lec 09 (review chap. 12)

8/6/2019 LEC 09 (Review Chap. 12)

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King Fahd University of Petroleum & Minerals

Mechanical Engineering

Dynamics ME 201

BY

Dr. Meyassar N. Al-Haddad Lecture # 9

8/6/2019 LEC 09 (Review Chap. 12)


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

8/6/2019 LEC 09 (Review Chap. 12)


12.1 Introduction

Mechanics

Rigid-body Deformable-body fluid

StaticEquilibrium body

DynamicsAccelerated motion body

Kinematics(Geometric aspect of motion)

Kinetics(Analysis of force causing the motion)

8/6/2019 LEC 09 (Review Chap. 12)


KINEMATICS OF PARTICLESKINEMATICS OF PARTICLES

Kinematics of particles

Road MapRoad Map

Rectilinear motion Curvilinear motion

x-y coord. n-t coord. r- U coord.

Relative motion

8/6/2019 LEC 09 (Review Chap. 12)


Areas of mechanics (section12.1) 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, a2. Kinetics, is a study of forces cause the motion F, m,

motion

8/6/2019 LEC 09 (Review Chap. 12)


8/6/2019 LEC 09 (Review Chap. 12)


± Rectangular Components

� Position vector r = x i + y j + z k

� Velocity v = vx i + vy j + vz k (tangent to path)

� Acceleration a = ax i + ay j +az k (tangent to

hodograph)

± Normal and Tangential Components

� Radius of curvature ( V

� Velocity

� Acceleration

± Polar & Cylindrical Components

� Position r = r ur

� Velocity

� Acceleration

? A22

2/32

/

)/(1

dx yd

dxdy! V

tuv Y!

nt uua

2

V

YY !

UU uuv r r

r !

UU uua aa !

2U r r a

r !

UUU

r r a 2!

General Curvilinear Motion

8/6/2019 LEC 09 (Review Chap. 12)


t v x x x)( 00 !

gt vv y y! )( 0

2

002

1)( g t t y y y !

)(20 0

22 y yvv

y y!

ac= -g = 9.81 m/s2 = 32.2 ft/s2

Vertical MotionHorizontal Motion

12.6 Motion of a Projectile

8/6/2019 LEC 09 (Review Chap. 12)


� 12.9 Absolute Dependent Motion of Two Particles

± Position

± Velocity

± Acceleration

� 12.10 Relative-Motion Analysis of Two Particles UsingTranslating Axes

± Position

± Velocity

± Acceleration

l s s A B !

A BYY !

A Baa !

B A B Ar r r

B A B Avvv !

B A B Aaaa !

8/6/2019 LEC 09 (Review Chap. 12)


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

8/6/2019 LEC 09 (Review Chap. 12)


Continuous Motion� The position of a particle is s = (0.5t3+4t) ft, where

t is in second. Determine the velocity and the

acceleration of the particle when t = 3 s.

s ft t dt

dst

5.45.3!!!

!Y

2

3/93 s f t t

dt

d a

t !!!

!

Y

8/6/2019 LEC 09 (Review Chap. 12)


Projectile

� Determine the speed at which the

basketball at A must be thrown at the

angle of 30o so that it makes it to the

basket at B. At what speed does it

pass through the hoop?

t s s ooY!p

t o

A30cos010 Y!

2

21 t at s s c!o Y

2)81.9(2

130sin5.13 t t

o

A!

933.0!t s A /4.!Y

Horizontal

Vertical

8/6/2019 LEC 09 (Review Chap. 12)


Normal and Tangential

� At a given instant, the automobile

has a speed of 25 m/s and an

acceleration of 3 m/s2 acting in the

direction shown. Determine theradius of curvature of the path and

the rate of increase of the

automobile¶s speed.

2/30.20cos3 smao

t !!

mao

n324

)25(40sin3

22

!!! V V V

Y

8/6/2019 LEC 09 (Review Chap. 12)


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 U = 360o. The path is defined by the

spiral groove r = (5+ UT in., where U is in radians.

r r r

!!!!

!T

U

T

U

T U

752

032360 !!!! UUT Uo

sinr vr /955.03!!!

T

sinr v /21)3(7 !!! UU

222 /63)3(70 sinr r ar

U

2/73.5)3)(3

(202 sinr r a !!!T

UUU

8/6/2019 LEC 09 (Review Chap. 12)


8/6/2019 LEC 09 (Review Chap. 12)


Relative independent motion

� At the instant shown, cars A and B

are traveling at the speeds shown. If

B is accelerating at 1200 km/h2

while A maintains a constant speed,

determine the velocity andacceleration of A with respect to B.

B A B A /vvv

B A

oo

/vi65 j45sin20i45cos20 !

j14.14i14.79v / ! B A

hkm B A

/4.0)4.4()4.7(v / !!

B A B A /aaa !

B A

oo

/ai1 j4sin1.

)(i4cos

1.

)(!

j8 8i16 8a / ! B A

222

//32

602

82

8()162

8(hkma

B A!!

8/6/2019 LEC 09 (Review Chap. 12)


lec 09 (review chap. 12)

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