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ClassNotes - ME 270 Basic Mechanics I Prof Jones Rm ME 222B...

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ME 270 Basic Mechanics I Prof. Jones Rm: ME 222B Ph: 494-5691 Email: [email protected]
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2 1.0 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).
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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 0, 0 FM ⎛⎞ ⎜⎟ ⎝⎠ = = ∑∑ . 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 ( ) F ma = . Third Law : For each action there is an equal and opposite reaction ( ) FF A BB A =− .
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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, 12 xCvC a = + 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: miles hour 5280ft ft 60 88 hour 3600 s mile s ××=
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5 Accuracy of Numerical Answers Say that you do the following calculations: x zt y = + 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 10 -4 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 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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ClassNotes - ME 270 Basic Mechanics I Prof Jones Rm ME 222B...

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