13:I[70017,["/_next/static/immutable/chunks/2gtpnylaz50zo.js","/_next/static/immutable/chunks/22kg_k_j3c_ao.js","/_next/static/immutable/chunks/3s-qhi50ildb6.js"],""] 14:I[16632,["/_next/static/immutable/chunks/2gtpnylaz50zo.js","/_next/static/immutable/chunks/22kg_k_j3c_ao.js","/_next/static/immutable/chunks/3s-qhi50ildb6.js"],"default"] 15:I[3261,["/_next/static/immutable/chunks/2gtpnylaz50zo.js","/_next/static/immutable/chunks/22kg_k_j3c_ao.js","/_next/static/immutable/chunks/3s-qhi50ildb6.js"],"default"] 16:I[44578,["/_next/static/immutable/chunks/2gtpnylaz50zo.js","/_next/static/immutable/chunks/22kg_k_j3c_ao.js","/_next/static/immutable/chunks/3s-qhi50ildb6.js"],"default"] 17:T1cb2,{ "consigne": "Choisis d'abord la relation, puis calcule chaque valeur avec son unité. Les masses volumiques de référence sont dans les données.", "donnees": [ { "cle": "fer", "tex": "\\rho_{\\text{fer}} = 7{,}9\\ \\text{g.cm}^{-3}" }, { "cle": "huile", "tex": "\\rho_{\\text{huile}} = 0{,}92\\ \\text{g.mL}^{-1}" }, { "cle": "cuivre", "tex": "\\rho_{\\text{cuivre}} = 8{,}96\\ \\text{g.cm}^{-3}" }, { "cle": "ethanol", "tex": "\\rho_{\\text{éthanol}} = 0{,}79\\ \\text{g.mL}^{-1}" }, { "cle": "plomb", "tex": "\\rho_{\\text{plomb}} = 11{,}3\\ \\text{g.cm}^{-3}" }, { "cle": "lait", "tex": "\\rho_{\\text{lait}} = 1{,}03\\ \\text{g.mL}^{-1}" }, { "cle": "mercure", "tex": "\\rho_{\\text{mercure}} = 13{,}6\\ \\text{g.mL}^{-1}" }, { "cle": "alu", "tex": "\\rho_{\\text{aluminium}} = 2{,}7\\ \\text{g.cm}^{-3}" }, { "cle": "or", "tex": "\\rho_{\\text{or}} = 19{,}3\\ \\text{g.cm}^{-3}" }, { "cle": "litre", "tex": "1\\ \\text{L} = 1\\,000\\ \\text{mL}" }, { "cle": "kg", "tex": "1\\ \\text{kg} = 1\\,000\\ \\text{g}" } ], "questions": [ { "enonce": "Quelle ligne donne correctement les trois formes de la relation entre ρ, m et V ?", "donnees": [], "choix": [ "\\rho = m \\times V\\quad ; \\quad m = \\dfrac{\\rho}{V}\\quad ; \\quad V = \\dfrac{m}{\\rho}", "\\rho = \\dfrac{V}{m}\\quad ; \\quad m = \\dfrac{V}{\\rho}\\quad ; \\quad V = m \\times \\rho", "\\rho = \\dfrac{m}{V}\\quad ; \\quad m = \\rho \\times V\\quad ; \\quad V = \\dfrac{m}{\\rho}", "\\rho = \\dfrac{m}{V}\\quad ; \\quad m = \\dfrac{V}{\\rho}\\quad ; \\quad V = \\rho \\times m" ], "bonne": 2, "explication": "La masse volumique est la masse par unité de volume. On isole ensuite m ou V selon la grandeur cherchée." }, { "enonce": "Un morceau d'aluminium a une masse de 27 g pour un volume de 10 cm³. Quelle est sa masse volumique ?", "donnees": [], "reponse": 2.7, "tolerancePct": 2, "unite": "g.cm⁻³|g/cm³", "explication": "ρ = 27 ÷ 10 = 2,7 g.cm⁻³. C'est bien la masse volumique de l'aluminium." }, { "enonce": "On pèse 200 g d'eau, qui occupent 200 mL. Quelle est sa masse volumique ?", "donnees": [], "reponse": 1, "tolerancePct": 2, "unite": "g.mL⁻¹|g/mL", "explication": "ρ = 200 ÷ 200 = 1,00 g.mL⁻¹, soit 1 000 kg.m⁻³. C'est la valeur de référence de l'eau." }, { "enonce": "Quelle est la masse d'un objet en fer de 5,0 cm³ ?", "donnees": ["fer"], "reponse": 39.5, "tolerancePct": 2, "unite": "g", "aide": "Tu cherches une masse, donc isole m dans la relation.", "explication": "m = 7,9 × 5,0 = 39,5 g." }, { "enonce": "Quel volume occupent 92 g d'huile ?", "donnees": ["huile"], "reponse": 100, "tolerancePct": 2, "unite": "mL|cm³", "aide": "Tu cherches un volume, donc isole V dans la relation.", "explication": "V = 92 ÷ 0,92 = 100 mL." }, { "enonce": "Une bague en or a une masse de 96,5 g pour un volume de 5,0 cm³. Quelle est sa masse volumique ?", "donnees": [], "reponse": 19.3, "tolerancePct": 2, "unite": "g.cm⁻³|g/cm³", "explication": "ρ = 96,5 ÷ 5,0 = 19,3 g.cm⁻³. L'or est un métal très dense." }, { "enonce": "Quelle est la masse de 2,0 cm³ de cuivre ?", "donnees": ["cuivre"], "reponse": 17.92, "tolerancePct": 2, "unite": "g", "explication": "m = 8,96 × 2,0 = 17,92 g." }, { "enonce": "Quelle est la masse de 50 mL d'éthanol ?", "donnees": ["ethanol"], "reponse": 39.5, "tolerancePct": 2, "unite": "g", "explication": "m = 0,79 × 50 = 39,5 g." }, { "enonce": "Un liquide inconnu a une masse de 250 g pour 200 mL. Quelle est sa masse volumique ?", "donnees": [], "reponse": 1.25, "tolerancePct": 2, "unite": "g.mL⁻¹|g/mL", "explication": "ρ = 250 ÷ 200 = 1,25 g.mL⁻¹. Ce liquide est donc plus dense que l'eau." }, { "enonce": "Un bouchon de liège de 12 cm³ a une masse de 2,9 g. Quelle est sa masse volumique ?", "donnees": [], "reponse": 0.24, "tolerancePct": 3, "unite": "g.cm⁻³|g/cm³", "explication": "ρ = 2,9 ÷ 12 ≈ 0,24 g.cm⁻³. Le liège est bien moins dense que l'eau, donc il flotte." }, { "enonce": "Une pierre de 150 cm³ a une masse de 405 g. Quelle est sa masse volumique ?", "donnees": [], "reponse": 2.7, "tolerancePct": 2, "unite": "g.cm⁻³|g/cm³", "explication": "ρ = 405 ÷ 150 = 2,7 g.cm⁻³." }, { "enonce": "Quelle est la masse d'un plomb de pêche de 4,0 cm³ ?", "donnees": ["plomb"], "reponse": 45.2, "tolerancePct": 2, "unite": "g", "explication": "m = 11,3 × 4,0 = 45,2 g." }, { "enonce": "Quelle est la masse du lait contenu dans une brique de 1 000 mL ?", "donnees": ["lait"], "reponse": 1030, "tolerancePct": 2, "unite": "g", "explication": "m = 1,03 × 1 000 = 1 030 g. Un litre de lait pèse donc un peu plus d'un kilogramme." }, { "enonce": "Quel volume occupent 68 g de mercure ?", "donnees": ["mercure"], "reponse": 5, "tolerancePct": 2, "unite": "mL|cm³", "explication": "V = 68 ÷ 13,6 = 5,0 mL." }, { "enonce": "Quel est le volume d'une pièce d'aluminium de 54 g ?", "donnees": ["alu"], "reponse": 20, "tolerancePct": 2, "unite": "cm³|mL", "explication": "V = 54 ÷ 2,7 = 20 cm³." }, { "enonce": "Un bloc de glace de 2,0 L a une masse de 1,84 kg. Quelle est sa masse volumique ? Donne-la en g.mL⁻¹.", "donnees": ["litre", "kg"], "reponse": 0.92, "tolerancePct": 2, "unite": "g.mL⁻¹|g/mL", "aide": "Convertis d'abord : la masse en grammes, le volume en millilitres.", "explication": "1,84 kg = 1 840 g et 2,0 L = 2 000 mL, donc ρ = 1 840 ÷ 2 000 = 0,92 g.mL⁻¹. La glace est moins dense que l'eau, c'est pourquoi elle flotte." }, { "enonce": "Une poutre en chêne de 0,050 m³ a une masse de 36 kg. Quelle est sa masse volumique ? Donne-la en kg.m⁻³.", "donnees": [], "reponse": 720, "tolerancePct": 2, "unite": "kg.m⁻³|kg/m³", "explication": "ρ = 36 ÷ 0,050 = 720 kg.m⁻³." }, { "enonce": "Quelle est la masse de 3,0 L d'huile ? Réponds en grammes.", "donnees": ["huile", "litre"], "reponse": 2760, "tolerancePct": 2, "unite": "g", "aide": "La masse volumique est en g.mL⁻¹, donc exprime d'abord le volume en mL.", "explication": "3,0 L = 3 000 mL, donc m = 0,92 × 3 000 = 2 760 g." }, { "enonce": "Quel volume occupe un lingot d'or de 1,0 kg ? Réponds en cm³.", "donnees": ["or", "kg"], "reponse": 51.8, "tolerancePct": 2, "unite": "cm³|mL", "aide": "La masse volumique est en g.cm⁻³, donc exprime d'abord la masse en grammes.", "explication": "1,0 kg = 1 000 g, donc V = 1 000 ÷ 19,3 ≈ 51,8 cm³. Un kilogramme d'or occupe très peu de place." } ] } 18:T7fa,

\rho_{\text{fer}} = 7{,}9\ \text{g.cm}^{-3}

19:T804,

\rho_{\text{huile}} = 0{,}92\ \text{g.mL}^{-1}

1a:T806,

\rho_{\text{cuivre}} = 8{,}96\ \text{g.cm}^{-3}

1b:Ta06,

\rho_{\text{éthanol}} = 0{,}79\ \text{g.mL}^{-1}

1c:T806,

\rho_{\text{plomb}} = 11{,}3\ \text{g.cm}^{-3}

1d:T801,

\rho_{\text{lait}} = 1{,}03\ \text{g.mL}^{-1}

1e:T80a,

\rho_{\text{mercure}} = 13{,}6\ \text{g.mL}^{-1}

1f:T80c,

\rho_{\text{aluminium}} = 2{,}7\ \text{g.cm}^{-3}

20:T7fa,

\rho_{\text{or}} = 19{,}3\ \text{g.cm}^{-3}

21:T420,

1\ \text{kg} = 1\,000\ \text{g}

22:T1047,

\rho = m \times V\quad ; \quad m = \dfrac{\rho}{V}\quad ; \quad V = \dfrac{m}{\rho}

23:T1047,

\rho = \dfrac{V}{m}\quad ; \quad m = \dfrac{V}{\rho}\quad ; \quad V = m \times \rho

24:T1047,

\rho = \dfrac{m}{V}\quad ; \quad m = \rho \times V\quad ; \quad V = \dfrac{m}{\rho}

25:T102f,

\rho = \dfrac{m}{V}\quad ; \quad m = \dfrac{V}{\rho}\quad ; \quad V = \rho \times m

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