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Unformatted text preview: scalar quantity = Force Condition : Moment Condition : Force : Moment : 1 ME 270 Basic Mechanics I Prof. Jones Rm: ME 222B Ph: 4945691 Email: jonesjd@purdue.edu 2 1.02.3 INTRODUCTION Learning Objectives 1). To introduce and define the subject of mechanics . 2). To introduce Newton's Laws , and to understand the significance of these laws. 3). The review modeling, dimensional consistency , unit conversions and numerical accuracy issues. 4). To review basic vector algebra (i.e., vector addition and subtraction and scalar multiplication). 3 Definitions Mechanics : Study of forces acting on a rigid body a) Statics  body remains at rest b) Dynamics body moves Newton's Laws First Law : Given no net force , a body at rest will remain at rest and a body moving at a constant velocity will continue to do so along a straight path . Second Law : Given a net force is applied, a body will experience an acceleration in the direction of the force which is proportional to the net applied force . Third Law : For each action there is an equal and opposite reaction . 4 Models of Physical Systems Develop a model that is representative of a physical system Particle : a body of infinitely small dimensions (conceptually, a point). Rigid Body : a body occupying more than one point in space in which all the points remain a fixed distance apart. Deformable Body : a body occupying more that one point in space in which the points do not remain a fixed distance apart. Dimensional Consistency If you add together two quantities, these quantities need to have the same dimensions (units); e.g., if x, v and a have units of (L), (L/T) and (L/T 2 ), then C 1 and C 2 must have units of (T) and T 2 to maintain dimensional consistency. Many times algebraic errors in analysis lead to dimensional inconsistency. Use dimensional consistency as a check on your algebra. Unit Conversions Use a logical process in your unit conversions. For example, to convert 60 mph to ft/sec: 5 Accuracy of Numerical Answers Say that you do the following calculations: Say that you have used four significant digits for x and y but only two significant digits for t. The numerical value of z will not have more than two significant digits (and likely less than two). Examples of Significant Figures: 385.1 four significant figures 38.51 four significant figures 0.03851 four significant figures 3.851 x 10 7 four significant figures 7.04 x 104 three significant figures 25.5 three significant figures 0.51 two significant figures 0.00005 one significant figure 27.855 five significant figures 8.91 x 10 4 three significant figures 2200. May have two, three or four significant figures depending on the accuracy of the measurement that obtained the number. Where such doubt may 6 exist, it is better to write the number as 2.2 x 10 3 to show two significant figures; or as 2.20 x 10 3 to show three significant figures....
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 Spring '09
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