King Fahd University of

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Nov 14, 2013 (3 years and 11 months ago)

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King Fahd University of
Petroleum & Minerals

Mechanical Engineering

Dynamics ME
201

BY

Dr. Meyassar N. Al
-
Haddad

Lecture #
9


Review Chapter
12


12.1 Introduction


12.2 Rectilinear Kinematics


12.4 General Curvilinear Motion


12.5 Rectangular components


12.6 Motion of a Projectile


12.7 Normal and Tangential


12.8 Polar and Cylindrical


12.9 Absolute Dependent Motion Analysis


12.10 Relative motion of two particles

12.1
Introduction

Mechanics

Rigid
-
body

Deformable
-
body

fluid

Static

Equilibrium body

Dynamics

Accelerated motion body

Kinematics


(Geometric aspect of motion)

Kinetics

(Analysis of force causing the motion)

KINEMATICS OF PARTICLES

Kinematics of particles

Road Map

Rectilinear motion

Curvilinear motion

x
-
y coord.

n
-
t coord.

r
-


coord.

Relative motion

Areas of mechanics (section
12.1
)

1)
Statics

(CE
-
201
)

-

Concerned with body at rest

2)
Dynamics

-
Concerned with body in motion

1.
Kinematics
, is a study the geometry of the motion


s, v,
a

2
.

Kinetics
, is a study of forces cause the motion F, m,
motion

12.2
Rectilinear Kinematics


Time dependent acceleration


Constant acceleration

dt
ds
v

)
(
t
s
2
2
dt
s
d
dt
dv
a


dv
v
ds
a

t
a
v
v
c


0
2
0
0
2
1
t
a
t
v
s
s
c



)
(
2
0
2
0
2
s
s
a
v
v
c



This applies to a freely falling object:

2
2
/
2
.
32
/
81
.
9
a
s
ft
s
m




Rectangular Components


Position vector r = x i + y j + z k


Velocity v = v
x

i + v
y

j + v
z

k
(tangent to path)


Acceleration
a = a
x

i + a
y

j +a
z

k

(tangent to
hodograph)


Normal and Tangential Components


Radius of curvature (
r)


Velocity


Acceleration


Polar & Cylindrical Components


Position
r = r
u
r


Velocity


Acceleration



2
2
2
/
3
2
/
)
/
(
1
dx
y
d
dx
dy


r
t
u
v


n
t
u
u
a
2
r







u
u
v


r
r
r




u
u
a
a
a
r
r


2




r
r
a
r









r
r
a
2


General Curvilinear Motion

t
v
x
x
x
)
(
0
0


gt
v
v
y
y


)
(
0
2
0
0
2
1
)
(
gt
t
v
y
y
y



)
(
2
0
0
2
2
y
y
g
v
v
y
y



a
c
=
-
g =
9.81
m/s
2

=
32.2
ft/s
2

Vertical Motion

Horizontal Motion

12.6
Motion of a Projectile


12.9
Absolute Dependent Motion of Two Particles


Position


Velocity


Acceleration



12.10
Relative
-
Motion Analysis of Two Particles Using
Translating Axes


Position


Velocity


Acceleration


l
s
s
A
B


A
B




A
B
a
a


B
A
B
A
r
r
r


B
A
B
A
v
v
v


B
A
B
A
a
a
a


Review problems


25
Examples


10
Homework Problems


10
Old Homework Problems


13
Problems in appendix D page
655
&
666


Problems included in the Lecture Notes

Continuous Motion


The position of a particle is s = (
0.5
t
3
+
4
t) ft, where
t is in second. Determine the velocity and the
acceleration of the particle when t =
3
s.


s
ft
t
dt
ds
t
/
5
.
17
4
5
.
1
3
2






2
3
/
9
3
s
ft
t
dt
d
a
t





Projectile


Determine the speed at which the
basketball at A must be thrown at the
angle of
30
o

so that it makes it to the
basket at B. At what speed does it
pass through the hoop?



t
s
s
o
o





t
o
A
30
cos
0
10



2
2
1
t
a
t
s
s
c
o
o






2
)
81
.
9
(
2
1
30
sin
5
.
1
3
t
t
o
A





933
.
0

t
s
m
A
/
4
.
12


Horizontal

Vertical

Normal and Tangential


At a given instant, the automobile
has a speed of
25
m/s and an
acceleration of
3
m/s
2

acting in the
direction shown. Determine the
radius of curvature of the path and
the rate of increase of the
automobile

s speed.

2
/
30
.
2
40
cos
3
s
m
a
o
t


m
a
o
n
324
)
25
(
40
sin
3
2
2



r
r
r

Polar and Cylindrical


The slotted fork is rotating about O at a
constant rate

of
3
rad/s. Determine the radial and transverse
components of velocity and acceleration of the pin
A at the instant


=
360
o
. The path is defined by the
spiral groove r = (
5
+
/p)

in., where


is in radians.

π
θ
r
r
r












p

p

p

7
5
2
0
3
2
360






p




o
s
in
r
v
r
/
955
.
0
3



p

s
in
r
v
/
21
)
3
(
7






2
2
2
/
63
)
3
(
7
0
s
in
r
r
a
r










2
/
73
.
5
)
3
)(
3
(
2
0
2
s
in
r
r
a





p







Dependent Motion


Determine the speed of
point P on the cable in
order to lift the platform at
2
m/s

l
s
s
P
A


4
s
m
A
P
/
8
)
2
(
4
4








Relative independent motion


At the instant shown, cars A and B
are traveling at the speeds shown. If
B is accelerating at
1200
km/h
2

while A maintains a constant speed,
determine the velocity and
acceleration of A with respect to B.

B
A
B
A
/
v
v
v


B
A
o
o
/
v
i
65
j
45
sin
20
i
45
cos
20




j
14
.
14
i
14
.
79
v
/



B
A
h
km
B
A
/
4
.
80
)
14
.
14
(
)
14
.
79
(
v
2
2
/




B
A
B
A
/
a
a
a


B
A
o
o
/
2
2
a
i
1200
j
45
sin
1
.
0
)
20
(
i
45
cos
1
.
0
)
20
(



j
2828
i
1628
a
/


B
A
2
2
2
/
/
3260
)
2828
(
)
1628
(
h
km
a
B
A