View of /trunk/NationalProblemLibrary/Rochester/setDiffEQ11ModelingWith2ndOrder/ur_de_11_3.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('differential equation' 'second order' 'linear' 'nonhomogeneous')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Second-Order Differential Equations')
   10 ## DBsection('Applications of Second-Order Differential Equations')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT() ;
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl",
   28 "PGdiffeqmacros.pl",
   29 ) ;
   30 #######
   31 $ss = random(2,7,1) ;
   32 $n = random (2,9,1) ;
   33 
   34 #######
   35 $ans = ivy (1,32,32*$ss,0,$n) ;
   36 
   37 TEXT(beginproblem()) ;
   38 $showPartialCorrectAnswers = 1 ;
   39 
   40 BEGIN_TEXT
   41 
   42 A hollow steel ball weighing 4 pounds is suspended from a spring.
   43 This stretches the spring \(\frac{1}{$ss} \) feet.
   44 
   45 The ball is started in motion from the
   46 equilibrium position
   47 with a downward velocity of \($n \) feet per second.
   48 The air resistance (in pounds) of the  moving ball
   49 numerically equals 4 times its
   50 velocity (in feet per second) .
   51 $PAR
   52 Suppose that after t seconds the ball is y feet below its rest position.
   53 Find y in terms of t.  (Note that the positive direction is down.)
   54 
   55 $PAR
   56 Take as the gravitational acceleration 32 feet
   57 per second per second.
   58 $BR $BR
   59 \(y= \) \{ans_box(2,80)\}
   60 
   61 END_TEXT
   62 
   63 HINT(EV3(<<'EOF'));
   64 When using English units (lb, ft, etc.) you need to be a bit careful with equations involving
   65 mass. This is causing some confusion --- I hope this hint helps:
   66 $PAR
   67 Pounds (lb) is a unit of force, not mass.  Using   mg=F and g=32 ft/sec^2 we see that
   68 an object at the surface of the earth which weighs 32 lbs (i.e. the force on it is 32 lbs) will
   69 have a mass of 1 (the unit of mass in the English units is called the slug -- really!)  So one
   70 slug weighs 32 lbs at the surface of the earth ( or lb = (1/32)*slug*ft/sec^2 ).
   71 $PAR
   72 When using metric units, kilogram is a unit of mass not force or weight.  A 1 kilogram mass will weigh
   73 1 * 9.8  newtons on the surface of the earth.  (g= 9.8 m/sec^2 and newton = kg*m/sec^2 ).
   74 $PAR
   75 Saying that a mass "weighs" 1 kilogram is technically incorrect useage, but it is often used.
   76 What one really means is that it has 1 kilogram of mass and therefore weighs 9.8 newtons.
   77 $PAR
   78 EOF
   79 
   80 ANS(fun_cmp($ans , var=>"t",reltol=>1 )) ;
   81 
   82 ENDDOCUMENT() ;
   83 
   84 
   85 
   86 
   87 
   88 
   89 
   90 ##################################################
   91 my $XML_INFORMATION = <<'END_OF_XML_TRAILER_INFO';
   92 <?xml version="1.0"?>
   93 <metaPGdata>
   94         <author>David Prill</author>
   95         <course>MTH163</course>
   96         <description>spring problem, underdamping</description>
   97         <fullPath>setDESOLinear/15.pg</fullPath>
   98         <institution>University of Rochester</institution>
   99         <keywords>spring problem, underdamping</keywords>
  100         <libraryPath>setDESOLinear/15.pg</libraryPath>
  101         <libraryURL>http://webhost.math.rochester.edu/mth163lib/discuss/msgReader$404</libraryURL>
  102         <modified><dateTime.iso8601>20000718T13:05:40</dateTime.iso8601></modified>
  103         <msgNum>404</msgNum>
  104         <pgProblem>true</pgProblem>
  105         <preface></preface>
  106         <problemVariants></problemVariants>
  107         <probNum></probNum>
  108         <psvn></psvn>
  109         <revisedVersions></revisedVersions>
  110         <setName>DESOLinear</setName>
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  113 
  114 END_OF_XML_TRAILER_INFO
  115 ##################################################
  116