// Numbas version: exam_results_page_options {"name": "Resultant of a force-couple system", "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°

numeric part of students answer, which is a quantity.

", "definition": "matchnumber(studentAnswer,['plain','en'])[1]"}], "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.

Does clumsy substitution to

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1. replace '-' with ' '

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2. replace '°' with ' deg'

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to allow answers like 10 ft-lb and 30°

", "name": "student_units"}, {"definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n", "description": "", "name": "good_units"}, {"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", "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.

", "name": "student_quantity"}, {"definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n ", "description": "", "name": "percent_error"}, {"definition": "percent_error <= settings['right']\n", "description": "", "name": "right"}, {"definition": "right_sign and percent_error <= settings['close']", "description": "

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

", "name": "close"}, {"definition": "sign(student_scalar) = sign(correct_quantity) ", "description": "", "name": "right_sign"}], "settings": [{"input_type": "code", "evaluate": true, "hint": "The correct answer given as a JME quantity.", "default_value": "", "label": "Correct Quantity.", "help_url": "", "name": "correctAnswer"}, {"input_type": "code", "evaluate": true, "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "default_value": "0.2", "label": "% Accuracy for right.", "help_url": "", "name": "right"}, {"input_type": "code", "evaluate": true, "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "default_value": "1.0", "label": "% Accuracy for close.", "help_url": "", "name": "close"}, {"input_type": "percent", "hint": "Partial Credit for close value with appropriate units.  if correct answer is 100 N and close is ±1%,
99  N is accepted.", "default_value": "75", "label": "Close with units.", "help_url": "", "name": "C1"}, {"input_type": "percent", "hint": "Partial credit for forgetting units or using wrong sign.
If the correct answer is 100 N, both 100 and -100 N are accepted.", "default_value": "50", "label": "No units or wrong sign", "help_url": "", "name": "C2"}, {"input_type": "percent", "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.", "default_value": "25", "label": "Close, no units.", "help_url": "", "name": "C3"}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Resultant of a force-couple system", "tags": [], "metadata": {"description": "

Determine the single force which is equivalent to a force and a couple.

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

{geogebra_applet('xfrg2ewr',[['F', scalar(F) ],['M',scalar(M)],['α',alpha+'°'],['unitsF','\"'+units[0]+'\"' ],['unitsD','\"'+units[1]+'\"' ]])}

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Replace the force-couple system acting at the origin with a single force which has the same effect.  Specify the magnitude and direction of the resultant force and the coordinate $x_A$ $y_A$ of the point on the x y-axis through which the line of action of this force passes.

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F: {F} Fx: {Fx} Fy: {Fy}

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M:  {M} $x_A$: {dx} $y_A$: {dy}

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The equivalent force has the same magnitude and direction as the original force, but its line of action must be changed in such a way as to produce the same moment about A with the same direction as the original moment M.  You may move the force horizontally to $x_A$ where $F_y x_A = M$ or vertically to $y_A$ where $F_y y_A = M$.

", "rulesets": {}, "extensions": ["geogebra", "quantities"], "variables": {"dy": {"name": "dy", "group": "Ungrouped variables", "definition": "siground(-1*M/Fx,3)", "description": "", "templateType": "anything"}, "version": {"name": "version", "group": "Ungrouped variables", "definition": "random(0..1)", "description": "", "templateType": "anything"}, "dx": {"name": "dx", "group": "Ungrouped variables", "definition": "siground(M/Fy,3)", "description": "", "templateType": "anything"}, "F": {"name": "F", "group": "Ungrouped variables", "definition": "quantity(random(1,2,3,4,5)*random(10,20,30,50),units[0])", "description": "", "templateType": "anything"}, "M": {"name": "M", "group": "Ungrouped variables", "definition": "Quantity(scalar(F)random(-1,1)random(1..6#0.1),units[0]+ \" \" +units[1])", "description": "

The moment.  Counterclockwise is positive

", "templateType": "anything"}, "Fx": {"name": "Fx", "group": "Ungrouped variables", "definition": "F * cos(radians(alpha))", "description": "", "templateType": "anything"}, "Fy": {"name": "Fy", "group": "Ungrouped variables", "definition": "F * sin(radians(alpha))", "description": "", "templateType": "anything"}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "random(['N','m'],['lb','in'],['lb','ft'])", "description": "", "templateType": "anything"}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything"}, "alpha": {"name": "alpha", "group": "Ungrouped variables", "definition": "random(0..360#10 except[0,90,180,270,360])", "description": "

the direction of the force

$F$ = [[3]] acting at an angle of [[0]] measured [[1]] from the [[2]],
and passing through the x-axis y-axis at $x_A$  $y_A$ = [[4]].