Ecrit par ✅ Quiz : Contraction Des Longueurs
Ce quiz contient 20 questions.
Note : Placeholder pour valider la structure. Le JSON converti est conservé ci-dessous pour l’import final des vraies questions Tutor LMS.
JSON Tutor LMS-ready
{
"quiz_title": "Contraction Des Longueurs",
"quiz_slug": "06_contraction_des_longueurs_quiz",
"quiz_description": "Quiz Edu509 : Contraction Des Longueurs",
"quiz_settings": {
"time_limit": {
"time_value": 0,
"time_type": "minutes"
},
"hide_quiz_time_display": false,
"attempts_allowed": 0,
"passing_grade": 70,
"max_questions_for_answer": 0,
"questions_order": "rand",
"hide_question_number_overview": false,
"short_answer_characters_limit": 200
},
"questions": [
{
"question_order": 1,
"question_title": "Quelle est la formule de la contraction des longueurs en relativité restreinte ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La formule correcte de la contraction des longueurs est \\\\(L = L_0 \\\\sqrt{1 - \\\\frac{v^2}{c^2}}\\\\), selon la relativité restreinte d’Einstein.",
"answers": [
{
"answer_title": "\\\\(L = L_0 \\\\sqrt{1 - \\\\frac{v^2}{c^2}}\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(L = L_0 (1 + \\\\frac{v}{c})\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(L = L_0 \\\\frac{v}{c}\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(L = L_0 \\\\sqrt{1 + \\\\frac{v^2}{c^2}}\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 2,
"question_title": "Un vaisseau spatial de longueur propre \\\\(L_0 = 100\\\\,\\\\mathrm{m}\\\\) se déplace à \\\\(v = 0{,}6c\\\\) par rapport à la Terre. Quelle est sa longueur mesurée depuis la Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La longueur contractée est \\\\(L = 100 \\\\times \\\\sqrt{1 - (0{,}6)^2} = 100 \\\\times 0{,}8 = 80\\\\,\\\\mathrm{m}\\\\).",
"answers": [
{
"answer_title": "80 m",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "60 m",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "100 m",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "64 m",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 3,
"question_title": "La contraction des longueurs concerne uniquement :",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La contraction des longueurs ne concerne que la direction du mouvement, les dimensions perpendiculaires restent inchangées.",
"answers": [
{
"answer_title": "La direction du mouvement",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Toutes les directions",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "Les directions perpendiculaires au mouvement",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "La masse de l’objet",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 4,
"question_title": "Pour un objet au repos dans un référentiel, la longueur mesurée est appelée :",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La longueur mesurée dans le référentiel où l’objet est au repos est la longueur propre \\\\(L_0\\\\).",
"answers": [
{
"answer_title": "Longueur propre",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Longueur contractée",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "Longueur apparente",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Longueur relative",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 5,
"question_title": "Un proton se déplace à \\\\(v = 2{,}4 \\\\times 10^8\\\\,\\\\mathrm{m/s}\\\\). Sa longueur propre est \\\\(1{,}0 \\\\times 10^{-15}\\\\,\\\\mathrm{m}\\\\). Quelle est sa longueur mesurée par un observateur fixe ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La longueur contractée est \\\\(L = 1{,}0 \\\\times 10^{-15} \\\\times \\\\sqrt{1 - (0{,}8)^2} = 1{,}0 \\\\times 10^{-15} \\\\times 0,6 = 6,0 \\\\times 10^{-16}\\\\,\\\\mathrm{m}\\\\).",
"answers": [
{
"answer_title": "6,0 \\\\(\\\\times 10^{-16}\\\\) m",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "8,0 \\\\(\\\\times 10^{-16}\\\\) m",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "1,0 \\\\(\\\\times 10^{-15}\\\\) m",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "2,4 \\\\(\\\\times 10^{-16}\\\\) m",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 6,
"question_title": "Si la vitesse relative \\\\(v = 0\\\\), alors la longueur contractée \\\\(L\\\\) vaut :",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Si \\\\(v = 0\\\\), alors \\\\(L = L_0 \\\\sqrt{1 - 0} = L_0\\\\).",
"answers": [
{
"answer_title": "La longueur propre \\\\(L_0\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Zéro",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "La moitié de \\\\(L_0\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Deux fois \\\\(L_0\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 7,
"question_title": "Un train de longueur propre \\\\(L_0 = 200\\\\,\\\\mathrm{m}\\\\) doit entrer dans un tunnel de \\\\(170\\\\,\\\\mathrm{m}\\\\) (mesuré depuis la Terre). Quelle doit être sa vitesse minimale ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La vitesse minimale est \\\\(v = c \\\\sqrt{1 - (\\\\frac{170}{200})^2} = 3,00 \\\\times 10^8 \\\\times 0,527 = 1,58 \\\\times 10^8\\\\,\\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "1,58 \\\\(\\\\times 10^8\\\\) m/s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "2,40 \\\\(\\\\times 10^8\\\\) m/s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "1,00 \\\\(\\\\times 10^8\\\\) m/s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "3,00 \\\\(\\\\times 10^8\\\\) m/s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 8,
"question_title": "Pour que la contraction des longueurs soit significative, il faut que :",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La contraction des longueurs n’est significative que pour des vitesses proches de celle de la lumière.",
"answers": [
{
"answer_title": "La vitesse soit proche de celle de la lumière",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "La vitesse soit très faible",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "L’objet soit très lourd",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "L’objet soit au repos",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 9,
"question_title": "Un astronaute mesure une règle de 2,00 m dans son vaisseau (au repos pour lui). Le vaisseau file à \\\\(0{,}9c\\\\) par rapport à la Terre. Quelle longueur cette règle a-t-elle pour un observateur terrestre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La longueur contractée est \\\\(L = 2,00 \\\\times \\\\sqrt{1 - (0,9)^2} = 2,00 \\\\times 0,436 = 0,872\\\\,\\\\mathrm{m}\\\\).",
"answers": [
{
"answer_title": "0,872 m",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "1,00 m",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "1,80 m",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "2,00 m",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 10,
"question_title": "Laquelle des affirmations suivantes est correcte concernant la contraction des longueurs ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La longueur contractée est toujours inférieure à la longueur propre et la contraction ne concerne que la direction du mouvement.",
"answers": [
{
"answer_title": "La longueur contractée est toujours inférieure à la longueur propre",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "La longueur contractée est toujours supérieure à la longueur propre",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "La contraction s’applique dans toutes les directions",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "La contraction dépend de la masse de l’objet",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 11,
"question_title": "Un vaisseau spatial mesure 50 m dans son propre référentiel. Il passe devant la Terre à \\\\(2,7 \\\\times 10^8\\\\,\\\\mathrm{m/s}\\\\). Quelle est sa longueur mesurée depuis la Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le rapport \\\\(v/c = 0,9\\\\). \\\\(L = 50 \\\\times \\\\sqrt{1 - (0,9)^2} = 50 \\\\times 0,436 = 21,8\\\\,\\\\mathrm{m}\\\\).",
"answers": [
{
"answer_title": "21,8 m",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "50 m",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "40,0 m",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "15,0 m",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 12,
"question_title": "Si la longueur contractée d’un objet est la moitié de sa longueur propre, quel est le rapport \\\\(v/c\\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Si \\\\(L = \\\\frac{L_0}{2}\\\\), alors \\\\(\\\\sqrt{1 - \\\\frac{v^2}{c^2}} = 0,5\\\\), donc \\\\(1 - \\\\frac{v^2}{c^2} = 0,25\\\\), donc \\\\(\\\\frac{v^2}{c^2} = 0,75\\\\), donc \\\\(v/c = 0,866\\\\).",
"answers": [
{
"answer_title": "0,866",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0,5",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,707",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "0,6",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 13,
"question_title": "Laquelle des situations suivantes n’entraîne PAS de contraction des longueurs ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Il n’y a pas de contraction des longueurs si l’objet est au repos par rapport à l’observateur.",
"answers": [
{
"answer_title": "L’objet est au repos par rapport à l’observateur",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "L’objet se déplace à 0,8c",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "L’objet se déplace à 0,5c",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "L’objet se déplace à 0,9c",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 14,
"question_title": "Si un objet a une longueur propre de 10 m et se déplace à 0,6c, quelle est sa longueur contractée ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La longueur contractée est \\\\(L = 10 \\\\times \\\\sqrt{1 - (0,6)^2} = 10 \\\\times 0,8 = 8,0\\\\,\\\\mathrm{m}\\\\).",
"answers": [
{
"answer_title": "8,0 m",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "6,0 m",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "10,0 m",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "7,0 m",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 15,
"question_title": "Quelle grandeur physique reste inchangée lors de la contraction des longueurs ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Seules les dimensions perpendiculaires au mouvement restent inchangées lors de la contraction des longueurs.",
"answers": [
{
"answer_title": "Les dimensions perpendiculaires au mouvement",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "La dimension dans la direction du mouvement",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "La longueur contractée",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "La vitesse de l’objet",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 16,
"question_title": "Un objet a une longueur contractée de 4,0 m lorsqu’il se déplace à 0,8c. Quelle est sa longueur propre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On a \\\\(L = L_0 \\\\sqrt{1 - (0,8)^2}\\\\), donc \\\\(L_0 = \\\\frac{L}{0,6} = \\\\frac{4,0}{0,6} = 6,67\\\\,\\\\mathrm{m}\\\\).",
"answers": [
{
"answer_title": "6,67 m",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "4,0 m",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "5,0 m",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "8,0 m",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 17,
"question_title": "Laquelle des affirmations suivantes est vraie ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La contraction des longueurs est une conséquence directe de la relativité restreinte d’Einstein.",
"answers": [
{
"answer_title": "La contraction des longueurs est une conséquence de la relativité restreinte",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "La contraction des longueurs dépend de la température",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "La contraction des longueurs dépend de la masse",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "La contraction des longueurs existe à toutes les vitesses",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 18,
"question_title": "Un objet se déplace à \\\\(0,99c\\\\). Quelle est la valeur de \\\\(\\\\sqrt{1 - \\\\frac{v^2}{c^2}}\\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule \\\\(\\\\sqrt{1 - (0,99)^2} = \\\\sqrt{1 - 0,9801} = \\\\sqrt{0,0199} = 0,141\\\\).",
"answers": [
{
"answer_title": "0,141",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0,01",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,9",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "0,707",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 19,
"question_title": "Si la vitesse d’un objet augmente, que devient sa longueur contractée ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Plus la vitesse augmente, plus la longueur contractée diminue.",
"answers": [
{
"answer_title": "Elle diminue",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Elle augmente",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "Elle reste constante",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Elle devient nulle",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 20,
"question_title": "Un objet de longueur propre 5,0 m se déplace à \\\\(0,8c\\\\). Quelle est sa longueur contractée ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La longueur contractée est \\\\(L = 5,0 \\\\times \\\\sqrt{1 - (0,8)^2} = 5,0 \\\\times 0,6 = 3,0\\\\,\\\\mathrm{m}\\\\).",
"answers": [
{
"answer_title": "3,0 m",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "4,0 m",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "5,0 m",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "2,0 m",
"is_correct": false,
"answer_order": 4
}
]
}
]
}