View of /trunk/rochester_physics_problib/type16/prob17.pg

    1 
    2    DOCUMENT();
    3 
    4 loadMacros( "PG.pl",
    5                "PGbasicmacros.pl",
    6                "PGauxiliaryFunctions.pl",
    7                "PGchoicemacros.pl",
    8                "PGanswermacros.pl",
    9                "PGgraphmacros.pl",
   10                "PG_CAPAmacros.pl"
   11    );
   12 
   13    TEXT(beginproblem());
   14 
   15 
   16 ## *************************************
   17 ##
   18 ## Conservation of linear momentum
   19 ## Part 1
   20 ## By Frank L. H. Wolfs, Wolfs@nsrl.rochester.edu
   21 ## No unauthorized commercial use
   22 ## Imported Files
   23 ## ${CAPA_Tools}Problem
   24 ## ${CAPA_GraphicsDirectory}Gtype16/prob17a.eps
   25 ## Values needing defined:
   26 ## prob_val (number, e.g. /LET prob_val=1)
   27 ## prob_try (number, e.g. /LET prob_try=5)
   28 ##
   29 ## Last modified 07/21/97
   30 ## by: Patrick D. Freivald, patrick@freivald.org
   31 ##
   32 ## **************************************
   33 ##
   34 $mass_girl = random( 30.0   , 50.0   , 1.0   )   ;
   35 $mass_wagon = random( 5.0   , 15.0   , 1.0   )   ;
   36 $mass_weights = random( 12.5   , 0.5 * $mass_girl   , 0.5   )   ;
   37 $vrel = random( 2.5   , 10.0   , 0.5   )   ;
   38 $p_initial = 0.0   ;
   39 $p_final = $p_initial   ;
   40 $p_weights = 2.0 * $mass_weights * ( -1.0 * $vrel    )   ;
   41 $p_girl = $p_final  - $p_weights   ;
   42 $v_girl = $p_girl /  ( $mass_girl  + $mass_wagon    )   ;
   43 $p_weight_1 = $mass_weights * ( -1.0 * $vrel    )   ;
   44 $p_girl_1 = $p_final  - $p_weight_1   ;
   45 $v_girl_1 = $p_girl_1 /  ( $mass_girl  + $mass_wagon  + $mass_weights    )   ;
   46 $p_weight_2 = $mass_weights * ( $v_girl_1  - $vrel    )   ;
   47 $p_girl_2 = $p_girl_1  - $p_weight_2   ;
   48 $v_girl_2 = $p_girl_2 /  ( $mass_girl  + $mass_wagon    )   ;
   49 ##
   50 CAPA_import( " ${CAPA_Tools}Problem " );
   51 TEXT(CAPA_EV (<<'END_OF_TEXT'));
   52 A \{  spf( $mass_girl    , "%0.0f" ) \}-\{ $kg_u \} girl stands on a \{  spf( $mass_wagon    , "%0.0f" ) \}-\{ $kg_u \} wagon holding two \{  spf( $mass_weights    , "%0.1f" ) \}-\{ $kg_u \} weights.  She throws the weights horizontally off the back of the wagon at a speed of \{  spf( $vrel    , "%0.1f" ) \} \{ $mPs_u \} relative to herself.  $BR
   53 \{ CAPA_web( ''  , '\noindent {\centerline {\epsfxsize 2.0in \epsffile{${CAPA_GraphicsDirectory}Gtype16/prob17a.eps}}}'  , '<img src = ${CAPA_Graphics_URL}Gtype16/prob17a.gif align=center width=500>'  )  \}
   54 $BR$BR Assuming that the wagon was at rest initially, what is the speed of the girl after she throws both weights at the same time?
   55 END_OF_TEXT
   56 
   57 ##
   58 
   59 TEXT("$BR",ans_rule(30),"$BR");
   60 ANS( CAPA_ans( $v_girl   , 'format' => "%0.2e" , 'sig' => '3 PLUS 13', 'reltol' => 1   ,  'wgt' => $prob_val    ,  'tries' => $prob_try    ,  'unit' => 'm/s'    ) );
   61 ## *************************************
   62 ##
   63 ## Conservation of linear momentum
   64 ## By Frank L. H. Wolfs, Wolfs@nsrl.rochester.edu
   65 ## No unauthorized commercial use
   66 ## Imported Files
   67 ## ${CAPA_Tools}Problem
   68 ## ${CAPA_GraphicsDirectory}Gtype16/prob17a.eps
   69 ## Values needing defined:
   70 ## prob_val (number, e.g. /LET prob_val=1)
   71 ## prob_try (number, e.g. /LET prob_try=5)
   72 ##
   73 ## Last modified 07/21/97
   74 ## by: Patrick D. Freivald, patrick@freivald.org
   75 ##
   76 ## **************************************
   77 ##
   78 CAPA_import( " ${CAPA_Tools}Problem " );
   79 TEXT(CAPA_EV (<<'END_OF_TEXT'));
   80 $BR Assuming that the wagon was at rest initially, what is the speed with which the girl will move after she throws the weights one at a time, each with a speed of \{  spf( $vrel    , "%0.1f" ) \} \{ $mPs_u \} relative to herself?
   81 END_OF_TEXT
   82 
   83 ##
   84 
   85 TEXT("$BR",ans_rule(30),"$BR");
   86 ANS( CAPA_ans( $v_girl_2   , 'format' => "%0.2e" , 'sig' => '3 PLUS 13', 'reltol' => 1   ,  'wgt' => $prob_val    ,  'tries' => $prob_try    ,  'unit' => 'm/s'    ) );
   87 ENDDOCUMENT();
   88 #####################
   89 
   90 ###Error: $kg_u not defined in this file
   91 ###Error: $kg_u not defined in this file
   92 ###Error: $kg_u not defined in this file
   93 ###Error: $mPs_u not defined in this file
   94 ###Error: $prob_val not defined in this file
   95 ###Error: $prob_try not defined in this file
   96 ###Error: $mPs_u not defined in this file
   97 ###Error: $prob_val not defined in this file
   98 ###Error: $prob_try not defined in this file
   99 
  100 #####################
  101 
  102 
  103 #################################################
  104 ## Processing time =  1 secs ( 0.87 usr  0.00 sys =  0.87 cpu)
  105 #################################################