// Numbas version: finer_feedback_settings {"name": "Find tension in rope attached to mass", "extensions": [], "custom_part_types": [], "resources": [["question-resources/tension_image.png", "/srv/numbas/media/question-resources/tension_image.png"], ["question-resources/tension_image_rzq44LZ.png", "/srv/numbas/media/question-resources/tension_image_rzq44LZ.png"], ["question-resources/mass.png", "/srv/numbas/media/question-resources/mass.png"], ["question-resources/mass2.png", "/srv/numbas/media/question-resources/mass2.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["mass", "grams", "g", "a1", "a2", "u", "a3", "b", "showgrams"], "name": "Find tension in rope attached to mass", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "

First we can draw a diagram of the forces acting on the block.

Remember that when resolving $F=ma$ we have to work in $\\mathrm{kg}$ for mass. So we need to convert $\\var{showgrams}\\ \\mathrm{g}$ to $\\var{mass} \\ \\mathrm{kg}$.

a)

When the block is moving upwards we resolve $F=ma$ in the vertical direction, with upwards being positive.

\\begin{align}
F & = ma \\\\
T - mg & = ma \\\\
T & = \\left(\\var{mass} \\times \\var{g}\\right) + \\left( \\var{mass} \\times \\var{a1} \\right) \\\\
& = \\var{precround(mass*g + mass*a1,3)}.
\\end{align}

The tension in the rope is $\\var{precround(mass*g + mass*a1,3)} \\ \\mathrm{N}$.

b)

When the block is moving downwards we resolve vertically downwards, as this is the direction of acceleration.

\\begin{align}
F & = ma \\\\
mg - T & = ma \\\\
T & = \\left( \\var{mass} \\times \\var{g} \\right) - \\left( \\var{mass} \\times \\var{b}\\right) \\\\
& = \\var{precround(mass*g - mass*b,3)}.
\\end{align}

The tension in the rope is $\\var{precround(mass*g - mass*b,3)} \\ \\mathrm{N}$.

c)

Here, constant speed means acceleration $a=0$. Therefore we can resolve $F=ma$ in the upward direction of acceleration but set $a=0 \\ \\mathrm{ms^{-2}}$.

\\begin{align}
F & = ma \\\\
T - mg & = m \\times 0 \\\\
T & = m \\times g \\\\
& = \\var{mass} \\times 9.8 \\\\
& = \\var{precround(mass*9.8,3)}
\\end{align}

The tension in the rope is $\\var{precround(mass*g,3)} \\ \\mathrm{N}$.

d)

The block is moving downwards but decelerating at a rate of $a= -\\var{a3} \\ \\mathrm{ms^{-2}}$.

\\begin{align}
F & = ma \\\\
mg - T & = ma \\\\
T & = mg - ma \\\\
& = \\left( \\var{mass} \\times \\var{g} \\right) - \\left(\\var{mass} \\times \\var{-a3}\\right) \\\\
& = \\var{precround(mass*g + mass*a3,3)}
\\end{align}

The tension in the rope is $\\var{precround(mass*g+mass*a3,3)} \\ \\mathrm{N}$.

", "rulesets": {}, "parts": [{"precisionType": "dp", "prompt": "

When the block moves upward with an acceleration of $\\var{a1}\\ \\mathrm{ms^{-2}}$.

", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "mass*g+(mass*a1)", "strictPrecision": false, "minValue": "mass*g+(mass*a1)", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "3", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "

When the block moves downwards with an acceleration of $\\var{a1+a2}\\ \\mathrm{ms^{-2}}$.

", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "mass*g-mass*(a1+a2)", "strictPrecision": false, "minValue": "mass*g-mass*(a1+a2)", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "3", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "

When the block of mass moves upward with a constant speed of $\\var{u}ms^{-1}$.

", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "mass*g", "strictPrecision": false, "minValue": "mass*g", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "3", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "

When the block of mass moves downward with a deceleration of $\\var{a3}ms^{-2}$.

", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "mass*g-(mass*-1*a3)", "strictPrecision": false, "minValue": "mass*g-(mass*-1*a3)", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "3", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "

A block of mass $\\var{showgrams} \\, \\mathrm{g}$ is attached to a vertical rope.

The acceleration due to gravity is $9.8 \\, \\mathrm{ms}^{-2}$.

Find the tension in the rope, in Newtons to 3 decimal places, in the following situations.

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LaTeX encoding of the weight in grams, with thousands separator.

"}, "mass": {"definition": "random(1..10#0.25)", "templateType": "randrange", "group": "Ungrouped variables", "name": "mass", "description": ""}}, "metadata": {"description": "

A mass attached to a vertical rope. Finding the tension in the rope for different accelerations. Using $F=ma$.

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