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Adding Wolfe Chapter 9, Statics and Torque
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‎Contrib/Keele/College_Physics_Wolfe/9.Statics_and_Torque/9-02.Second_Condition_Equilibrium/NU_U17_09_02_001.pg‎

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## DESCRIPTION
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# originally written by Caroline Promnitz and Connor Wilson, Brock University 2017-2018
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# cleaned up, added solution and re-written to use NumberWithUnits
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## ENDDESCRIPTION
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## DBsubject(Waves)
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## DBchapter(Physics of Hearing)
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## DBsection(Sound Interference Resonance)
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## Date(November 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('9.2')
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## Problem1('1')
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## KEYWORDS(angle, force, torque, vector)
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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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'parserPopUp.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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$r = NumberWithUnits( random(0.8, 0.9, 0.001), 'm');
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$F = NumberWithUnits( random(50, 60, 1), 'N');
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$torque = NumberWithUnits( $r * $F, 'N*m');
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$popup = PopUp(['?', 'yes', 'no'], 'no');
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ANS( $torque->cmp );
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ANS( $popup->cmp );
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Context()->texStrings;
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BEGIN_TEXT
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a) When opening a door, you push on it perpendicularly with a force of \($F\)
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at a distance of \($r\) from the hinges.
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What torque are you exerting relative to the hinges?
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$PAR
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\( \tau = \) \{ans_rule(15)\}
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$PAR
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b) Does it matter if you push at the same height as the hinges?
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\{ $popup->menu() \}
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END_TEXT
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BEGIN_HINT
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Recall the definition of torque. What is the angle between the radius vector and the applied force?
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END_HINT
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BEGIN_SOLUTION
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$PAR $BBOLD SOLUTION $EBOLD $PAR
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Torque is given by \( \tau = F \times r \) where the force is perpendicular to the radius vector.
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$PAR
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\( \tau = $F \times $r = $torque \)
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$PAR
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(b)
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It does not matter at which height you push.
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END_SOLUTION
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COMMENT('Uses NumberWithUnits');
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ENDDOCUMENT();

‎Contrib/Keele/College_Physics_Wolfe/9.Statics_and_Torque/9-02.Second_Condition_Equilibrium/NU_U17_09_02_002.pg‎

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## DESCRIPTION
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# originally written by Caroline Promnitz and Connor Wilson, Brock University 2017-2018
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# cleaned up, added solution and re-written to use NumberWithUnits
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## ENDDESCRIPTION
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## DBsubject(Waves)
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## DBchapter(Physics of Hearing)
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## DBsection(Sound Interference Resonance)
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## Date(November 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('9.2')
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## Problem1('2')
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## KEYWORDS(angle, force, torque, vector)
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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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$r = NumberWithUnits( random(0.138,0.159,0.001), 'm');
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$F = NumberWithUnits( random(160,170,1), 'N');
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$torque = NumberWithUnits( $r*$F, 'N*m');
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$torqueftlb = Real(0.738) * $torque;
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ANS( $torque->cmp );
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ANS( $torqueftlb->cmp );
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Context()->texStrings;
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BEGIN_TEXT
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When tightening a bolt, you push perpendicularly on a wrench with a force of \($F\)
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at a distance of \($r\) from the centre of the bolt.
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$PAR
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a) How much torque are you exerting (relative to the centre of the bolt)?
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$PAR
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\( \tau = \) \{ans_rule(15)\}
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$PAR
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b) Convert this torque to footpounds.
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$PAR
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\( \tau_{ft \cdot lb} = \) \{ans_rule(15)\} \(\textrm{ft}\) · \(\textrm{lb}\)
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END_TEXT
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BEGIN_HINT
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Recall the definition of torque. What is the angle between the radius vector and the applied force?
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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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(a)
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\( \tau = F \times r = $F \times $r = $torque \)
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$PAR
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(b)
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\( \tau = $torqueftlb \ \rm ft \cdot lb \)
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END_SOLUTION
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COMMENT('Uses NumberWithUnits');
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ENDDOCUMENT();

‎Contrib/Keele/College_Physics_Wolfe/9.Statics_and_Torque/9-02.Second_Condition_Equilibrium/NU_U17_09_02_003.pg‎

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## DESCRIPTION
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# originally written by Caroline Promnitz and Connor Wilson, Brock University 2017-2018
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# cleaned up, added solution and re-written to use NumberWithUnits
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## ENDDESCRIPTION
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## DBsubject(Mechanics)
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## DBchapter(Static and Torque)
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## DBsection(Second Condition Equilibrium)
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## Date(November 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('9.2')
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## Problem1('3')
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## KEYWORDS(angle, force, torque, vector, equilibrium)
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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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$r1 = NumberWithUnits( random(0.58, 0.659, 0.001), 'm');
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$r2 = NumberWithUnits( random(0.408, 0.500, 0.001), 'm');
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$F1 = NumberWithUnits( random(16.5, 17.90, 0.01), 'N');
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$F2 = $F1 * $r1 / $r2;
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ANS( $F2->cmp );
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Context()->texStrings;
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BEGIN_TEXT
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Two children push on opposite sides of a door during play. Both push horizontally and
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perpendicular to the door. One child pushes with a force of \($F\) at a distance of
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\($r1\) from the hinges, and the second child pushes at a distance of \($r2\).
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$PAR
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What force must the second child exert to keep the door from moving?
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Assume friction is negligible.
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$PAR
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\( F = \) \{ans_rule(15)\}
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END_TEXT
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BEGIN_HINT
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Recall the second condition for static equilibrium. Choose your pivot wisely so as to eliminate unknown forces.
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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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To keep the door from moving, the torques must balance, so
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\( F_2 \times r_2 = F_1 \times r_1 \)
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$PAR
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\( \displaystyle F_2 = F_1 \frac{r_1}{r_2} = $F1 \left( \frac{ $r1 }{ $r2 } \right) = $F2 \)
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END_SOLUTION
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COMMENT('Uses NumberWithUnits');
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ENDDOCUMENT();

‎Contrib/Keele/College_Physics_Wolfe/9.Statics_and_Torque/9-02.Second_Condition_Equilibrium/NU_U17_09_02_004/NU_U17_09_02_004.pg‎

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## DESCRIPTION
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# originally written by Caroline Promnitz and Connor Wilson, Brock University 2017-2018
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# cleaned up, added solution and re-written to use NumberWithUnits
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## ENDDESCRIPTION
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## DBsubject(Mechanics)
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## DBchapter(Static and Torque)
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## DBsection(Second Condition Equilibrium)
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## Date(November 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('9.2')
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## Problem1('4')
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## RESOURCES('NU_U17_09_02_004.png')
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## KEYWORDS(angle, force, weight, torque, vector, equilibrium)
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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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$g = NumberWithUnits( 9.8, 'm*s^-2');
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$m1 = NumberWithUnits( random(25, 30, 0.1), 'kg');
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$m2 = NumberWithUnits( random(32, 36, 0.1), 'kg');
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$r1 = NumberWithUnits( random(1.6, 1.65, 0.01), 'm');
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$Fp = NumberWithUnits( ($m1 + $m2) * $g, 'N');
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ANS( $Fp->cmp );
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Context()->texStrings;
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BEGIN_TEXT
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\{ image( "NU_U17_09_02_004.png", width=>600, height=>300,
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tex_size=>700, extra_html_tags=>'alt="Children on Seesaw."' ) \}
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$PAR
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The two children shown in the figure above are balanced on a seesaw of negligible mass.
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The leftmost child has a mass of \($m1\) and sits \($r1\) from the pivot.
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The second child has a mass of \($m2\).
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Use the second condition for equilibrium to calculate \(F_p\).
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$PAR
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\( F_p = \) \{ans_rule(15)\}
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$PAR
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(take \( g = $g \) )
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END_TEXT
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BEGIN_HINT
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Can you use the second condition for static equilibrium to write and solve two simultaneous equations,
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one in which the unknown variable is the distance from the heavier child to the fulcrum and the other,
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the supporting force?
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You will have to select a different pivot for each.
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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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\( F_p = m_1 g + m_2 g = ($m1 + $m2) \, $g = $Fp \)
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END_SOLUTION
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COMMENT('Uses NumberWithUnits');
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ENDDOCUMENT();

‎Contrib/Keele/College_Physics_Wolfe/9.Statics_and_Torque/9-02.Second_Condition_Equilibrium/NU_U17_09_02_004/NU_U17_09_02_004.png‎

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