ppt lecture- intro to dynamics & kinematic motion

5/21/2018 PPT Lecture- Intro to Dynamics & Kinematic Motion

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L E C T U R E N O T E S

B Y :

E N G R . F R A N C I S F . V I L L A R E A L

D L S U - D / C E A T / 1 S T S E M S Y 2 0 1 4 - 2 0 1 5

Engineering Mechanics

(Dynamics)


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INTRODUCTION

Dynamics includes:

- Kinematics: study of the geometry of motion. Kinematics isused to relate displacement, velocity, acceleration, and timewithout reference to the cause of motion.

- Kinetics: study of the relationsexistingbetween the forcesacting on a body, the mass of the body, and the motion of thebody. Kinetics is used to predict the motion caused by givenforces or to determine the forces required to produce a given

motion.


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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)


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KINEMATICS OF PARTICLES

Rectilinearmotion: position, velocity, andacceleration of a particle as it moves along a straightline.

Curvilinearmotion: position, velocity, andacceleration of a particle as it moves along a curvedline in two or three dimensions.


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KINEMATICS OF PARTICLES

Kinematics of

particles

Road Map

Rectilinear motion Curvilinear motion

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

Relative motion


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RECTILINEAR MOTION

Particle moving along a straight line is said to be in rectilinear

motion.


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Determination of the Motion of a Particle

Recall, motionof a particle is known if itspositionis known for all time t.

Typically, conditions of motion are specified by the type of acceleration

experienced by the particle. Determination of velocity and position requires

successive integrations.

Three types of motion may be defined for:

- acceleration given as a function of time, a=f(t)

- acceleration given as a function of position, a=f(x)

- acceleration given as a function of velocity, a=f(v)


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Graphical Solution of Rectilinear Motion

Given thex-tcurve, the v-tcurve is equal to

thex-tcurve slope.

Given the v-tcurve, the a-tcurve is equal to

the v-tcurve slope.


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Kinematic Equations

Consider particle which occupies positionPat time tand Pat t+Dt,

Average velocity

t

xv

t

x

t D

D

D

D

D 0

limInstantaneous velocity

Instantaneous velocity may be positive or negative.Magnitude of velocity is referred to asparticle speed.


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Kinematic Equations

Consider a particle with velocity vat time tand vatt+Dt,

Instantaneous acceleration

t

va

t D

D

D 0

lim


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RECTILINEAR MOTION FORMULAS

Average velocity: V = dS/dt

Average acceleration: a = d2S/dt2= dV/dt

Constant acceleration:

V V0= atS = V0t + (at

2)

V2V02= 2aS

This applies to a freely falling object:dvvdsa

22/2.32/81.9a sf tsm


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Application Problem 1

Consider a particle moving a straight line andassume that its position is defined by the equationwhere x is in meters and t in seconds.

Show the graphical representation of the 3 motioncurves where x is a function of t, v as a function of tand a as a function of t.

326 ttx


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The brake mechanism used to reduce recoil in certain types of guns asshown in the given figure consists essentially of a piston attached to thebarrel and moving in a fixed cylinder filled with oil. As the barrel recoilswith an initial v0, the piston moves and oil is forced through orifices inthe piston, causing the piston and the barrel to decelerate at a rate

proportional to their velocity; that is a = -kv. Express a.) v in terms of tb.) x in terms of t c.) v in terms of x and d.) draw the correspondingmotion curves.



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Cars A and B approached each other on a straightroad from a point where the 2 cars are 450 metersapart. Car A has an initial velocity of 70 kph and is

being decelerated at a rate of 0.40m/s2. Cars B hasan initial velocity of 20 kph and is accelerating at arate of 0.30m/s2. When will the cars meet and howfar will Car A have traveled? Show accompanying

figure.



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FREELY FALLING BODIES

In the absence of air resistance, it is found that all bodies at the

same location above the earth fall vertically with the same

acceleration.

Furthermore, if the distance of the fall is small compared to theradius of the earth, the accelerationremains essentially

constant throughout the fall.

This idealized motion, in which air resistance is neglected and

the acceleration is nearly constant, is known as free-fall.

Since the acceleration is constant in free-fall, the equations of

kinematicscan be used.


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GalileoGalilei (1564-1642)

Father of Kinematics

Concluded that all objects fallat same rate of acceleration.

Demonstrated the scientificmethod in developing thekinematics of free fallmotion.

Tested his hypothesisthrough experimentation.


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Sir Isaac Newton (1642-1727)

Father of dynamics(why)

Published Three laws

of motion and

universal law ofgravitation in 1687.

InertiaF=ma

Action/reaction


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Acceleration Due to Gravity

Galileo calculated that all freely falling objectsaccelerate at a rate of

9.8 m/s2

This value, as an acceleration, is known as g


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Free Fall An Object Dropped

Initial velocity is zero

Use the kinematic equations Generally use y instead of x since y

is verticalAcceleration is ay= g= 9.80 m/s

2

vo= 0

a =g

Section 2.7


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Free Fall Object Thrown Upward

Initial velocity is upward,

so positive

The instantaneous velocity

at the maximum height is

zero.

ay= -g = -9.80 m/s2

everywhere in the motion

v = 0

vo 0a = -g

Section 2.7


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A ball is tossed with a velocity of 10m/s directed vertically upward from a window of abuilding located 20 meters above the ground. Determine the following:

Velocity v of the ball at any time t with graphical motion diagram

Elevation y of the ball at any time t with graphical motion diagram

Highest elevation in meters reached by the ball and value of time in seconds

Time in seconds when the ball hits the ground

V0= 10m/s

20 m


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A stone is thrown vertically upward over the top of a well with a velocity of21m/s and the splash is heard in 5.05 sec. If the velocity of sound is constant at350m/s, determine the depth of the well to which the stone falls.

v0= 21m/s

depth


water


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CURVILINEAR MOTION

Particle moving along a curve other than a straightline is in curvilinear motion

Position vectorof a particle at time tis defined by a

vector between origin Oof afixed reference frameand the position occupied by particle.


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Plane Curvilinear Motion


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Speed and Velocity


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Acceleration


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Visualization of Motion


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The Coordinate System

RECTANGULAR, x-y

NORMAL TANGENTIAL, n-t

POLAR, r-


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Rectangular Coordinate System


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Projectile Motion (x-y coordinate )


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A rocket has expended all its fuel when it reaches point A, where it hasvelocity u at angle with respect to the horizontal. It then beginsunpowered flight and attains a maximum added height h at position Bafter traveling a horizontal s from A. Determine the expression for hand s, the time t of flight from A to B and the equation of the path. For

the interval concerned, assume a flat earth with a constant accelerationg and neglect any atmospheric resistance.


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Normal-Tangential Coordinate System


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Acceleration (n-t coordinate )


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Acceleration (n-t coordinate )


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Direction of Acceleration (n-t coordinate)


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Circular Motion (n-t coordinate)


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When a skier reaches point A along the parabolic path, he has a speed of 6m/swhich is increasing at 2m/s2. Determine the direction of his velocity anddirection and magnitude of his acceleration at this instant. Neglect the size ofthe skier.



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Polar Coordinate System


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Velocity and Acceleration (r-)


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Geometric Interpretation (r-)


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Circular Motion (r-)


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The searchlight shown in the given figure casts a spot of light along the face of awall that is located 100m from the searchlight. Determine the magnitudes ofthe velocity and acceleration at which the spot travels across the wall at theinstant = 450. The searchlight at a constant rate of 4 rad/sec.


ppt lecture- intro to dynamics & kinematic motion

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