// Numbas version: exam_results_page_options {"name": "Equilibrium of a particle: four forces", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 12, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/12/edit"}, "name": "Angle quantity 2020", "short_name": "angle", "description": "

Adjusts all angles to 0 < $\\theta$ < 360.

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Accepts '°' and 'deg' as units.

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Penalizes if not close enough or no units.

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90° = -270° = 450°

Retuns the scalar part of students answer (which is a quantity) as a number.

", "definition": "matchnumber(studentAnswer,['plain','en'])[1]"}, {"name": "student_scalar", "description": "

Normalize angle with mod 360

", "definition": "mod(original_student_scalar,360)\n"}, {"name": "student_unit", "description": "

Allows student to use degree symbol or 'deg' for units.

", "definition": "if(trim(student_unit)='\u00b0','deg',student_unit)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(mod(student_scalar,360),'deg')"}, {"name": "close", "description": "", "definition": "withintolerance(student_scalar, correct_scalar,decimal(settings['close_tol']))"}, {"name": "correct_scalar", "description": "

", "definition": "mod(scalar(settings['expected_answer']),360)"}, {"name": "right", "description": "", "definition": "withintolerance(student_scalar, correct_scalar, decimal(settings['right_tol']))"}, {"name": "good_unit", "description": "", "definition": "same(qty(1,interpreted_unit),qty(1,'deg'))"}, {"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "assert(close,incorrect('Incorrect.');end());\nif(right,correct('Correct angle.'), set_credit(1 - settings['close_penalty'],'Angle is close.'));\nassert(good_unit,sub_credit(settings['unit_penalty'], 'Missing or incorrect units.'))"}], "settings": [{"name": "expected_answer", "label": "Expected Answer", "help_url": "", "hint": "Expected angle as a quantity.", "input_type": "code", "default_value": "qty(30,'deg')", "evaluate": true}, {"name": "unit_penalty", "label": "Unit penalty", "help_url": "", "hint": "Penalty for not including degree sign or 'deg'.", "input_type": "percent", "default_value": "20"}, {"name": "close_penalty", "label": "Close Penalty", "help_url": "", "hint": "Penalty for close answer.", "input_type": "percent", "default_value": "20"}, {"name": "close_tol", "label": "Close", "help_url": "", "hint": "Angle must be $\\pm$ this many degrees to be marked close.   ", "input_type": "code", "default_value": "0.5", "evaluate": false}, {"name": "right_tol", "label": "Right ", "help_url": "", "hint": "Angle must be $\\pm$ this many degrees to be marked correct.  ", "input_type": "code", "default_value": "0.1", "evaluate": false}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "

A value with units marked right if within an adjustable % error of the correct value.  Marked close if within a wider margin of error.

Modify the unit portion of the student's answer by

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1. replacing \"ohms\" with \"ohm\"  case insensitive

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2. replacing '-' with ' '

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3. replacing '°' with ' deg'

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to allow answers like 10 ft-lb and 30°

", "definition": "replace_regex('ohms','ohm',\n replace_regex('\u00b0', ' deg',\n replace_regex('-', ' ' ,\n studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "

This fixes the student answer for two common errors.

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If student_units are wrong  - replace with correct units

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If student_scalar has the wrong sign - replace with right sign

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If student makes both errors, only one gets fixed.

", "definition": "switch(not good_units, \n student_scalar * correct_units, \n not right_sign,\n -quantity(student_scalar, student_units),\n quantity(student_scalar,student_units)\n)\n \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "

Only marked close if the student actually has the right sign.

", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units.  if correct answer is 100 N and close is ±1%,
99  N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.
If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.
This value would be close if the expected units were provided.  If the correct answer is 100 N, and close is ±1%,
99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Equilibrium of a particle: four forces", "tags": ["angle from reference", "Equlibrium", "Mechanics", "mechanics", "Particle Equilbrium", "Statics", "statics"], "metadata": {"description": "

Three random forces act on a particle.  Determine the force required for equilibirum.

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

{applet} {alpha} {beta} {gamma}

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Four forces with magnitudes $A$ = {qty(maga,units)}, $B$ = {qty(magb,units)}, and $C$ = {qty(magC,units)}, act on a particle in the directions shown.

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Determine the magnitude and direction of force $\\mathbf{D}$ required for equilibrium.

Begin by drawing a free body diagram of the particle. Since the direction of force $\\mathbf{D}$ is unknown you will have to make an assumption about which way it points.

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Set up and solve the equilibrium equations based on your assumed direction for $\\mathbf{D}$

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\\begin{align} \\Sigma F_x &= 0\\\\ A_x + B_x + C_x + D_x &= 0\\\\ \\simplify[!collectNumbers]{{enground(A[0])} + {enground(B[0])} + {enground(C[0])} - D_x} &= 0 \\\\ D_x &= \\var{qty(enground(A[0] +B[0] +C[0]),units)}&(1)\\\\\\\\ \\Sigma F_y &= 0\\\\ A_y + B_y + C_y + D_y &= 0\\\\ \\simplify[!collectNumbers]{{enground(A[1])} + {enground(B[1])} + {enground(C[1])} + D_y } &= 0\\\\ D_y &= \\var{qty(- enground(A[1] +B[1] +C[1]),units)} & (2) \\end{align}

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If your calculations result in a negative value for $D_x$ or $D_y$, then your assumed direction is opposite of the component's actual direction.

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Draw a sketch showing $D_x$, $D_y$, and $D$ pointing in their actual directions and define angle $\\theta$.

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Resolve the components using right triangle trigonometry to find $D$ and $\\theta$.

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$D = \\var{enground(abs(D))}$ {units},

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$\\theta = \\var{siground(theta,4)}$° measured counterclockwise from the $x$-axis.

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Your value of $\\theta$ will depend on the reference angle you choose. Choose one that makes $\\theta$ less than 90° to avoid sign errors.

$D$ = [[3]]  ({siground(magd,4)}) acting at  [[0]] measured [[1]] from the [[2]]. ({siground(theta,4)}°)