// Numbas version: exam_results_page_options
{"name": "Cable & Solutions", "extensions": [], "custom_part_types": [], "resources": [["question-resources/vect11.png", "/srv/numbas/media/question-resources/vect11.png"], ["question-resources/hw2sol6.png", "/srv/numbas/media/question-resources/hw2sol6.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Cable & Solutions", "tags": [], "metadata": {"description": "<p>resultant force</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p><em><img src=\"resources/question-resources/vect11.png\" width=\"241\" height=\"363\"/></em></p>\n<p><em>&nbsp;</em>Known: $P_1=\\var{P1}$N, $P_2=\\var{P2}$N.</p>", "advice": "<p>If the resultant force is directed along $BC$, its component in the direction perpendicular to $BC$ should be zero.</p>\n<p>Let the axis $y$ be directed along the line $BC$ and the axis $x$ be perpendicular to $BC$:</p>\n<p><img src=\"resources/question-resources/hw2sol6.png\" width=\"239\" height=\"231\"/></p>\n<p>The $x$ component of the resultant:</p>\n<p style=\"text-align: center;\">$P_2 \\cos 30^\\circ+P_1 \\cos 55^\\circ-F_{AC}\\cos 10^\\circ = 0$</p>\n<p style=\"text-align: left;\">Solving this equation for $F_{AC}$:</p>\n<p style=\"text-align: center;\">$F_{AC}=\\dfrac{P_2 \\cos 30^\\circ+P_1 \\cos 55^\\circ}{\\cos 10^\\circ}=\\dfrac{(\\var{P2}\\text{N})\\cos 30^\\circ+(\\var{P1}\\text{N}) \\cos 55^\\circ}{\\cos 10^\\circ}=\\var{FAC}\\,\\text{N}\\quad\\blacktriangleleft$</p>", "rulesets": {}, "extensions": [], "variables": {"P1": {"name": "P1", "group": "Ungrouped variables", "definition": "random(20 .. 140#10)", "description": "", "templateType": "randrange"}, "Fac": {"name": "Fac", "group": "Ungrouped variables", "definition": "precround(({P1}*cos(radians(55))+{P2}*cos(radians(30)))/cos(radians(10)),1)", "description": "", "templateType": "anything"}, "P2": {"name": "P2", "group": "Ungrouped variables", "definition": "random(35 .. 100#5)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["P1", "P2", "Fac"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the required tension in cable&nbsp;<i>AC </i>(in N), knowing that&nbsp;the resultant of the three forces exerted at Point&nbsp;<i>C </i>&nbsp;on the bar<i> BC&nbsp;</i>(i.e.<i> $F_{AC}$, $P_1$ and $P_2$</i>) is directed along <em>BC.</em></p>", "minValue": "{Fac}-0.5", "maxValue": "{Fac}+0.5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Vladimir Vingoradov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1862/"}]}]}], "contributors": [{"name": "Vladimir Vingoradov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1862/"}]}