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{"name": "Stick a balloon to the ceiling", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Yellow_toy_balloon.svg", "/srv/numbas/media/question-resources/Yellow_toy_balloon.svg"], ["question-resources/327px-Yellow_toy_balloon.svg.png", "/srv/numbas/media/question-resources/327px-Yellow_toy_balloon.svg.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Stick a balloon to the ceiling", "tags": ["elec", "field", "force", "tut3"], "metadata": {"description": "Recollection of formulae, combining and re-arranging equations, and evaluating quantities, all while keeping appropriate units in place.", "licence": "All rights reserved"}, "statement": "<p><img width=\"20%\" style=\"float: left;\" src=\"resources/question-resources/327px-Yellow_toy_balloon.svg.png\"/>Estimate the electric field strength, $E$, required to make a balloon stick to a ceiling due to electrostatic force. Assume that the balloon has a mass of {massg}&nbsp;g and has an area of contact with the ceiling of {areacm}&nbsp;cm$^2$, and note that the force due to gravity is $mg$ (pointing towards the centre of the Earth).<br/> <br/>When providing numerical answers you may express them using scientific notation.&nbsp; Express values to four significant figures and use the values of physical constants as provided in the course notes.</p>", "advice": "<p>The force due to gravity, or weight, at the Earth's surface is written as $mg$, where $m$ is the mass and $g$ is the acceleration due to gravity.&nbsp; The electric field force can be either written in terms of the force on a charge ($F=qE$), or, as is required in this case, in terms of the energy stored in the field, $F=\\displaystyle{\\varepsilon E^2 A\\over 2}$, where $A$ is the contact area, $\\varepsilon$ is the permittivity of air (a balloon stuck to the ceiling is likely to be in air!) and $E$ is the electric field strength.&nbsp; For NUMBAS we need to express the electric field as a different symbol as $E$ is reserved as {e}, the base of the natural logarithm.&nbsp;&nbsp;</p>\n<p>For the electric field to just balance the weight we can equate the two forces and re-arrange for $E$:</p>\n<p style=\"text-align: center;\">$\\displaystyle{\\varepsilon E^2 A\\over 2}=mg\\Rightarrow E=\\sqrt{\\displaystyle{2mg\\over \\varepsilon A}}$.</p>\n<p style=\"text-align: left;\">You have to remember that the equations work for SI units, so the mass should be in kg and the area in m$^2$.</p>", "rulesets": {}, "extensions": [], "variables": {"area": {"name": "area", "group": "Ungrouped variables", "definition": "areacm/10000", "description": "<p>Area in m^2</p>", "templateType": "anything"}, "epsr": {"name": "epsr", "group": "Ungrouped variables", "definition": "1.0005", "description": "<p>Relative permittivity of air.</p>", "templateType": "anything"}, "massg": {"name": "massg", "group": "Ungrouped variables", "definition": "random(0.5..1.5#0.1)", "description": "<p>Mass of the balloon in g.</p>", "templateType": "anything"}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "9.8", "description": "<p>Acceleration due to gravity on Earth, m/s^2</p>", "templateType": "anything"}, "Efield": {"name": "Efield", "group": "Ungrouped variables", "definition": "sqrt(2*mass*g/(eps0*epsr*area))", "description": "<p>Computed E-field that JUST balances the weight.&nbsp;&nbsp;</p>", "templateType": "anything"}, "mass": {"name": "mass", "group": "Ungrouped variables", "definition": "massg/1000\n", "description": "<p>Mass in kg.</p>", "templateType": "anything"}, "eps0": {"name": "eps0", "group": "Ungrouped variables", "definition": "8.854*10^-12", "description": "<p>Permittivity of free space, F/m.</p>", "templateType": "anything"}, "areacm": {"name": "areacm", "group": "Ungrouped variables", "definition": "random(0.5..1.5#0.1)", "description": "<p>Area of contact in cm^2</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["areacm", "massg", "eps0", "epsr", "g", "Efield", "mass", "area"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Weight", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The force due to gravity, i.e. the weight&nbsp;of the balloon is given by the expression</p>\n<p style=\"text-align: center;\">$F_{\\rm gravity}=$&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "weight", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "m g", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "g", "value": ""}, {"name": "m", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Electrostatic force", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The force from the elecrtic field opposing the weight&nbsp;of the balloon is given by an expression&nbsp;in terms of&nbsp;the permiitivity, $\\varepsilon$ (epsilon), the contact area, $A$&nbsp;and the electric field strength, $E_1$ (E_1):</p>\n<p style=\"text-align: center;\">$F_{\\rm electrostatic}=$&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "weight", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "epsilon E_1^2 A /2 ", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "a", "value": ""}, {"name": "e_1", "value": ""}, {"name": "epsilon", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "E-field", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the value of $E$ that balances the weight.</p>\n<p style=\"text-align: center;\">$E=$[[0]] V/m</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "E-field", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Efield*0.995", "maxValue": "Efield*1.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Jon Goss", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3925/"}]}]}], "contributors": [{"name": "Jon Goss", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3925/"}]}