A block of given mass is sliding down the plane, with given acceleration or a given coeff-of-friction. Find the normal reaction force, the parallel force and the missing value of a and mu.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "{draw_block()}
\nA block of mass {mass} kg slides down a rough plane which is inclined at an angle $\\theta$ = {theta}$^{\\circ}$ to the horizontal. {q_string}.
\nThe acceleration due to gravity is g={g} ms$^{-2}$.
", "advice": "To find the normal reaction force $F_N$, we resolve the forces perpendicular to the plane.
\n
$F_N =$ mg cos $\\theta$,
$F_N =$ {mass} $\\times$ {g} cos( {theta}$^{\\circ}$),
And so the normal force $F_N$ is {fn} N.
\nTo find the force $F_P$ parallel to the plane, we resolve the forces parallel to the plane.
\n
$F_P =$ mg sin $\\theta$,
$F_P =$ {mass} $\\times$ {g} sin ({theta}$^{\\circ}$),
And so the parallel force $F_P$ is {fp} N.
\nTo find the force accerating the block {if(switcharoo=0,\"you must calculate the frictional force and subtract this from the gravitational force parallel to the plane\",\"you must factor the mass against the acceration\")}
\n{if(switcharoo=0,\"F = F<sub>P</sub> - F<sub>F</sub>\",\"F=ma\")}
\n{if(switcharoo=0,\"F<sub>F</sub> = μ<sub>K</sub> * F<sub>N</sub>\",\"F = \"+mass+\" * \"+a)}
\n{if(switcharoo=0,\"F = \"+FP+\" - (\"+mu+\" * \"+FN+\")\",\" \")}
\nSo the force accerating the block is { F} N.
\n\nd)
\nTo find the {if(switcharoo=0,\"acceleration of the block, you must calculate divide the force down the slope by the mass\",\"co-efficient of friction, you must factor the forces\")}.
\n{if(switcharoo=0,\"F=ma\",\"F = F<sub>P</sub> - F<sub>F</sub>\")}
\n{if(switcharoo=0,\"a = F/m\",\"F<sub>F</sub> = μ<sub>K</sub> * F<sub>N</sub>\")}
\n{if(switcharoo=0,\"a = \"+F+\" / \"+mass,\"μ<sub>K</sub> = (F<sub>P</sub> - F) / F<sub>N</sub>\")}
\n{if(switcharoo=0,\" \",\"μ<sub>K</sub> = (\"+FP+\" - \"+F+\") / \"+FN)}
\n\nSo, {if(switcharoo=0,\"the acceration of the block is \"+answer+\" m/s<sup>-2</sup>\",\"the coefficient of friction μ<sub>K</sub> between the block and the plane is \"+mumu)}.
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", "templateType": "anything", "can_override": false}, "q_string": {"name": "q_string", "group": "calculated variables", "definition": "if(switcharoo=0,\"The slope has a kinetic co-efficient of friction $\\\\mu_K$ of \"+dpformat(mu,2),\"The mass accelerates at \"+dpformat(a,1)+\" ms$^\\{-2\\}$\")", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "F>0.1", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "random variables", "variables": ["mass", "theta", "switcharoo", "a", "mu"]}, {"name": "calculated variables", "variables": ["FN", "FP", "F", "aa", "mumu", "answer", "q_string", "a_string"]}, {"name": "constants", "variables": ["g"]}, {"name": "marks", "variables": ["minf", "maxf"]}], "functions": {"draw_block": {"parameters": [], "type": "html", "language": "javascript", "definition": "// Takes variables\n\n// showing K or C?\n//k_c = Numbas.jme.unwrapValue(scope.variables.k_c_switch);\n//\n//if (k_c = 0) {\n// var k_c_corr =0;\n// var k_c_str=\"K\";\n//} else {\n// var k_c_corr =-273;\n// var k_c_str=\"\u00b0C\";\n//}\n\n//Set values\ntheta = Numbas.jme.unwrapValue(scope.variables.theta);\nr_theta = theta * Math.PI / 180. \nm = Numbas.jme.unwrapValue(scope.variables.mass);\n//et = Numbas.jme.unwrapValue(scope.variables.end_temp)+k_c_corr;\n//pt1 = Numbas.jme.unwrapValue(scope.variables.phase1_temp)+k_c_corr;\n//pt2 = Numbas.jme.unwrapValue(scope.variables.phase2_temp)+k_c_corr;\n\n\n// The function provided by the JSXGraph extension wraps the board up in\n// a div tag so that it's easier to embed in the page.\nvar div = Numbas.extensions.jsxgraph.makeBoard('300px','260px',\n//{boundingBox: [-0.1,-0.1,1.,1.],\n {boundingBox: [1.,0.8,-0.1,-0.1],\n axis: false,\n showNavigation: false,\n grid: false\n });\n\n// div.board is the object created by JSXGraph, which you use to\n// manipulate elements\nvar board = div.board;\n\n\n\n// create the x-axis.\n//var xaxis = board.create('line',[[0,0],[1,0]], {strokeColor: 'black', fixed: true});\n//var xticks = board.create('ticks',[xaxis,20],{\n// drawLabels: true,\n// minorTicks: 0\n//});\n\n// create the y-axis\n\n//var yaxis = board.create('line',[[0,0],[0,1]], { strokeColor: 'black', fixed: true });\n//var yticks = board.create('ticks',[yaxis,parseInt((et-st)/50.)*10],{\n//drawZero:true,\n//drawLabels: true,\n//label: {offset: [20, 0]},\n//minorTicks: 0\n//});\n\n\n// each line needs four coordinates start x,y and end x,y - 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