// Numbas version: exam_results_page_options {"name": "Machine: excavator", "extensions": ["geogebra", "quantities", "visjs", "weh"], "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.

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": [["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"], ["question-resources/FBD.png", "/srv/numbas/media/question-resources/FBD.png"], ["question-resources/FBD_UvxNguf.png", "/srv/numbas/media/question-resources/FBD_UvxNguf.png"], ["question-resources/FBD_ZA7RKPO.png", "/srv/numbas/media/question-resources/FBD_ZA7RKPO.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "

Draw and number neat, labeled free body diagrams.

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Given: $W$ = {load}

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Find the necessarys angles.

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Let $\\theta_B$  and $\\theta_D$ be the angles that BC  and DE make with the horizontal.

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$\\theta_B = \\tan^{-1} \\left(\\dfrac{\\var{y1+y2}}{\\var{x2}}\\right) = \\var{siground(theta_B,4)}° \\qquad \\theta_D = \\left(\\tan^{-1} \\dfrac{\\var{y4}}{\\var{x4}} \\right)= \\var{siground(theta_D,4)}°$

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Use Free Body Diagram I to solve for the force in cylinder $BC$.

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\\begin{align} \\textrm{I: } \\Sigma M_B &= 0 \\\\ BC_x ( \\var{y2}) - BC_y(\\var{x2}) + W ( \\var{x_t}) &= 0\\\\ BC ( -\\var{scalar(y2)} \\cos \\theta_B + \\var{scalar(x2)} \\sin \\theta_B) &= \\var{scalar(x_t)} W \\\\ BC &= W \\left(\\dfrac{\\var{x_t}}{\\var{siground(dperp_B,4)}}\\right) \\\\ &= \\var{siground(BC,4)} \\textrm{ (compression)} \\end{align}

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Use Free Body Diagram II to solve for the force in cylinder $DE$.

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\\begin{align} \\textrm{II: } \\Sigma M_F &= 0 \\\\ -DE_x ( \\var{y5}) - DE_y(\\var{x5}) + W ( \\var{x6}) &= 0\\\\ DE ( \\var{scalar(y5)} \\cos \\theta_D + \\var{scalar(x5)} \\sin \\theta_d) &= \\var{scalar(x6)} W \\\\ DE &= W \\left(\\dfrac{\\var{x6}}{\\var{siground(dperp_D,4)}}\\right) \\\\ &= \\var{siground(DE,4)} \\textrm{ (tension)} \\end{align}

", "metadata": {"description": "

Determine the forces which in an hydraulicly operated excavator.

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "type": "question", "rulesets": {}, "preamble": {"css": "", "js": ""}, "variables": {"y3": {"description": "", "group": "inputs", "templateType": "anything", "definition": "round((1.2 L random(0.9..1.1#0.05)),units[2])", "name": "y3"}, "x3": {"description": "", "group": "inputs", "templateType": "anything", "definition": "round((2.6 L random(0.9..1.1#0.05)),units[2])", "name": "x3"}, "BC": {"description": "", "group": "inputs", "templateType": "anything", "definition": "load x_t /dperp_B", "name": "BC"}, "x2": {"description": "", "group": "inputs", "templateType": "anything", "definition": "round((3.9 L random(0.9..1.1#0.05)),units[2])", "name": "x2"}, "units": {"description": "

units[2] large rounding base

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units[3] small rounding base

", "group": "inputs", "templateType": "anything", "definition": "random(['kN','m', \"5 cm\"],['lbf','ft', \"0.05 ft\"])", "name": "units"}, "DE": {"description": "", "group": "inputs", "templateType": "anything", "definition": "load x6 /dperp_D", "name": "DE"}, "dperp_D": {"description": "", "group": "inputs", "templateType": "anything", "definition": "y5 cos(radians(theta_D)) + x5 sin(radians(theta_d))", "name": "dperp_D"}, "y6": {"description": "", "group": "inputs", "templateType": "anything", "definition": "round((9.4 L random(0.9..1.1#0.05)),units[2])", "name": "y6"}, "L": {"description": "

scaling value for all lengths, which are also randomly perterbed actual value as scaled.

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The motion of the excavator is controled by three hydraulic cylinders.  Determine the force exerted by cylinders $BC$ and $DE$ when supporting a {load} downward vertical load at $G$.  Neglect the weights of the parts.

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$BC$ = [[0]] [[1]]

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$DE$ = [[2]] [[3]]

"}], "functions": {"dy": {"type": "number", "parameters": [["ix", "number"]], "definition": "let(n,ix,['y' + n,'\\\"'+ scalar(precround(eval(expression('y' + n)),2))\n + '\\\"'])", "language": "jme"}, "dx": {"type": "number", "parameters": [["ix", "number"]], "definition": "let(n,ix,['x' + n,'\\\"'+ scalar(precround(eval(expression('x' + n)),2))+ '\\\"'])", "language": "jme"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "

{geogebra_applet('cbh4g7zm', {map(dx(n),n,1..6)} + {map(dy(n),n,1..6)} )}

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Diagram units are in:  [{units[1]}]

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", "extensions": ["geogebra", "quantities", "visjs", "weh"], "tags": ["equilibrium", "Equilibrium", "machine", "mechanics", "Mechanics", "rigid body", "statics", "Statics"], "variable_groups": [{"variables": [], "name": "Unnamed group"}, {"variables": ["L", "x1", "x2", "x3", "x4", "x5", "x6", "y1", "y2", "y3", "y4", "y5", "y6", "load", "units", "x_t", "dperp_B", "BC", "dperp_D", "DE"], "name": "inputs"}, {"variables": ["theta_b", "theta_d"], "name": "outputs"}], "ungrouped_variables": [], "name": "Machine: excavator", "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/"}]}