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PH15010 Laboratory Techniques - An Introduction to MATHCAD

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Introduction Review of Last WeekReview of Last Week Modelling Projectile MotionModelling Projectile Motion

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Review of Last Week Assessed ExerciseAssessed Exercise –Sheet Layout –Spelling –Units –Inverse Trig functions –Defining Your Own Functions

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Sheet Layout Change sheet to A4 formatChange sheet to A4 format – –File|Page Setup…|Paper Size|A4 Put your initials/email in page headerPut your initials/email in page header – –Format|Header/Footers… Use Page BreaksUse Page Breaks – –Insert|Page Break

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More Layout & Spelling Watch the right hand marginWatch the right hand margin Can force print in single columnCan force print in single column – –File|Page Setup…|Print Single Page Width

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Aligning Regions Align RegionsAlign Regions –Select with mouse –Format|Align Regions|… –Or select button from toolbar

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Aligning Regions – Before and After

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Separating Regions Overlapping RegionsOverlapping Regions –Looks bad –Makes debugging difficult Format|Separate Regions

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Spelling Check Check spelling in worksheetCheck spelling in worksheet – –Edit|Check Spelling…

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Units Don’t do your own conversions on answersDon’t do your own conversions on answers Use mathCADs facilitiesUse mathCADs facilities

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Unit conversions of answers

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Inverse Trig Functions Sometimes written as sin -1 (x)Sometimes written as sin -1 (x) Use asin(x), acos(x), atan(x) etcUse asin(x), acos(x), atan(x) etc Pronounced arcsin, arccos, arctan…Pronounced arcsin, arccos, arctan…

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User Defined Functions in MathCAD Define OnceDefine Once Use many timesUse many times

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User Defined Functions in MathCAD #2 Bad Example:Bad Example: Not using functionNot using function No point in using functionNo point in using function

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User Defined Functions in MathCAD #3 Good Example:Good Example: Function Defined ONCEFunction Defined ONCE Used several timesUsed several times

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Example Worksheet - Projectile Motion Projectile MotionProjectile Motion Cannon BallCannon Ball Neglect Air ResistanceNeglect Air Resistance Use standard equations of motionUse standard equations of motion Supplied parametersSupplied parameters –vMuzzle, , g Copy worksheet from: http://users.aber.ac.uk/dpl/ph15010/h andouts/cannonball.mcdCopy worksheet from: http://users.aber.ac.uk/dpl/ph15010/h andouts/cannonball.mcd http://users.aber.ac.uk/dpl/ph15010/h andouts/cannonball.mcd http://users.aber.ac.uk/dpl/ph15010/h andouts/cannonball.mcd

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Projectile Motion #2

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Projectile Motion #3 Use simple trig to get x- and y- components of velocityUse simple trig to get x- and y- components of velocity

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Projectile Motion #4 Function to model x-axis motionFunction to model x-axis motion –pX(t) position of X w.r.t. timeposition of X w.r.t. time

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Projectile Motion #5 Function to model y-axis motionFunction to model y-axis motion –pY(t) –Uses s=ut+1/2at 2 –Watch sign of acceleration

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Projectile Motion #6 Graph of pX(t) & pY(t) vs t

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Projectile Motion #7 Want to:Want to: –Determine time of impact –Plot parabola of pY vs pX

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Projectile Motion #8 Determine time of impactDetermine time of impact –Zoom in on graph & estimate –Use Solve Block

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Projectile Motion #9 The solve block MathCAD can solve systems of equationsMathCAD can solve systems of equations StructureStructure – – –given – – –Find(v)=

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The Solve Block Guess Value ‘Given’ followed by system of equations Bold = sign Find(t) function

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Range Variables Like for…next loop in basicLike for…next loop in basic Variable takes on a range of valuesVariable takes on a range of values Can then plot pY(t) vs pX(t)Can then plot pY(t) vs pX(t)

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Projectile Motion pY vs pX

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