MECHANICS Ms. Peace Introduction

Sequence 1.1 What is Mechanics? 1.1 What is Mechanics? 1.2 Fundamental Concepts and Principles 1.2 Fundamental Concepts and Principles 1.3 Systems of Units 1.3 Systems of Units 1.4 Conversion of One System to Another 1.4 Conversion of One System to Another 1.5 Method of Problem Solution 1.5 Method of Problem Solution 1.6 Numerical Accuracy 1.6 Numerical Accuracy

1.1 What is Mechanics? The science which describes and predicts the conditions of rest or motion of bodies under the action of forces. The science which describes and predicts the conditions of rest or motion of bodies under the action of forces. Mechanics of Rigid Bodies Mechanics of Rigid Bodies Mechanics of Deformable Bodies Mechanics of Deformable Bodies Mechanics of Fluids Mechanics of Fluids

1.1 What is Mechanics? 3 Parts 3 Parts Mechanics of Rigid Bodies Mechanics of Rigid Bodies Mechanics of Deformable Bodies Mechanics of Deformable Bodies Mechanics of Fluids Mechanics of Fluids

1.1 What is Mechanics? Mechanics of Rigid Bodies is subdivided into 2 Parts Mechanics of Rigid Bodies is subdivided into 2 Parts Statics Statics Bodies at Rest Bodies at Rest Dynamics Dynamics Bodies in Motion Bodies in Motion

1.1 What is Mechanics? Some Consider Some Consider Mechanics as an Engineering Field Mechanics as an Engineering Field Mechanics as a Mathematics Field Mechanics as a Mathematics Field Mechanics is Mechanics is A Physical Science A Physical Science Does not have the empiricism of most Engineering Fields i.e. does not rely on experience or observation alone Does not have the empiricism of most Engineering Fields i.e. does not rely on experience or observation alone Not abstract or even pure science Not abstract or even pure science An applied science An applied science

1.2 Fundamental Concepts and Principles Trailblazers Trailblazers Aristotle ( B.C.) Aristotle ( B.C.) Archimedes ( B.C.) Archimedes ( B.C.) Newton ( ) Newton ( ) Newtonian Mechanics is still the basis for today’s engineering sciences Newtonian Mechanics is still the basis for today’s engineering sciences

1.2 Fundamental Concepts and Principles Space Space Position of a point P defined by three lengths measured from a certain reference point, origin, in three given directions. Position of a point P defined by three lengths measured from a certain reference point, origin, in three given directions. Time Time When the event takes place When the event takes place Mass Mass Two bodies of the same mass will be attracted by earth in the same manner Two bodies of the same mass will be attracted by earth in the same manner Force Force Action of one body on another Action of one body on another Point of application, magnitude and direction Point of application, magnitude and direction Represented by a vector Represented by a vector

1.2 Fundamental Concepts and Principles Six Fundamental Principles Based on Experimental Evidence Six Fundamental Principles Based on Experimental Evidence The Parallelogram Law for Addition of Forces The Parallelogram Law for Addition of Forces The Principle of Transmissibility The Principle of Transmissibility Newton’s Three Fundamental Laws Newton’s Three Fundamental Laws First Law First Law Second Law Second Law Third Law Third Law Newton’s Law of Gravitation Newton’s Law of Gravitation

1.2 Fundamental Concepts and Principles The Parallelogram Law for the Addition of Forces The Parallelogram Law for the Addition of Forces Two forces acting on a particle may be replaced by a single force, called their resultant. Two forces acting on a particle may be replaced by a single force, called their resultant. Resultant is obtained by drawing the diagonal of the parallelogram which has sides equal to the given forces. Resultant is obtained by drawing the diagonal of the parallelogram which has sides equal to the given forces.

1.2 Fundamental Concepts and Principles The Principle of Transmissibility The Principle of Transmissibility The conditions of equilibrium or of motion of rigid body will remain unchanged if a force acting at a given point of the rigid body is replaced by a force of the same magnitude and same direction, but acting at a different point The conditions of equilibrium or of motion of rigid body will remain unchanged if a force acting at a given point of the rigid body is replaced by a force of the same magnitude and same direction, but acting at a different point

1.2 Fundamental Concepts and Principles Newton’s Three Fundamental Laws Newton’s Three Fundamental Laws First Law First Law If the resultant force acting on a particle is zero, the particle will remain at rest (if originally at rest) or will move with constant speed in a straight line (if originally in motion) If the resultant force acting on a particle is zero, the particle will remain at rest (if originally at rest) or will move with constant speed in a straight line (if originally in motion) Second Law Second Law Acceleration proportional to the magnitude of resultant and in the direction of this resultant force Acceleration proportional to the magnitude of resultant and in the direction of this resultant force F = ma F = ma

1.2 Fundamental Concepts and Principles Third Law Third Law The forces of action and reaction between bodies in contact have the same magnitude, same line of action and opposite sense. The forces of action and reaction between bodies in contact have the same magnitude, same line of action and opposite sense.

1.2 Fundamental Concepts and Principles Newton’s Law of Gravitation Newton’s Law of Gravitation Two particles of mass M and m are mutually attracted with equal and opposite forces F and –F. Two particles of mass M and m are mutually attracted with equal and opposite forces F and –F. Show equation Show equation r is the distance between two particles r is the distance between two particles G = universal constant called the constant of gravitation G = universal constant called the constant of gravitation

1.2 Fundamental Concepts and Principles Another case of great importance is the attraction of the earth on a particle on its surface Another case of great importance is the attraction of the earth on a particle on its surface Force is F exerted by the earth on a particle and then becomes W weight of the particle Force is F exerted by the earth on a particle and then becomes W weight of the particle M equals the mass of the particle M equals the mass of the particle r is equal to the radius R of the earth and introducing the constant r is equal to the radius R of the earth and introducing the constant Show equation Show equation

1.2 Fundamental Concepts and Principles The magnitude W of the weight of a particle of mass m may be expressed as The magnitude W of the weight of a particle of mass m may be expressed as W = mg W = mg

1.2 Fundamental Concepts and Principles Value of g varies with the position of the point Value of g varies with the position of the point As long as it remains on the surface of the earth As long as it remains on the surface of the earth g is equal to g is equal to 9.81 m/s^2 or 32.2 ft/s^ m/s^2 or 32.2 ft/s^2

1.3 System of Units International System of Units (SI Units) International System of Units (SI Units) LENGTH LENGTH meter (m) meter (m) MASS MASS kilogram (kg) kilogram (kg) TIME TIME second (s) second (s)

1.3 System of Units Force Force Newton Newton 1N = (1kg) (1 m/s^2) = 1 kg m/s^2 1N = (1kg) (1 m/s^2) = 1 kg m/s^2 Diagram Diagram Weight of a Body or Force of Gravity exerted on that body should be expressed in Newtons Weight of a Body or Force of Gravity exerted on that body should be expressed in Newtons W = mg W = mg = (1 kg) (9.81 m/s^2) = (1 kg) (9.81 m/s^2) = 9.81 N

1.3 System of Units 1 km = 1000 m 1 km = 1000 m 1mm = m 1mm = m 1 Mg = 1000 kg 1 Mg = 1000 kg 1g = kg 1g = kg 1 kN = 1000N 1 kN = 1000N

1.3 System of Units US Customary Units US Customary Units Mile = 5280 ft Mile = 5280 ft Inch = 1/12 ft Inch = 1/12 ft Kilopound (kip) = 1000 lb Kilopound (kip) = 1000 lb Ton = 2000 lb Ton = 2000 lb 1lb = (1 slug) ( 1 ft /s^2) 1lb = (1 slug) ( 1 ft /s^2) Invert equation for 1 slug equivalence Invert equation for 1 slug equivalence

1.3 System of Units Convert to ft/s Convert to ft/s Velocity is given as v = 30 mi / h Velocity is given as v = 30 mi / h Show Relationships Show Relationships

1.4 Conversion from One System to Another Units of Length Units of Length 1 ft = m 1 ft = m Units of Force Units of Force 1 lb = N 1 lb = N Units of Mass Units of Mass 1 slug = 1lb s^2 / ft = kg 1 slug = 1lb s^2 / ft = kg

1.4 Conversion from One System to Another Convert Convert M = 47 lb in to Nm M = 47 lb in to Nm

1.4 Conversion from One System to Another = 47 (4.448 N) (25.4 mm) = 47 (4.448 N) (25.4 mm) = 5310 N mm = 5.31 N m

1.5 Method of Problem Solution Solution must be based on six fundamental principles stated in section 1.2 Solution must be based on six fundamental principles stated in section 1.2 Every step must justify those things Every step must justify those things Statement of Problem should be clear and precise Statement of Problem should be clear and precise Contain the given data Contain the given data A neat diagram A neat diagram Separate diagrams for all bodies Separate diagrams for all bodies

1.6 Numerical Accuracy Accuracy Depends on Two Items Accuracy Depends on Two Items Accuracy of given data Accuracy of given data Accuracy of the computations performed Accuracy of the computations performed Data seldom known with accuracy greater than 0.2 percent Data seldom known with accuracy greater than 0.2 percent

1.6 Numerical Accuracy Typical Practice Typical Practice Numbers that begin with a “1” Numbers that begin with a “1” Record with four digits Record with four digits lb lb All other numbers All other numbers Record with three digits Record with three digits 40.0 lb 40.0 lb