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Merge pull request #929 from duffee/main
Reinvigorating Keele's Physics contribution
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‎Contrib/Keele/College_Physics_Wolfe/11.Fluid_Statics/11-02.Density/NU_U17-11-02-001.pg‎

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##DESCRIPTION
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# originally written by Brandon Lostracco and Sara Hesse, Brock University, 2018
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# cleaned up, added solution and re-written to use NumberWithUnits
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##ENDDESCRIPTION
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## DBsubject(Fluids)
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## DBchapter(Fluid Statics)
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## DBsection(Density)
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## Date(December 2021)
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## Institution(Keele University)
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## Author(Boyd Duffee)
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## TitleText1('College Physics')
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## AuthorText1('Wolfe et. al')
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## EditionText1('2015')
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## Section1('11.2')
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## Problem1('1')
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## MO(1)
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## Static(1)
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## KEYWORDS('volume','density','mass')
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DOCUMENT();
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loadMacros(
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'PGstandard.pl',
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'parserNumberWithUnits.pl',
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);
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TEXT(beginproblem());
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Context("Numeric")->flags->set( tolerance => 0.005 );
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$showPartialCorrectAnswers = 1;
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$showHint = 3;
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$volume = NumberWithUnits( 31.103 / 19.32, 'cm^3');
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ANS( $volume->cmp );
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Context()->texStrings;
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BEGIN_TEXT
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Gold is sold by the troy ounce \((31.103 \, \rm g)\).
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What is the volume of 1 troy ounce of pure gold?
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The density of gold is \(19.32 \, \rm g \, cm^{-3}\).
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$PAR
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\( V = \) \{ans_rule(15)\}
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END_TEXT
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BEGIN_HINT
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Consider the relationship between volume and density.
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END_HINT
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BEGIN_SOLUTION
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$PAR $BBOLD SOLUTION $EBOLD $PAR
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\( \displaystyle V = \frac{m}{\rho} = \frac{31.103 }{ 19.32} = $volume \)
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END_SOLUTION
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COMMENT('Uses NumberWithUnits');
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ENDDOCUMENT();

‎Contrib/Keele/College_Physics_Wolfe/11.Fluid_Statics/11-02.Density/NU_U17-11-02-002.pg‎

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##DESCRIPTION
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# originally written by Brandon Lostracco and Sara Hesse, Brock University, 2018
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# cleaned up, added solution and re-written to use NumberWithUnits
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##ENDDESCRIPTION
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## DBsubject(Fluids)
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## DBchapter(Fluid Statics)
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## DBsection(Density)
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## Date(December 2021)
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## Institution(Keele University)
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## Author(Boyd Duffee)
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## TitleText1('College Physics')
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## AuthorText1('Wolfe et. al')
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## EditionText1('2015')
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## Section1('11.2')
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## Problem1('2')
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## MO(1)
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## KEYWORDS('mass','density','conversion','volume')
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DOCUMENT();
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loadMacros(
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'PGstandard.pl',
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'parserNumberWithUnits.pl',
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);
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TEXT(beginproblem());
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Context("Numeric")->flags->set( tolerance => 0.005 );
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$showPartialCorrectAnswers = 1;
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$showHint = 3;
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$mass = NumberWithUnits( random(30, 40, 0.1), 'kg');
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$density = NumberWithUnits( 13.6, 'g/cm^3');
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$volume = Real($mass->value / $density->value);
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ANS( $volume->cmp );
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Context()->texStrings;
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BEGIN_TEXT
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Mercury is commonly supplied in flasks containing \($mass\).
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What is the volume in liters of this much mercury?
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The density of Mercury is \($density\).
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$PAR
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\{ans_rule(20)\} \(\textrm{L}\)
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END_TEXT
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BEGIN_HINT
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Consider the unit conversion between kilograms and grams.
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END_HINT
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BEGIN_SOLUTION
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$PAR $BBOLD SOLUTION $EBOLD $PAR
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\( \displaystyle V = \frac{m}{\rho} = \frac{$mass}{$density} = $volume \ \rm L \)
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END_SOLUTION
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ENDDOCUMENT();

‎Contrib/Keele/College_Physics_Wolfe/11.Fluid_Statics/11-02.Density/NU_U17-11-02-003.pg‎

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##DESCRIPTION
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# originally written by Brandon Lostracco and Sara Hesse, Brock University, 2018
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# cleaned up, added solution and re-written to use NumberWithUnits
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##ENDDESCRIPTION
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## DBsubject(Fluids)
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## DBchapter(Fluid Statics)
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## DBsection(Density)
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## Date(December 2021)
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## Institution(Keele University)
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## Author(Boyd Duffee)
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## TitleText1('College Physics')
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## AuthorText1('Wolfe et. al')
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## EditionText1('2015')
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## Section1('11.2')
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## Problem1('3')
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## MO(1)
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## KEYWORDS('volume','mass','conversion','density')
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DOCUMENT();
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loadMacros(
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'PGstandard.pl',
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'parserNumberWithUnits.pl',
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);
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TEXT(beginproblem());
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Context("Numeric")->flags->set( tolerance => 0.005 );
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$showPartialCorrectAnswers = 1;
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$showHint = 3;
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$volume = NumberWithUnits( random(1.5, 2.5, 0.01), 'L');
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$density = NumberWithUnits( 1.29, 'g*cm^-3');
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$mass = NumberWithUnits( $volume * $density, 'g');
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ANS( $mass->cmp );
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Context()->texStrings;
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BEGIN_TEXT
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What is the mass of a deep breath of air having a volume of \($volume\)?
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The density of air is \($density\).
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$PAR
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\( m = \) \{ans_rule(15)\}
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END_TEXT
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BEGIN_HINT
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Consider the conversion between liters and cubic centimeters.
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END_HINT
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BEGIN_SOLUTION
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$PAR $BBOLD SOLUTION $EBOLD $PAR
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\( m = \rho V = ($density)($volume) = $mass \)
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END_SOLUTION
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COMMENT('Uses NumberWithUnits');
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ENDDOCUMENT();

‎Contrib/Keele/College_Physics_Wolfe/11.Fluid_Statics/11-02.Density/NU_U17-11-02-004.pg‎

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##DESCRIPTION
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# originally written by Brandon Lostracco and Sara Hesse, Brock University, 2018
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# cleaned up, added solution and re-written to use NumberWithUnits
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##ENDDESCRIPTION
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## DBsubject(Fluids)
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## DBchapter(Fluid Statics)
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## DBsection(Density)
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## Date(December 2021)
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## Institution(Keele University)
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## Author(Boyd Duffee)
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## TitleText1('College Physics')
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## AuthorText1('Wolfe et. al')
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## EditionText1('2015')
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## Section1('11.2')
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## Problem1('4')
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## MO(1)
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## KEYWORDS('mass','density','volume','Archimedes')
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DOCUMENT();
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loadMacros(
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'PGstandard.pl',
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'parserNumberWithUnits.pl',
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);
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TEXT(beginproblem());
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Context("Numeric")->flags->set( tolerance => 0.005 );
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$showPartialCorrectAnswers = 1;
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$showHint = 3;
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$mass = NumberWithUnits( random(200, 300, 0.1), 'g');
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$volume = NumberWithUnits( random(60, 100, 0.1), 'cm^3');
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$density = NumberWithUnits( $mass/$volume, 'g/cm^3');
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ANS( $density->cmp );
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Context()->texStrings;
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BEGIN_TEXT
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A straightforward method of finding the density of an object is to measure its mass
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and then measure its volume by submerging it in a graduated cylinder.
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What is the density of a \($mass\) rock that displaces \($volume\) of water?
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(Note that the accuracy and practical applications of this technique are more limited
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than a variety of others that are based on Archimedes' principle.)
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$PAR
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\( \rho = \) \{ans_rule(15)\}
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END_TEXT
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BEGIN_HINT
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Consider relationship between volume, mass, and density.
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END_HINT
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BEGIN_SOLUTION
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$PAR $BBOLD SOLUTION $EBOLD $PAR
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\( \displaystyle \rho = \frac{m}{V} = \frac{$mass}{$volume} = $density \)
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END_SOLUTION
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COMMENT('Uses NumberWithUnits');
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ENDDOCUMENT();

‎Contrib/Keele/College_Physics_Wolfe/11.Fluid_Statics/11-02.Density/NU_U17-11-02-005.pg‎

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##DESCRIPTION
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# originally written by Brandon Lostracco and Sara Hesse, Brock University, 2018
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# cleaned up, added solution and re-written to use NumberWithUnits
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##ENDDESCRIPTION
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## DBsubject(Fluids)
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## DBchapter(Fluid Statics)
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## DBsection(Density)
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## Date(December 2021)
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## Institution(Keele University)
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## Author(Boyd Duffee)
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## TitleText1('College Physics')
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## AuthorText1('Wolfe et. al')
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## EditionText1('2015')
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## Section1('11.2')
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## Problem1('5')
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## MO(1)
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## KEYWORDS('volume','radius','density','mass','depth')
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DOCUMENT();
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loadMacros(
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'PGstandard.pl',
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'parserNumberWithUnits.pl',
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);
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TEXT(beginproblem());
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Context("Numeric")->flags->set( tolerance => 0.005 );
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$showPartialCorrectAnswers = 1;
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$showHint = 3;
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$mass = NumberWithUnits( random(300, 400, 0.1), 'g');
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$depth = NumberWithUnits( random(5, 10, 0.1), 'cm');
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$density = NumberWithUnits( 1, 'g*cm^-3');
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$radius = NumberWithUnits( sqrt($mass /($density * Real($PI) * $depth)), 'cm');
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ANS( $radius->cmp );
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Context()->texStrings;
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BEGIN_TEXT
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Suppose you have a coffee mug with a circular cross section and vertical sides (uniform radius).
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What is its inside radius if it holds \($mass\) of coffee
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when filled to a depth of \($depth\)?
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Assume coffee has the same density as water.
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$PAR
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\( r = \) \{ans_rule(15)\}
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END_TEXT
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BEGIN_HINT
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Consider volume of a cylinder.
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END_HINT
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BEGIN_SOLUTION
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$PAR $BBOLD SOLUTION $EBOLD $PAR
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\( \displaystyle r = \sqrt{ \frac{m}{\rho \pi d} }
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= \sqrt{ \frac{$mass}{($density) \pi ($depth)} }
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= $radius
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\)
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END_SOLUTION
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COMMENT('Uses NumberWithUnits');
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ENDDOCUMENT();

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