dynamics week 1a

8/13/2019 Dynamics Week 1a

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Dynamics MCB 2043

Introduction

September 2013 SemesterDereje Engida Woldemichael (PhD, CEng MIMechE)

[email protected]

Lesson Outcomes At the end of this lecture you should be able to:

Identify classifications of dynamics


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Overview Statics vs Dynamics

Mechanics

Basic Concepts

Particles

Rigid bodies

Newtons Laws of motion

Why Dynamics

So Important?

Statics VS.Dynamics

Bodies at RESTor in equilibrium

Bodies in MOTION

Dynamics of

Solid Bodies

Dynamics of

Gasses/Air

Dynamics of

Liquids

e.g. Hydrodynamicse.g. Robotics

e.g. Aerodynamics


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Basic Concepts

Particles: - a body of negligible dimensions- a body with dimensions irrelevant to the motion or

the action of forces upon it

A

B

A

BEquivalentParticle

= Rigid Body: - important overall dimensions of the body or changes

in position of the body- negligible deformation (change in shape) of the body

Flexible Body: - deformed body under loads- beyond the scope of this course

Negligible springdeformation

=Rigid body

Newtons Laws of Motion

These are fundamental laws relating forces and motion.

Law I. A particle remains at rest or continues to move in a straight

line with a constant velocity if there is no unbalanced force

acting on it.Sir Isaac Newton

(1643-1727)

Law II. The acceleration of a particle is proportional to the resultant

force acting on it and is in the direction of this force.

F=0 In equilibrium

F=ma Out of equilibrium

Law III. The forces of action and reaction between interacting bodies

are equal in magnitude, opposite in direction, and collinear.

F= F'F F'

Laws Iand IIare strictly true only in an absolute frame of reference (i.e. A particledoes not acceleratefor Law Iand does not rotatefor Law II)


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Law II (Most commonly used in dynamics)

F=ma

Where F: resultant force acting on a body (vector)

m: mass of the body (scalar)

a: the resulting acceleration of the body (vector)

F

m

=F=F1+F2+F3+F4+..Fn-1+Fn=ma

F1Fn

F2

F3F4

Fn-1

m

This equation relates applied forces (F) to the motion of a body (a).

Motion can be constrained (forced to follow a specific path: e.g. car trip, train

on tracks)

or unconstrained(can move in any direction: e.g. aircraft flight path, trajectory

of a ball after it is thrown)

Tennis Ball Bouncing

Unconstrained MotionTrain Running on Tracks

Constrained Motion

2-D Coordinate Systems to Describe Motion:

Rectangularcoordinate (x, y)

Polarcoordinate (r,)

Normal(perpendicular) and Tangent(along the path) coordinates

yP

x

r

t

n


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An Overview of Mechanics

Statics: The study of

bodies in equilibrium.Dynamics:1. Kinematics concerned with

the geometric aspects of motion

2. Kinetics - concerned with

the forces causing the motion

Mechanics: The study of how bodiesreact to forces acting on them.

Tips for solving dynamics problems1.Read the problem carefully and try to correlate the actual physical

situation with the theory you have studied.

2.Draw any necessary diagrams and tabulate the problem data.

3.Establish a coordinate system and apply the relevant principles,

generally in mathematical form.

4.Solve the necessary equations algebraically as far as practical; then, use a

consistent set of units and complete the solution numerically. Report the

answer with no more significant figures than the accuracy of the given

data.

5.Study the answer using technical judgment and common sense todetermine whether or not it seems reasonable.

6.Once the solution has been completed, review the problem. Try to think

of other ways of obtaining the same solution


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Summary Questions1. In dynamics, a particle is assumed to have _________.

A) both translation and rotational motions

B) only a mass

C) a mass but the size and shape cannot be neglected

D) no mass or size or shape, it is just a point

References: R.C. Hibbeler, Engineering Mechanics: Dynamics, SI 13th

Edition, Prentice-Hall, 2012.

dynamics week 1a

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