// Numbas version: exam_results_page_options {"name": "Machine: lopping shears", "extensions": ["geogebra", "weh", "quantities"], "custom_part_types": [{"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

\n

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

\n

2. replacing '-' with ' ' 

\n

3. replacing '°' with ' deg' 

\n

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.  

\n

If student_units are wrong  - replace with correct units

\n

If student_scalar has the wrong sign - replace with right sign

\n

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/shearFBD.png", "/srv/numbas/media/question-resources/shearFBD.png"], ["question-resources/shearFBD.gif", "/srv/numbas/media/question-resources/shearFBD.gif"], ["question-resources/shear.gif", "/srv/numbas/media/question-resources/shear.gif"], ["question-resources/shearFBD_XWaIQSM.png", "/srv/numbas/media/question-resources/shearFBD_XWaIQSM.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Machine: lopping shears", "tags": ["machine", "Mechanics", "mechanics", "rigid body equilibrium", "Rigid body equilibrium", "Statics", "statics"], "metadata": {"description": "

Determine the mechanical advantage of a pair of compound lopping shears.

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

{geogebra_applet('csq3j7yg', {map(dist(n),n,1..9)} )}

\n

Determine

\n

a) the mechanical advantage of the lopping shears shown, and 

\n

b) the {statement[version]}.

\n

Note: The mechanical advantage of the shears is the ratio of the cutting force developed at $A$ to the force $P$ applied to the handles.

\n

", "advice": "

1. Draw and number a neat, consistent, labeled set of free body diagrams for the parts of the shears.

\n

Note link DE is a two force member with a slope of $m = \\dfrac{\\var{d_7}} {\\var{d_9 - d_4}}$, in tension.  The free body diagrams must be consistent with each other and internal forces must occur in action-reaction pairs.

\n

\n

\n

2. Find the necessary angle.

\n

Let $\\theta$ be the angle that DE makes with the horizontal.

\n

$\\theta = \\tan^{-1} \\dfrac{\\var{d_7}}{\\var{d_9-d_4}} = \\var{siground(theta,4)}°$

\n

3. Use FBD II  and take moments about C to find the tension in DE.

\n

$\\begin{align}\\textrm{II: }\\Sigma M_C &= 0 \\\\ DE_x (\\var{d_6}) + DE_y(\\var{d_3}) &= P \\,(\\var{d_3 + d_4 })\\\\ DE &= \\left ( \\dfrac{\\var{scalar(d_3 + d_4 )}}{\\var{scalar(d_6)} \\cos \\theta + \\var{scalar(d_3)}\\sin \\theta} \\right)  P  \\\\&= \\left(\\dfrac{\\var{d_3 + d_4 }}{\\var{siground(dp_1,4)}} \\right )P \\\\&= \\var{siground(ma_1,4)} \\,P \\textrm{ (tension) } \\end{align}$

\n

4. FBD III and take moments about B to find the cutting force at A.

\n

$\\begin{align}\\textrm{III: }\\Sigma M_B &= 0 \\\\ A (\\var{d_1}) &=DE_x (\\var{d_5 +d_6 +d_7 }) + DE_y(\\var{d_8-d_1}) \\\\ A &= \\left ( \\dfrac{\\var{scalar(d_5 +d_6 +d_7 )}\\cos \\theta + \\var{scalar(d_8-d_1)}\\sin \\theta}{\\var{scalar(d_1 )}} \\right) DE \\\\&= \\left(\\dfrac{\\var{siground(dp_2,4)}}{\\var{d_1 }} \\right )DE \\\\&= \\var{siground(ma_2,4)} \\,DE \\\\ &= \\var{siground(ma_2,4)}\\, ( \\var{siground(ma_1,4)} \\,P )\\\\ &= \\var{siground(ma_t,4)} P \\end{align}$

\n

5.  Find the mechanical advantage

\n

Mechanical Advantage =  $\\dfrac{A}{P} = \\var{siground(ma_t,4)}$

\n

6. Find the {statement[version]}.

\n

$A = \\var{siground(ma_t,4)} P$, so for $A$ $P$ = {given[version]}:

\n

\n

$A = \\var{siground(ma_t,4)} (\\var{given[0]}) = \\var{siground(answer[0],4)}$

\n

$P = \\dfrac{\\var{given[1]}}{\\var{siground(ma_t,4)}} = \\var{siground(answer[1],4)}$

", "rulesets": {}, "extensions": ["geogebra", "quantities", "weh"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"units": {"name": "units", "group": "Ungrouped variables", "definition": "random(['N','mm', \"10 mm\", \"1 mm\" ],['lb','in', \"0.1 in\", \"0.1 in\"])", "description": "

units[2] large rounding base

\n

units[3] small rounding base

", "templateType": "anything", "can_override": false}, "d_6": {"name": "d_6", "group": "Ungrouped variables", "definition": "round((2.59 / 24.4 L random(0.9..1.1#0.05)),units[3])", "description": "", "templateType": "anything", "can_override": false}, "ma_2": {"name": "ma_2", "group": "Unnamed group", "definition": "scalar(dp_2)/scalar(d_1)", "description": "

mechanical advantage 2

", "templateType": "anything", "can_override": false}, "Statement": {"name": "Statement", "group": "Unnamed group", "definition": "[\"shearing force created at A when a \" + \n given[0] + \" force is applied to the handles at P\", \n 'force P that must be applied to the handles in order to create a '\n + given[1] + ' shearing force at A']", "description": "", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "Unnamed group", "definition": "degrees(atan2(scalar(d_7),scalar(d_9-d_4)))", "description": "", "templateType": "anything", "can_override": false}, "d_9": {"name": "d_9", "group": "Ungrouped variables", "definition": "d_4+ round((0.4 / 24.4 L random(0.9..1.1#0.05)),units[3])", "description": "", "templateType": "anything", "can_override": false}, "dp_1": {"name": "dp_1", "group": "Unnamed group", "definition": "(d_6 cos(radians(theta)) + d_3 sin(radians(theta)))", "description": "

perpendicular distance from DE to C

", "templateType": "anything", "can_override": false}, "d_7": {"name": "d_7", "group": "Ungrouped variables", "definition": "round((1.3 / 24.4 L random(0.9..1.1#0.05)),units[3])", "description": "", "templateType": "anything", "can_override": false}, "ma_1": {"name": "ma_1", "group": "Unnamed group", "definition": "scalar(d_3 + d_4 )/scalar(dp_1)", "description": "

mechanical advantage 1

", "templateType": "anything", "can_override": false}, "d_5": {"name": "d_5", "group": "Ungrouped variables", "definition": "round((0.47 / 24.4 L random(0.9..1.1#0.05)),units[3])", "description": "", "templateType": "anything", "can_override": false}, "d_1": {"name": "d_1", "group": "Ungrouped variables", "definition": "round((4.1 / 24.4 L random(0.9..1.1#0.05)),units[2])", "description": "", "templateType": "anything", "can_override": false}, "d_3": {"name": "d_3", "group": "Ungrouped variables", "definition": "round((5.2 / 24.4 L random(0.9..1.1#0.05)),units[2])", "description": "", "templateType": "anything", "can_override": false}, "dp_2": {"name": "dp_2", "group": "Unnamed group", "definition": "(d_5 + d_6 +d_7 ) cos(radians(theta)) + (d_8-d_1) sin(radians(theta))", "description": "

perpendicular distance from DE to B

", "templateType": "anything", "can_override": false}, "version": {"name": "version", "group": "Unnamed group", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "L": {"name": "L", "group": "Ungrouped variables", "definition": "round(qty(random(24..36#2),'in') in units[1],units[2])", "description": "", "templateType": "anything", "can_override": false}, "d_8": {"name": "d_8", "group": "Ungrouped variables", "definition": "L-d_9", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Unnamed group", "definition": "[given[0] * ma_t, given[1] / ma_t]", "description": "", "templateType": "anything", "can_override": false}, "d_2": {"name": "d_2", "group": "Ungrouped variables", "definition": "round((3 / 24.4 L random(0.9..1.1#0.05)),units[2])", "description": "", "templateType": "anything", "can_override": false}, "ma_t": {"name": "ma_t", "group": "Unnamed group", "definition": "ma_1 * ma_2", "description": "

total mechanical advantage

", "templateType": "anything", "can_override": false}, "d_4": {"name": "d_4", "group": "Ungrouped variables", "definition": "L - (d_1 + d_2 + d_3)", "description": "", "templateType": "anything", "can_override": false}, "given": {"name": "given", "group": "Unnamed group", "definition": "[qty(random(10..40#5),units[0]),qty(random(50..200#10),units[0])]", "description": "

]]

", "templateType": "anything", "can_override": false}, "test": {"name": "test", "group": "Ungrouped variables", "definition": "dist(1)[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["units", "L", "d_1", "d_2", "d_3", "d_4", "d_5", "d_6", "d_7", "d_8", "d_9", "test"], "variable_groups": [{"name": "Unnamed group", "variables": ["theta", "dp_1", "ma_1", "dp_2", "ma_2", "ma_t", "version", "given", "Statement", "answer"]}], "functions": {"dist": {"parameters": [["ix", "number"]], "type": "list", "language": "jme", "definition": "let(n,ix,['d_' + n,'\\\"$'+ scalar(precround(eval(expression('d_' + n)),2))+ ' \\\\textrm{ ' + units[1] +'}$'+ '\\\"'])"}, "ggbtex": {"parameters": [["q", "quantity"]], "type": "string", "language": "jme", "definition": ""}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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": "

Mechanical advantage = [[0]]    $\\var{if(version=0,latex('A'),latex('P'))}$ = [[1]] 

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "Advantage", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(MA_t,\"\")", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Force", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "answer[version]", "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/"}]}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}