![](\"resources/question-resources/Connected_particles.png\")
Suppose that there is a light box attached to a vertical light inextensible string. The box holds two masses $A$ and $B$ as shown in the diagram below, where $A$ rests upon $B$.
\n
Suppose that the mass of $A$ is $m_1 = \\var{massa} \\, \\mathrm{kg}$ and the mass of $B$ is $m_2 = \\var{massb} \\, \\mathrm{kg}$. The acceleration due to gravity is $g=9.8 \\, \\mathrm{ms^{-2}}$.
\nGive your answers to the following questions to 3 decimal places.
", "name": "Connected particles 1", "preamble": {"css": "", "js": ""}, "variables": {"massa": {"name": "massa", "definition": "random(0.25..1.5#0.25)", "description": "", "group": "Ungrouped variables", "templateType": "randrange"}, "massb": {"name": "massb", "definition": "random(1.6..3#0.1)", "description": "", "group": "Ungrouped variables", "templateType": "randrange"}, "a": {"name": "a", "definition": "precround((T-massa*g-massb*g)/mass,3)", "description": "acceleration 3d.p.
", "group": "Ungrouped variables", "templateType": "anything"}, "mass": {"name": "mass", "definition": "massa+massb", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "g": {"name": "g", "definition": "9.8", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "T": {"name": "T", "definition": "random(45..80#0.05)", "description": "tension in string
", "group": "Ungrouped variables", "templateType": "randrange"}}, "extensions": [], "rulesets": {}, "variable_groups": [], "ungrouped_variables": ["massa", "massb", "T", "g", "mass", "a"], "advice": "a) We can draw a diagram to show the forces acting on the system. As all parts are moving in the same straight line (vertically) we can resolve for the whole system.
\n![](\"resources/question-resources/Connected_particles2.png\")
We have that
\n\\begin{align} T - m_1g - m_2g & = (m_1 + m_2)a, \\\\
\\var{T} - \\var{massa}g - \\var{massb}g & = \\var{mass}a, \\\\
a & =\\frac{\\var{T} - \\var{massa}g - \\var{massb}g}{\\var{mass}}, \\\\
& = \\var{a}\\mathrm{ms^{-2}}.\\end{align}
The acceleration of the system is $\\var{a}\\mathrm{ms^{-2}}$.
\nb) To find the force exerted on mass $B$ by mass $A$ we can find the force exerted on $A$ by $B$ (the normal reaction, $R$) and use Newton's 3rd Law to say that the force exerted on $B$ by $A$ will have the same magnitude.
\n![](\"resources/question-resources/Connected_particles3.png\")
We resolve the forces to find $R$, using the 3d.p. value for $a$ from part a).
\n\\begin{align} R - m_1g & = m_1a, \\\\
R & = m_1g + m_1a, \\\\
& = \\var{massa} \\left(9.8 + \\var{a}\\right), \\\\
& = \\var{precround(massa*(9.8+a),3)} \\mathrm{N}.\\end{align}
So the force exerted on $B$ by $A$ is $\\var{precround(massa*(9.8+a),3)} \\mathrm{N}$.
\nc) To find the force exerted on mass $B$ by the box we find the force exerted on the box by $B$ and then use Newton's 3rd Law to say that the force exerted on $B$ by the box has the same magnitude but is in the opposite direction.
\nLooking only at the box we have
\n\\begin{align} T - F & = 0 \\times a, \\\\
T & = F, \\\\
\\var{T} \\mathrm{N} & = F. \\end{align}
Where here $F$ is the force exerted on the box by $B$ and the mass of the box is $0$ as it is modelled as being light.
\nSo the force exerted on $B$ by the box is $\\var{T} \\mathrm{N}$ upwards.
", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "Two masses in a box which is attached to a string. Finding acceleration by modelling the two masses as the whole system. Find forces exerted by the two masses.
"}, "functions": {}, "tags": [], "parts": [{"precision": "3", "precisionPartialCredit": 0, "strictPrecision": false, "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "marks": 1, "mustBeReducedPC": 0, "minValue": "(T-massa*g-massb*g)/mass", "scripts": {}, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "prompt": "Suppose that the tension in the string is $\\var{T} \\, \\mathrm{N}$ and that the box is raised vertically, using the string. With what acceleration, in $\\mathrm{ms^{-2}}$, is the box raised?
", "allowFractions": false, "showFeedbackIcon": true, "mustBeReduced": false, "type": "numberentry", "showPrecisionHint": false, "maxValue": "(T-massa*g-massb*g)/mass"}, {"precision": "3", "precisionPartialCredit": 0, "strictPrecision": false, "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "marks": 1, "mustBeReducedPC": 0, "minValue": "massa*g+a*massa", "scripts": {}, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "prompt": "Using the acceleration in $\\mathrm{ms^{-2}}$ found in part a), find the force in Newtons ($\\mathrm{N}$) exerted on mass $B$ by mass $A$.
", "allowFractions": false, "showFeedbackIcon": true, "mustBeReduced": false, "type": "numberentry", "showPrecisionHint": false, "maxValue": "massa*g+a*massa"}, {"precision": "3", "precisionPartialCredit": 0, "strictPrecision": false, "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "marks": 1, "mustBeReducedPC": 0, "minValue": "T", "scripts": {}, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "prompt": "Find the force in Newtons ($\\mathrm{N}$) exerted on mass $B$ by the box.
", "allowFractions": false, "showFeedbackIcon": true, "mustBeReduced": false, "type": "numberentry", "showPrecisionHint": false, "maxValue": "T"}], "type": "question", "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}]}]}], "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}]}