// Numbas version: exam_results_page_options
{"name": "plano inclinado", "extensions": [], "custom_part_types": [], "resources": [["question-resources/inclined_solution_2.png", "/srv/numbas/media/question-resources/inclined_solution_2.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "plano inclinado", "tags": [], "metadata": {"description": "<p>Una part&iacute;cula se proyecta hacia arriba de un plano rugoso a una velocidad dada. Dado el &aacute;ngulo de la pendiente y el coeficiente de fricci&oacute;n, encuentre la distancia que recorre la part&iacute;cula antes de llegar al reposo instant&aacute;neo.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Una particula de masa $\\var{mass} \\mathrm{kg}$ es lanzada con velocidad $\\var{u}\\ \\mathrm{ms^{-1}}$ por un plano inclinado. El coeficiente de roce entre la particula y el roce es $\\var{mu}$. El plano posee una inclinacion $\\theta = \\var{theta}^{\\circ}$ con respecto a la horizonta..</p>\n<p>La aceleracion de gravedad es $g = 9.8 \\mathrm{ms^{-2}}$.</p>", "advice": "<p>Se puede dibujar un diagrama para mostrar las fuerzas que act&uacute;an sobre la part&iacute;cula.</p>\n<p><img src=\"resources/question-resources/inclined_solution_2.png\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>Aqu&iacute; la part&iacute;cula se dibuja en tres posiciones, mostrando su velocidad original cuando se proyecta desde el fondo de la pendiente, su posici&oacute;n en alg&uacute;n punto de la pendiente y su posici&oacute;n cuando se detiene instant&aacute;neamente m&aacute;s arriba de la pendiente.</p>\n<p>La pendiente es &aacute;spera por lo que la fricci&oacute;n ($\\mu N $ N) act&uacute;a cuesta abajo, en contra de la direcci&oacute;n del movimiento.</p>\n<h4>a)</h4>\n<p>La reacci&oacute;n normal $N$, se encuentra resolviendo las fuerzas perpendiculares al plano.</p>\n<p>\\begin{align} <br/>R - mg \\cos \\theta &amp; = 0, \\\\<br/>R &amp; = mg \\cos \\theta, \\\\<br/>&amp; = (\\var{mass} \\times 9.8) \\cos (\\var{theta}^{\\circ}), \\\\<br/>&amp;= \\var{precround(R,3)} \\mathrm{N}. <br/>\\end{align}</p>\n<p>La fuerza de reacci&oacute;n normal entre la part&iacute;cula y el plano es $\\var{precround(R,3)} \\mathrm{N}$.</p>\n<h4>b)</h4>\n<p>Para encontrar la aceleraci&oacute;n de la part&iacute;cula resolvemos las fuerzas paralelas al plano.</p>\n<p>\\begin{align} <br/>- mg \\sin \\theta - \\mu R &amp; = ma, \\\\<br/>- \\var{mass} \\times 9.8&nbsp;\\sin (\\var{theta}^{\\circ})&nbsp;- (\\var{precround(R,3)} \\times \\var{mu}) &amp; = \\var{mass}a, \\\\<br/>a &amp; = \\frac{&nbsp;- \\var{mass} \\times 9.8&nbsp;\\sin (\\var{theta}^{\\circ})&nbsp;- (\\var{precround(R,3)} \\times \\var{mu}) }{\\var{mass}}, \\\\<br/>&amp; = \\var{precround(a,3)} \\mathrm{ms^{-2}}. <br/>\\end{align}</p>\n<p>Por lo tanto, la desaceleraci&oacute;n de la part&iacute;cula es $\\var{precround(-a,3)} \\mathrm{ms^{-2}}$ ya que es el negativo de la aceleraci&oacute;n.</p>\n<h4>c)</h4>\n<p>La part&iacute;cula viajar&aacute; cuesta arriba hasta que llegue al reposo instant&aacute;neo; en este punto su velocidad ser&aacute; $0$. Podemos usar la ecuaci&oacute;n $v^2 = u^2 + 2as$ para encontrar la distancia que viajar&aacute; la part&iacute;cula.</p>\n<p>Sabemos $u = \\var{u}, v= 0$ y $a = \\var{precround(a,3)}$.</p>\n<p>\\begin{align} <br/>v^2 &amp; = u^2 + 2as, \\\\<br/>0 &amp; = \\simplify{{u}^2+{precround(2a,3)}s}, \\\\<br/>s &amp; = \\frac{\\var{u}^2}{\\var{precround(-2a,3)}}, \\\\[0.5em]<br/>&amp; = \\var{precround(u^2/(-2*a),3)} \\mathrm{m}. <br/>\\end{align}</p>\n<p>La distancia que la part&iacute;cula viajar&aacute; por el plano antes de llegar al reposo instant&aacute;neo es $\\var{precround(u^2/(-2*a),3)} \\mathrm{m}$.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"mass": {"name": "mass", "group": "Ungrouped variables", "definition": "random(2 .. 10#1)", "description": "<p>The mass of the particle.</p>", "templateType": "randrange", "can_override": false}, "mu": {"name": "mu", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.95#0.01)", "description": "<p>The coefficient of friction between the particle and the plane.</p>", "templateType": "randrange", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "9.8", "description": "<p>La aceleracion debido a la gravedad</p>", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "-(mu*R+mass*g*sin(radians(theta)))/mass", "description": "<p>The acceleration of the particle along the slope.</p>", "templateType": "anything", "can_override": false}, "R": {"name": "R", "group": "Ungrouped variables", "definition": "mass*g*cos(radians(theta))", "description": "<p>The normal reaction force of the plane against the particle.</p>", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "Ungrouped variables", "definition": "random(30 .. 60#0.5)", "description": "<p>The angle of the slope.</p>", "templateType": "randrange", "can_override": false}, "u": {"name": "u", "group": "Ungrouped variables", "definition": "random(5 .. 15#1)", "description": "<p>The initial speed of the particle.</p>", "templateType": "randrange", "can_override": false}, "s": {"name": "s", "group": "Ungrouped variables", "definition": "-u^2/(2*a)", "description": "<p>The distance travelled before the particle comes to rest.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "a<0", "maxRuns": 100}, "ungrouped_variables": ["g", "mu", "theta", "u", "mass", "R", "a", "s"], "variable_groups": [], "functions": {}, "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": "<p>&iquest;Cual es la fuerza normal $N$ entre la part&iacute;cula y el plano? De su respuesta en Newtons hasta 3 decimales</p>\n<p>$N = $ [[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "R", "maxValue": "R", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "r", "part": "p0g0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Usando el valor de $N$ de la parte <strong>a), </strong>encuentre la aceleracion de la particula a medida que se mueve hacia arriba en el planot</p>\n<p>De su respuesta en unidades de $\\mathrm{ms^{-2}}$.</p>", "minValue": "-a", "maxValue": "-a", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "a", "part": "p1", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Encuentre la distancia que se mover&aacute; la part&iacute;cula antes de que llegue al reposo.</p>\n<p>De su respuesta en $m$.</p>", "minValue": "-u^2/(2*a)", "maxValue": "-u^2/(2*a)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}, {"name": "Ivan Munoz", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18334/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}, {"name": "Ivan Munoz", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18334/"}]}