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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

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

    • File|Page Setup…|Paper Size|A4

  • Put your initials/email in page header

    • Format|Header/Footers…

  • Use Page Breaks

    • Insert|Page Break


More Layout & Spelling

  • Watch the right hand margin

  • Can force print in single column

    • File|Page Setup…|Print Single Page Width


Aligning Regions

  • Align Regions

    • Select with mouse

    • Format|Align Regions|…

    • Or select button from toolbar


Aligning Regions –Before and After


Separating Regions

  • Overlapping Regions

    • Looks bad

    • Makes debugging difficult

  • Format|Separate Regions


Spelling Check

  • Check spelling in worksheet

    • Edit|Check Spelling…


Units

  • Don’t do your own conversions on answers

  • Use mathCADs facilities


Unit conversions of answers


Inverse Trig Functions

  • Sometimes written as sin-1(x)

  • Use asin(x), acos(x), atan(x) etc

  • Pronounced arcsin, arccos, arctan…


User Defined Functions in MathCAD

  • Define Once

  • Use many times


User Defined Functions in MathCAD #2

  • Bad Example:

  • Not using function

  • No point in using function


User Defined Functions in MathCAD #3

  • Good Example:

  • Function Defined ONCE

  • Used several times


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


Projectile Motion #2


Projectile Motion #3

  • Use simple trig to get x- and y- components of velocity


Projectile Motion #4

  • Function to model x-axis motion

    • pX(t)

  • position of X w.r.t. time


Projectile Motion #5

  • Function to model y-axis motion

    • pY(t)

    • Uses s=ut+1/2at2

    • Watch sign of acceleration


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


Projectile Motion #7

  • Want to:

    • Determine time of impact

    • Plot parabola of pY vs pX


Projectile Motion #8

  • Determine time of impact

    • Zoom in on graph & estimate

    • Use Solve Block


Projectile Motion #9The solve block

  • MathCAD can solve systems of equations

  • Structure

    • <Guess Values>

    • given

    • <System of equations>

    • Find(v)=


The Solve Block

Guess Value

‘Given’ followed by system of equations

Bold = sign

Find(t) function


Range Variables

  • Like for…next loop in basic

  • Variable takes on a range of values

  • Can then plot pY(t) vs pX(t)


Projectile MotionpY vs pX


Projectile MotionpY vs pX


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