PRE-REQUISITE: ENGINEERING MECHANICS/STATIC

ERT250 DYNAMICS

MRS SITI KAMARIAH BINTI MD SA’ATBIOSYSTEMS ENGINEERING

The course covers

• the kinematics of particles which includes displacement, velocity and acceleration,

• kinetics of particles; Newton’s law of motion, equation of motion, work, impulse, momentum, principle of work and energy, principle of impulse and momentum,

• planar kinetics and kinematics of rigid bodies, three dimensional kinematics of rigid bodies, three dimensional kinetics of rigid bodies and

• mechanical vibration.

Course Synopsis

• CO1: Ability to analyze the problems in the kinematics of particle and rigid body.

• CO2: Ability to analyze problems related to kinetics of particle involving force and acceleration, work, energy and momentum.

• CO3: Ability to evaluate the problems in the kinetics of rigid bodies in 2D and 3D.

• CO4: Ability to formulate the solutions of the problems for damped and undamped vibrations.

Course Outcomes

• Continuous Assessment– Assignments 20 %

– Quizzes 10 %

• Examination– Mid term Examinations 20 %

– Final Examination 50 %

Course Evaluation

• 2 hours lectures/week

• 1 hour tutorial/week

LECTURES AND TUTORIAL

TEXT BOOK & REFERENCES BOOKS

• HISTORY AND MODERN APPLICATIONS

• BASIC CONCEPTS

• NEWTON’S LAWS

• UNITS

• DIMENSIONS

• GRAVITATION

• SOLVING PROBLEMS IN DYNAMICS

• QUIZ 1

INTRODUCTION TO DYNAMICS

An Overview of Mechanics

MechanicsThe study of how bodies react to forces

acting on them.

StaticsThe study of bodies in

equilibrium.

Dynamics

1. Kinematics – concerned with the geometric

aspects of motion

2. Kinetics - concerned with

the forces causing the

motion

• Dynamics : branch of mechanics which deal with motion of bodies under the action of forces.

• The study of dynamics usually follow the study of statics; which deals with the effect of _________ on bodies in __________.

• Dynamics has two parts:– _____________: the study of motion without the reference

to the forces to cause motion

– _____________: relates the action of forces on bodies to their resulting motions

HISTORY AND MODERN APPLICATIONS

• The beginning of rational understanding of dynamics is credited to Galileo Galilei (1564-1642), who made observations concerning: – bodies in free fall,

– motion on incline plane and

– motion of pendulum

• Newton (1642-1727), guided by Galileo’s work, was able to make an accurate formulation of the laws of motion. Newton was first to correctly formulate the law of universal gravitation.

History of Dynamics

• The principles of mechanics dynamics:– Basic to analysis and design of moving structures

– To fixed structures subject to shock loads

– To robotic and automatic control systems

– To rocket, missile and spacecraft

– To ground and space transportation

– To machinery of all types : turbines, pumps, reciprocating machines, hoists, and machine tool

• In Biosystems and Agricultural Engineering?

Applications of Dynamics

• Space

• Time

• Mass

• Force

• Particle

• Rigid body

• Vector and scalar

BASIC CONCEPTS

• Law I : – A particle remains at rest or continuous to move with

uniform velocity if there is no force acting on it.

• Law II– The acceleration of a particle is proportional to the

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

• Law III– The forces of action and reaction between interacting

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

NEWTON’S LAWSF = ma

• SI Units

UNITS

Quantity Dimensional Symbol

SI Unit

Unit Symbol

Mass M kg kg

Length L meter m

Time T second s

Force F newton N

1 N = 1 kg/m.s2

• The principle of dimensional homogeneity: all physical relations must be dimensionally homogeneous.

• Example:

• F = ML/T2

• Fx = ½ mv2

DIMENSIONS

• Newton’s Law of gravitation

GRAVITATION

221

2

227

221

1067.6

Constant nalGravitatio UniversalG

alityproportion ofconstant

r

mmGF

kgNmxG

Gr

mmF

g

g

earth eLEAVING th areyou when thisUse

earth on the areyou when thisUse

221

r

mmGF

mgF

g

g

Effect of Altitude

mxr

kgxM

r

MGg

r

MmGmg

6

24

2

2

1037.6 Earth theof radius

1097.5Earth theof Mass

226

2427

/81.9)1037.6(

)1097.5)(1067.6(sm

x

xxg

The variation of g with altitude is easily determined from the gravitational law. If go represents the absolute acceleration due to gravity at sea level, the absolute value at altitude h is

mxr

hr

rgg o

6

2

2

1037.6 Earth theof radius

• The gravitational attraction of the earth on a body.

• If a force of attraction of true weight of the body, W, because the body falls with absolute acceleration, g gives

• W = mg

Apparent Weight

1. Formulate the problem– State the given data

– State the desired result

– State your assumption and approximation

2. Develop the solution– Draw any needed diagram and include coordinate

appropriate for the problem

– State the principles to be applied to your solution; formula

– Make your calculation

– Used consistent unit

– Ensure the answer are reasonable in term of magnitude and directions, etc

– Draw conclusion

SOLVING PROBLEMS IN DYNAMICS-Steps

• Don’t simply memorize the kinetics and kinematics equations but expose to the wide variety problem situation. DO AN EXERCISES

Key note

1. State Newton’s law of motion

2. Express the law of gravitation.

3. Discuss the effect of altitude and rotation of the earth on the acceleration due to gravity.

4. A space-shuttle module has a mass of 50 kg and rests on the surface of the earth at latitude of 45o north.

a. Determine the surface level weight of the module.b. The module is taken to an altitude of 300 km

above the surface of the earth, determine its weight under this condition.

c. If a cargo bay is fixed inside the space shuttle and the shuttle is in a circular orbit at altitude 300 km above the surface, determine the weight of the module.

QUIZ 1

Thank You