// Numbas version: finer_feedback_settings {"name": "Equilibrium of a particle: hanging weight", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 24, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/24/edit"}, "name": "Angle quantity", "short_name": "angle-quantity-from-reference", "description": "
Angle as a quantity in degrees.
", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['correct_quantity'])", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\ncorrect_scalar:\nscalar(correct_quantity)\n \n\ncorrect_quantity:\nsettings['correct_quantity']\n\ncorrect_units:\nunits(correct_quantity)\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\njoin(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n\n\ngood_units:\ntry(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)\n\nstudent_quantity:\nswitch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)\n\nangle_in_range:\nif(settings['restrict_angle'], abs(student_scalar) <= 90, true)\n\nright:\nwithinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])\n\nclose:\nwithinTolerance(student_scalar, correct_scalar, settings['close'])", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)"}, {"name": "correct_scalar", "description": "", "definition": "scalar(correct_quantity)\n "}, {"name": "correct_quantity", "description": "", "definition": "settings['correct_quantity']"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "", "definition": "join(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n"}, {"name": "good_units", "description": "", "definition": "try(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)"}, {"name": "student_quantity", "description": "", "definition": "switch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity)"}, {"name": "angle_in_range", "description": "", "definition": "if(settings['restrict_angle'], abs(student_scalar) <= 90, true)"}, {"name": "right", "description": "Will check for correct sign elswhere.
", "definition": "withinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])"}, {"name": "close", "description": "Must have correct sign to be close.
", "definition": "withinTolerance(student_scalar, correct_scalar, settings['close'])\n"}], "settings": [{"name": "correct_quantity", "label": "Correct Angle as quantity ", "help_url": "", "hint": "", "input_type": "code", "default_value": "qty(45,'deg')", "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 amount from the correct value.", "input_type": "code", "default_value": "0.1", "evaluate": true}, {"name": "restrict_angle", "label": "Less than 90\u00b0", "help_url": "", "hint": "When checked, angle must be between -90° and +90°.", "input_type": "checkbox", "default_value": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units.", "input_type": "percent", "default_value": "75"}, {"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 amount from the correct value.", "input_type": "code", "default_value": "0.5", "evaluate": true}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value without units.", "input_type": "percent", "default_value": "25"}], "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.
", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n right and good_units and right_sign, add_credit(1.0,'Correct.'),\n right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n close and good_units, add_credit(settings['C1'],'Close.'),\n close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n replace_regex('\u00b0', ' deg',\n replace_regex('-', ' ' ,\n studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(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\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n right and good_units and right_sign, add_credit(1.0,'Correct.'),\n right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n close and good_units, add_credit(settings['C1'],'Close.'),\n close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto 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.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf 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%,The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.
", "help_url": "", "input_widget": "radios", "input_options": {"correctAnswer": "if(eval(settings[\"correct_answer_expr\"]), 0, 1)", "hint": {"static": true, "value": ""}, "choices": {"static": true, "value": ["Yes", "No"]}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nif(studentanswer=correct_answer,\n correct(),\n incorrect()\n)\n\ninterpreted_answer:\nstudentAnswer=0\n\ncorrect_answer:\nif(eval(settings[\"correct_answer_expr\"]),0,1)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "if(studentanswer=correct_answer,\n correct(),\n incorrect()\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "studentAnswer=0"}, {"name": "correct_answer", "description": "", "definition": "if(eval(settings[\"correct_answer_expr\"]),0,1)"}], "settings": [{"name": "correct_answer_expr", "label": "Is the answer \"Yes\"?", "help_url": "", "hint": "An expression which evaluates totrue
or false
.", "input_type": "mathematical_expression", "default_value": "true", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Equilibrium of a particle: hanging weight", "tags": ["Mechanics, statics, equilibrium, particle equilibrium, 2-d, tension"], "metadata": {"description": "Find the tensions in two ropes supporting a weight.
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "Equilibrium of a particle: $\\Sigma \\mathbf{F} = 0 \\therefore \\Sigma F_x = 0 \\text{ and } \\Sigma F_y =0$
\n{geogebra_applet('GbauxKWS',params)}
\nFind the tensions in the two cables when they are supporting a {qty(W,units[0])} load.
\n$h = \\var{qty(h,units[1])}, d_1 = \\var{qty(d_1,units[1])}, \\text{ and } d_2 = \\var{qty(d_2,units[1])}$.
\n", "advice": "Draw a free body diagram of the particle. Apply the equations of equilibrium to get\\[\\Sigma F_x\\!:\\ AC_x = BC_x \\qquad \\Sigma F_y\\!: \\ AC_y + BC_y =W\\]
\nExpress the components in terms of the magnitudes $AB$ and $BC$ and directions $\\alpha$ and $\\beta$, then solve the two equations simultaneously for the unknown tensions.
", "rulesets": {}, "extensions": ["geogebra", "quantities"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"load": {"name": "load", "group": "results", "definition": "if(units[0]='kg',W 9.81, W)", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "results", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Inputs", "definition": "random(3..6#0.5)", "description": "", "templateType": "anything", "can_override": false}, "d_1": {"name": "d_1", "group": "Inputs", "definition": "random(2..5#0.25)", "description": "Horizontal location of point C.
", "templateType": "anything", "can_override": false}, "Q_ac": {"name": "Q_ac", "group": "answer", "definition": "let(unit,if(units[0]='kg','N',units[0]),qty(AC,unit))", "description": "", "templateType": "anything", "can_override": false}, "d_2": {"name": "d_2", "group": "Inputs", "definition": "random(2..5#0.25)", "description": "", "templateType": "anything", "can_override": false}, "BC": {"name": "BC", "group": "results", "definition": "load cos(radians(alpha))/sin(radians(alpha+beta))", "description": "Tension in cable BC
", "templateType": "anything", "can_override": false}, "Q_bc": {"name": "Q_bc", "group": "answer", "definition": "let(unit,if(units[0]='kg','N',units[0]),qty(BC,unit))", "description": "", "templateType": "anything", "can_override": false}, "beta": {"name": "beta", "group": "results", "definition": "degrees(arctan(h/d_2))", "description": "", "templateType": "anything", "can_override": false}, "W": {"name": "W", "group": "Inputs", "definition": "random([10,20,25,40,50,75,100,120,150])", "description": "anans
", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Inputs", "definition": "random(['lb','ft'], ['N','m'], ['kN','m'], ['kg','m'] )", "description": "", "templateType": "anything", "can_override": false}, "AC": {"name": "AC", "group": "results", "definition": "load cos(radians(beta))/sin(radians(alpha+beta))", "description": "", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "results", "definition": "degrees(arctan(h/d_1))", "description": "", "templateType": "anything", "can_override": false}, "params": {"name": "params", "group": "Ungrouped variables", "definition": "[d_1: d_1, d_2: d_2, h: h]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["params"], "variable_groups": [{"name": "Inputs", "variables": ["W", "d_1", "d_2", "h", "units"]}, {"name": "results", "variables": ["alpha", "beta", "load", "BC", "AC", "debug"]}, {"name": "answer", "variables": ["Q_bc", "Q_ac"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Question 1", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Pick the correct statement:
\n[[0]]
", "gaps": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["The tension in $AC$ is greater than the tension in $BC$.", "The tension in $BC$ is greater than the tension in $AC$.", "Both tensions are the same and equal the weight $W$.", "Both tensions are the same and equal half the weight $W$.", "Both tensions are the same and greater than the weight $W$.", "Both tensions are the same and less than the weight $W$."], "matrix": ["award(4,alpha>beta)", "award(4,alphaDo you need to calculate the lengths of the cables to solve this problem?
", "settings": {"correct_answer_expr": "false"}}, {"type": "yes-no", "useCustomName": true, "customName": "Question 3", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [{"variables": [{"name": "BC", "value": "304.0454111793"}, {"name": "d_2", "value": "4.25"}, {"name": "beta", "value": "30.4655449195"}, {"name": "correct_units", "value": "\"N\""}, {"name": "AC", "value": "354.1734692843"}, {"name": "d_1", "value": "2.75"}, {"name": "W", "value": "40"}, {"name": "h", "value": "2.5"}, {"name": "units", "value": "[ \"kg\", \"m\" ]"}, {"name": "alpha", "value": "42.2736890061"}, {"name": "load", "value": "392.4"}], "name": "student says kg is not a force", "answer": {"empty": false, "value": 1, "valid": true}, "notes": [{"name": "mark", "expected": {"value": "true", "messages": ["Your answer is correct.\n\nYou were awarded 1 mark."], "warnings": [], "error": "", "valid": true, "credit": 1}}, {"name": "correct_answer", "expected": {"value": "1", "messages": [], "warnings": [], "error": "", "valid": true, "credit": 0}}]}, {"variables": [{"name": "BC", "value": "304.0454111793"}, {"name": "d_2", "value": "4.25"}, {"name": "beta", "value": "30.4655449195"}, {"name": "correct_units", "value": "\"N\""}, {"name": "AC", "value": "354.1734692843"}, {"name": "d_1", "value": "2.75"}, {"name": "W", "value": "40"}, {"name": "h", "value": "2.5"}, {"name": "units", "value": "[ \"kg\", \"m\" ]"}, {"name": "alpha", "value": "42.2736890061"}, {"name": "load", "value": "392.4"}], "name": "student says kg is a force", "answer": {"empty": false, "value": 0, "valid": true}, "notes": [{"name": "mark", "expected": {"value": "false", "messages": ["Your answer is incorrect."], "warnings": [], "error": "", "valid": true, "credit": 0}}, {"name": "interpreted_answer", "expected": {"value": "true", "messages": [], "warnings": [], "error": "", "valid": true, "credit": 0}}]}, {"variables": [{"name": "BC", "value": "90.9068004018"}, {"name": "d_2", "value": "3.25"}, {"name": "beta", "value": "24.7751405688"}, {"name": "correct_units", "value": "\"N\""}, {"name": "AC", "value": "103.1746031746"}, {"name": "d_1", "value": "2"}, {"name": "W", "value": "100"}, {"name": "h", "value": "1.5"}, {"name": "units", "value": "[ \"N\", \"m\" ]"}, {"name": "alpha", "value": "36.8698976458"}, {"name": "load", "value": "100"}], "name": "student says N is a force", "answer": {"empty": false, "value": 0, "valid": true}, "notes": [{"name": "mark", "expected": {"value": "true", "messages": ["Your answer is correct.\n\nYou were awarded 1 mark."], "warnings": [], "error": "", "valid": true, "credit": 1}}]}, {"variables": [{"name": "BC", "value": "90.9068004018"}, {"name": "d_2", "value": "3.25"}, {"name": "beta", "value": "24.7751405688"}, {"name": "correct_units", "value": "\"N\""}, {"name": "AC", "value": "103.1746031746"}, {"name": "d_1", "value": "2"}, {"name": "W", "value": "100"}, {"name": "h", "value": "1.5"}, {"name": "units", "value": "[ \"N\", \"m\" ]"}, {"name": "alpha", "value": "36.8698976458"}, {"name": "load", "value": "100"}], "name": "student says N is not a force", "answer": {"empty": false, "value": 1, "valid": true}, "notes": [{"name": "mark", "expected": {"value": "false", "messages": ["Your answer is incorrect."], "warnings": [], "error": "", "valid": true, "credit": 0}}]}], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Is the load a force?
", "settings": {"correct_answer_expr": " not(units[0] = 'kg')"}}, {"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Find the necessary angles:
\n$\\alpha$ = [[0]] $\\beta$ = [[1]]
", "gaps": [{"type": "angle-quantity-from-reference", "useCustomName": true, "customName": "alpha", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correct_quantity": "qty(round(alpha*100)/100,'deg')", "right": "0.2", "restrict_angle": true, "C1": "75", "close": "1.01", "C2": "50", "C3": "25"}}, {"type": "angle-quantity-from-reference", "useCustomName": true, "customName": "beta", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correct_quantity": "qty(round(beta*100)/100 ,'deg')", "right": "0.2", "restrict_angle": true, "C1": "75", "close": "1.01", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Magnitudes", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Substitute the known weight and angles $\\alpha$ and $\\beta$ into your equations, then solve them simultaneously to find the tensions in cables $AC$ and $BC$
\n$AC$ = [[0]] {q_ac} $BC $= [[1]] {q_bc}
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