// Numbas version: finer_feedback_settings {"name": "Equilibrium of a particle: Block on Incline", "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.

Accepts '°' and 'deg' as units.

Penalizes if not close enough or no units.

90° = -270° = 450°

", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['expected_answer']) ", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "original_student_scalar:\nmatchnumber(studentAnswer,['plain','en'])[1]\n\nstudent_scalar:\nmod(original_student_scalar,360)\n\n\nstudent_unit:\nstudentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]\n\ninterpreted_unit:\nif(trim(student_unit)='\u00b0','deg',student_unit)\n\ninterpreted_answer:\nqty(mod(student_scalar,360),'deg')\n\nclose:\nwithintolerance(student_scalar, correct_scalar,decimal(settings['close_tol']))\n\ncorrect_scalar:\nmod(scalar(settings['expected_answer']),360)\n\nright:\nwithintolerance(student_scalar, correct_scalar, decimal(settings['right_tol']))\n\ngood_unit:\nsame(qty(1,interpreted_unit),qty(1,'deg'))\n\nmark:\nassert(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.'))", "marking_notes": [{"name": "original_student_scalar", "description": "

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": "

matchnumber(studentAnswer,['plain','en'])[0] is a string \"12.34\"

", "definition": "studentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]"}, {"name": "interpreted_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": "

Normalize expected_answer with mod 360

", "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.

", "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\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)"}, {"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

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

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.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

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": [["question-resources/soln.jpg", "soln.jpg"], ["question-resources/fbdb.png", "fbdb.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Equilibrium of a particle: Block on Incline", "tags": [], "metadata": {"description": "

Equilibrium of a particle, solution by rotating coordinate system.

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

A {qty(b, unitD)} $ \\times$ {qty(h, unitD)} block weighing {qty(W, unitF)} rests on a frictionless, inclined plane as shown. Determine force $\\mathbf{F}$ required to hold the block in equilibrium.

\n\n\n\n\n\n\n

{applet}

", "advice": "

Given:

$W = \\var{siground(qty(W,unitF),4)}, \\theta = \\var{theta}^\\circ$

Box: $b = \\var{qty(b,unitD)}, h = \\var{qty(h,unitD)}$

{geogebra_applet('jytha83z',params)}

Angle of force relative to plane:

$\\tan\\phi = \\frac{\\var{h}}{\\var{b}} ;\\Rightarrow; \\phi = \\var{precround(phi,1)}^\\circ$

For simplicity, we can choose a coordinate system parallel and perpendicular to the plane.

Force components along plane:

$W_{\\parallel} = W \\sin\\theta, \\quad F_{\\parallel} = F\\cos\\phi$

Equilibrium along incline:

$\\sum F_{\\parallel} = 0:\\quad F\\cos\\phi = W\\sin \\theta$

Solve:

$F = \\dfrac{\\var{W}\\sin(\\var{precround(theta,1)}^\\circ)}{\\cos(\\var{precround(phi,1)}^\\circ)} = \\var{siground(F,4)}$

Direction of $P$ from horizontal:

$\\theta_P = \\theta + \\phi = \\var{theta}^\\circ + \\var{precround(phi,1)}^\\circ = \\var{precround(theta+phi,1)}^\\circ$ CW from the -$x$ axis.

", "rulesets": {}, "extensions": ["geogebra", "quantities"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "random(h..4.5#0.5)", "description": "

width of box

", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(1.5..3#0.5)", "description": "

height of box

", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "Ungrouped variables", "definition": "random(12..36#2)", "description": "", "templateType": "anything", "can_override": false}, "params": {"name": "params", "group": "Ungrouped variables", "definition": "[b: b, h: h, theta: theta + \"\u00b0\"]", "description": "", "templateType": "anything", "can_override": false}, "applet": {"name": "applet", "group": "Ungrouped variables", "definition": "geogebra_applet('xcpghxt9', params)", "description": "", "templateType": "anything", "can_override": false}, "phi": {"name": "phi", "group": "Ungrouped variables", "definition": "degrees(arctan(h/b))", "description": "

angle from incline to force

", "templateType": "anything", "can_override": false}, "W": {"name": "W", "group": "Ungrouped variables", "definition": "random(20..100#5)", "description": "", "templateType": "anything", "can_override": false}, "F": {"name": "F", "group": "Ungrouped variables", "definition": "qty(w sin(radians(theta))/sin(radians(90+phi)),unitF)", "description": "

Magnitude of f

", "templateType": "anything", "can_override": false}, "unitf": {"name": "unitf", "group": "Ungrouped variables", "definition": "\"lb\"", "description": "", "templateType": "anything", "can_override": false}, "unitd": {"name": "unitd", "group": "Ungrouped variables", "definition": "\"ft\"", "description": "", "templateType": "anything", "can_override": false}, "DirF": {"name": "DirF", "group": "Ungrouped variables", "definition": "180-theta-phi", "description": "

direction of F from positive x-axis

", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "theta + phi <75 and b<> h", "maxRuns": 100}, "ungrouped_variables": ["b", "h", "theta", "params", "applet", "phi", "W", "F", "unitf", "unitd", "DirF", "debug"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "\ntarget_angle (the correct angle):\n mod(scalar(gaps[0][\"settings\"][\"correctAnswer\"]),360)\n\nreference (student choice of reference axis: 0,90,180,-90 ):\n answers[2]\n\nsign (student choice of directions: 1, -1):\n answers[1]\n\nstudent_angle (student input as as standard angle):\n reference + sign * scalar(answers[0])\n\nstudent_units:\n trim(studentAnswer[0][len(matchnumber(studentAnswer[0],['plain','en'])[0])..len(studentAnswer[0])])\n\n\ninterpreted_answer (student angle from his reference) :\n scalar(answers[0]) + \"\u00b0 \" + \n switch(sign=1,\"CCW\",sign=-1,\"CW\") + \n \" from the \" + switch(reference=0,\"+x\",reference=90,\"+y\",reference=180,\"-x\",reference=-90,\"-y\")+ \" axis.\"\n\ncorrect_angle (using student's reference):\n mod(precround((target_angle-reference)/sign,2),360) + \"\u00b0 \" + \n switch(sign=1,\"CCW\",sign=-1,\"CW\") + \n \" from the \" + switch(reference=0,\"+x\",reference=90,\"+y\",reference=180,\"-x\",reference=-90,\"-y\")+ \" axis.\"\n\ngood_angle:\n resultsequal(cos(radians(student_angle)),cos(radians(target_angle)),\"absdiff\", radians(0.1)) and\n resultsequal(sin(radians(student_angle)),sin(radians(target_angle)),\"absdiff\", radians(0.1))\n\ngood_units:\n if(student_units = \"deg\" or student_units=\"\u00b0\",\"\", sub_credit(0.1,\"Wrong units.\"))\n\nmark:\n if(good_angle,correct(),incorrect();feedback(\"Correct Answer: \" + correct_angle));\n apply(good_units)\n\n \n \n", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

$\\mathbf{F} = $ [[3]] at [[0]] measured [[1]] from the [[2]]

{siground(F,4)} at {precround(dirF,1)}

", "gaps": [{"type": "angle", "useCustomName": true, "customName": "angle", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "qty(precround(dirF,1),'deg')", "unit_penalty": "50", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.1"}}, {"type": "1_n_2", "useCustomName": true, "customName": "dir", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "interpreted_answer:\n [1,-1][indices( studentAnswer,[true])[0]]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showBlankOption": false, "showCellAnswerState": true, "choices": ["CCW", "CW"], "matrix": [0, 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Ref", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "interpreted_answer:\n [0,90,180,-90][indices(studentAnswer,[true])[0]]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showBlankOption": true, "showCellAnswerState": true, "choices": ["+x axis", "+y axis", "-x axis", "-y axis"], "matrix": [0, 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "engineering-answer", "useCustomName": true, "customName": "magnitude", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "siground(F,4)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "resources": ["question-resources/soln.jpg", "question-resources/fbdb.png"]}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}