King Fahd University of

Mechanics

Nov 14, 2013 (5 years and 1 month ago)

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King Fahd University of
Petroleum & Minerals

Mechanical Engineering

Dynamics ME
201

BY

Dr. Meyassar N. Al
-

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

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

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
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

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