 2 kg and mBC = 1 kg, respectively. Bar BC is
pin connected to a fixed support at C. Bar AB is pin connected at A to a uniform wheel of
radius R = 0.50 m and mass mw = 5 kg. At the instant shown, A is vertically aligned with O,
bar AB is horizontal and bar BC is vertical. For the given instant, bar BC is rotating with an
angular velocity of 2 rad/s and an angular acceleration of 1.2 rad/s2, both in clockwise
direction. Assuming that the wheel rolls without slipping, determine the force P that is
applied to the wheel. Also determine the coefficient of friction between the wheel and the
surface.
C
0.95 m
1.25 m
A
B
O
P
R = 0.50 m
r
wBC=2 rad/s aBC=1.2 rad/s2
m
PROBLEM 10
The 45 kg uniform flywheel shown is rotating
with an angular velocity of 30 rad/s and an
angular acceleration of 72 rad/s2 both in
counter clockwise direction. Bar AB has a
mass of 15 kg and a radius of gyration with
respect to its mass center of 325 mm. The
coefficient of friction between the pin at C and
the slot in bar AB is 0.10. When bar AB is in
the position shown, determine the force
exerted on the bar by the pin at support A and
the support reactions exerted on the flywheel
at point O.
B B
C C
G
A A
G
250 mm
300 mm
600 mm 700 mm
PROBLEM 11
The unbalanced 20 kg wheel with the mass center at G has a radius of gyration about G
of 202 mm. The wheel rolls down the 20o incline without slipping. In the position
shown. The wheel has an angular velocity of 3 rad/s. Calculate the friction force F
acting on the wheel at this position.
SOLUTION “General Motion”
FBD
N
mg
Ff
KD
=
am
aI
222816.0)202.0(20 kgmkmI
aa 25.0 raox x
y
jia
ikkikiaaa
yxaa
G
OGOG
075.0675.025.0
075.033075.025.0/
a
aa
604805
67502502020
.F
..FsinmgamF
f
fxefx
a
a
a
a
51367184
07502020
..N
.cosmgNamF yefy
aa 81602500750 .).(F).(NIM fefG N.N
N.F
s/rad.
f
971160
6172
59715 2
a
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