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PH15010

PH15010. Laboratory Techniques - An Introduction to MATHCAD. Introduction. Review of Last Week Modelling Projectile Motion. Review of Last Week. Assessed Exercise Sheet Layout Spelling Units Inverse Trig functions Defining Your Own Functions. Sheet Layout. Change sheet to A4 format

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PH15010

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  1. PH15010 Laboratory Techniques - An Introduction to MATHCAD

  2. Introduction • Review of Last Week • Modelling Projectile Motion

  3. Review of Last Week • Assessed Exercise • Sheet Layout • Spelling • Units • Inverse Trig functions • Defining Your Own Functions

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

  5. More Layout & Spelling • Watch the right hand margin • Can force print in single column • File|Page Setup…|Print Single Page Width

  6. Aligning Regions • Align Regions • Select with mouse • Format|Align Regions|… • Or select button from toolbar

  7. Aligning Regions –Before and After

  8. Separating Regions • Overlapping Regions • Looks bad • Makes debugging difficult • Format|Separate Regions

  9. Spelling Check • Check spelling in worksheet • Edit|Check Spelling…

  10. Units • Don’t do your own conversions on answers • Use mathCADs facilities

  11. Unit conversions of answers

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

  13. User Defined Functions in MathCAD • Define Once • Use many times

  14. User Defined Functions in MathCAD #2 • Bad Example: • Not using function • No point in using function

  15. User Defined Functions in MathCAD #3 • Good Example: • Function Defined ONCE • Used several times

  16. Example Worksheet - Projectile Motion • Projectile Motion • Cannon Ball • Neglect Air Resistance • Use standard equations of motion • Supplied parameters • vMuzzle, a, g • Copy worksheet from:http://users.aber.ac.uk/dpl/ph15010/handouts/cannonball.mcd

  17. Projectile Motion #2

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

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

  20. Projectile Motion #5 • Function to model y-axis motion • pY(t) • Uses s=ut+1/2at2 • Watch sign of acceleration

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

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

  23. Projectile Motion #8 • Determine time of impact • Zoom in on graph & estimate • Use Solve Block

  24. Projectile Motion #9The solve block • MathCAD can solve systems of equations • Structure • <Guess Values> • given • <System of equations> • Find(v)=

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

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

  27. Projectile MotionpY vs pX

  28. Projectile MotionpY vs pX

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