View of /trunk/NationalProblemLibrary/Rochester/instructiveProblems/OldProblems/ur_vc_12_2.pg

    1 ##DESCRIPTION
    2 #
    3 # File Created: 6/5/2000
    4 # Last Modified: 6/5/2000
    5 # Problem Author: Joseph Neisendorfer
    6 # WeBWorK Entry: David Etlinger
    7 # Location: University of Rochester
    8 #
    9 # Asks for the work done when moving a
   10 # particle in a vector field
   11 #
   12 ##ENDDESCRIPTION
   13 
   14 ##KEYWORDS('Multivariable','Vector','Work')
   15 
   16 DOCUMENT();        # This should be the first executable line in the problem.
   17 
   18 loadMacros(
   19 "PG.pl",
   20 "PGbasicmacros.pl",
   21 "PGchoicemacros.pl",
   22 "PGanswermacros.pl",
   23 "PGauxiliaryFunctions.pl",
   24 "PGcourse.pl",
   25 # source.pl"
   26 );
   27 
   28 TEXT( beginproblem() );
   29 $showPartialCorrectAnswers = 1;
   30 
   31 ###################
   32 #
   33 #  Setup
   34 
   35 $a = random( 1, 5, 1 );
   36 $b = random( 1, 5, 1 );
   37 $c = random( 1, 5, 1 );
   38 
   39 $ans = (1/2)*($a**2 + 2*$a + $b**2 + 2*$b + $c**2 + 2*$c);
   40 
   41 ###################
   42 #
   43 #  Text
   44 
   45 BEGIN_TEXT
   46 If C is the curve given by \( \mathbf{r} \left( t \right) = \left( 1 + $a \sin t
   47 \right) \mathbf{i} + \left( 1 + $b \sin^{2} t \right) \mathbf{j} + \left( 1 + $c
   48 \sin^{3} t \right) \mathbf{k} \), \( 0 \leq t \leq \frac{\pi}{2} \) and $BBOLD F
   49 $EBOLD is the radial vector field \( \mathbf{F} \left( x, y, z \right) = x
   50 \mathbf{i} + y \mathbf{j} + z \mathbf{k} \), compute the work done by $BBOLD F
   51 $EBOLD on a particle moving along C.
   52   $PAR
   53 \{ans_rule(40)\}
   54 END_TEXT
   55 
   56 ###################
   57 #
   58 #  Answer
   59 
   60 ANS(num_cmp($ans));
   61 
   62 ENDDOCUMENT();        # This should be the last executable line in the problem.