PRE-REQUISITE: ENGINEERING MECHANICS/STATIC ERT250 DYNAMICS

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 – Assignments20 % – Quizzes10 % Examination – Mid term Examinations20 % – Final Examination50 % 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 Mechanics The study of how bodies react to forces acting on them. 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

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 ( ), who made observations concerning: – bodies in free fall, – motion on incline plane and – motion of pendulum Newton ( ), 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 LAWS F = m a

SI Units UNITS QuantityDimensional Symbol SI Unit UnitSymbol MassMkg LengthLmeterm TimeTseconds ForceFnewtonN 1 N = 1 kg/m.s 2

The principle of dimensional homogeneity: all physical relations must be dimensionally homogeneous. Example: F = ML/T 2 Fx = ½ mv 2 DIMENSIONS

Newton’s Law of gravitation GRAVITATION

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

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 = m g 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 45 o 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

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