ECOR1101 - Lecture 1.pdf

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Carleton University
Engineering Common Core Courses
ECOR 1101
Jack Vandenberg

Lecture 1 ECOR1101 Mechanics I ECOR1101 –Mechanics I 1 What is Mechanics? • Study of the state of rest or motion of bodies when acted upon by forces • Either the bodies or the forces can be large ECOR1101 –Mechanics I 2 Branches of Mechanics Mechanics Deformable Rigid Body Body Fluid Statics Dynamics Compressible Incompressible At rest or with constant V Variable V (a) ECOR1101 –Mechanics I 3 Fundamental Units (Dimensions) • Four fundamental physical quantities (dimensions) –Length: to locate a body in space and measure dimension of bodies (m, inch) –Mass: measure of a quantity of matter in a body (kg, lb) –Time: measure of succession of events (s) –Force: a “push” or “pull” exerted by one body on another (N, lbf) ECOR1101 –Mechanics I 4 Systems of Units • We will work with two (2) systems of units in mechanics (statics and dynamics) –International System (SI – Système International d’Unités) –US Customary (imperial units) • Both systems have 3 base units and 1 derived ECOR1101 –Mechanics I 5 Base and Derives Units =m·g =F/g ECOR1101 –Mechanics I 6 Conversion of Units ECOR1101 –Mechanics I 7 Dimensional Analysis • Unit conversions are easily solved through the process of dimensional analysis • Facts of dimensional analysis –Conversion factor is a statement of equal relations –Conversion factor in ratio form = 1 –Units cancel out like variables ECOR1101 –Mechanics I 8 Dimensional Homogeneity • The terms of all equations must be dimensionally homogeneous. –Dimension of LHS = Dimension of RHS • Consider the kinematic equation: v  v  at f i m m m   2 s s s s ECOR1101 –Mechanics I 9 Models and Idealizations • Models and idealizations are often used in mechanics to simplify problems • Particle: has mass but negligible size. For example, the earth can be considered a particle with negligible size when viewed with respect to its orbit or other celestial bodies • Rigid body: A rigid body can be considered as a collection of particles but all particles remain fixed with respect to one another under load • Concentrated force: when the area of load application is small with respect to the size of the body ECOR1101 –Mechanics I 10 Newton’s Laws of Motion • Engineering mechanics is formulated on Newton’s Laws of Motion –The laws were postulated based on experimental observation –The laws apply to the motion of a particle with reference to a non-accelerating reference frame ECOR1101 –Mechanics I 11 Newton’s Laws of Motion st • 1 Law: A particle at rest or in motion will continue in its state of rest or motion unless acted upon by an unbalanced system of forces ECOR1101 –Mechanics I 12 Newton’s Laws of Motion • 2ndLaw: A particle of mass (m) acted upon by an unbalanced system of forces (F) experiences an acceleration (a) in the same direction as the force and with a magnitude proportional to the force. F =m ·a ECOR1101 –Mechanics I 13 Newton’s Laws of Motion rd • 3 Law: For every action, there is an equal and opposite reaction. ECOR1101 –Mechanics I 14 Newton’s Law of Gravitational Attraction • States that two bodies ar
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