Travail Et Energie — Quiz — Mouvement Sur Un Plan Incline

{
  "quiz_title": "Mouvement Sur Un Plan Incline",
  "quiz_slug": "04_mouvement_sur_un_plan_incline_quiz",
  "quiz_description": "Quiz Edu509 : Mouvement Sur Un Plan Incline",
  "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": "Un bloc de masse \\\\( 2{,}0 \\\\, \\\\mathrm{kg} \\\\) est posé sur un plan incliné d’un angle \\\\( 30^\\\\circ \\\\). On néglige les frottements. Quelle est la valeur de l’accélération du bloc le long du plan ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "L’accélération sur un plan incliné sans frottement est \\\\( a = g \\\\sin(\\\\alpha) \\\\). Ici, \\\\( g = 9{,}8 \\\\), \\\\( \\\\sin(30^\\\\circ) = 0{,}5 \\\\), donc \\\\( a = 9{,}8 \\\\times 0{,}5 = 4{,}9 \\\\, \\\\mathrm{m/s^2} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 4{,}9 \\\\, \\\\mathrm{m/s^2} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 9{,}8 \\\\, \\\\mathrm{m/s^2} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 2{,}0 \\\\, \\\\mathrm{m/s^2} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 3{,}5 \\\\, \\\\mathrm{m/s^2} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 2,
      "question_title": "Sur un plan incliné de \\\\( 20^\\\\circ \\\\), quelle est la composante du poids parallèle au plan pour un objet de \\\\( 5{,}0 \\\\, \\\\mathrm{kg} \\\\) ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La composante parallèle est \\\\( P_{\\\\parallel} = m g \\\\sin(\\\\alpha) = 5{,}0 \\\\times 9{,}8 \\\\times \\\\sin(20^\\\\circ) \\\\approx 5{,}0 \\\\times 9{,}8 \\\\times 0{,}342 = 16{,}8 \\\\, \\\\mathrm{N} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 16{,}8 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 9{,}8 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 46{,}0 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 23{,}4 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 3,
      "question_title": "Un objet de \\\\( 1{,}0 \\\\, \\\\mathrm{kg} \\\\) est posé sur un plan incliné de \\\\( 45^\\\\circ \\\\). Quelle est la composante du poids perpendiculaire au plan ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La composante perpendiculaire est \\\\( P_{\\\\perp} = m g \\\\cos(45^\\\\circ) = 1{,}0 \\\\times 9{,}8 \\\\times 0{,}707 = 6{,}93 \\\\, \\\\mathrm{N} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 6{,}93 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 9{,}8 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 4{,}9 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 0 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 4,
      "question_title": "Un bloc de \\\\( 3{,}0 \\\\, \\\\mathrm{kg} \\\\) descend un plan incliné de \\\\( 10^\\\\circ \\\\) sans frottement. Quelle est l’accélération du bloc ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "L’accélération est \\\\( a = g \\\\sin(\\\\alpha) = 9{,}8 \\\\times \\\\sin(10^\\\\circ) = 9{,}8 \\\\times 0{,}174 = 1{,}70 \\\\, \\\\mathrm{m/s^2} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 1{,}70 \\\\, \\\\mathrm{m/s^2} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 3{,}0 \\\\, \\\\mathrm{m/s^2} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 9{,}8 \\\\, \\\\mathrm{m/s^2} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 0{,}98 \\\\, \\\\mathrm{m/s^2} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 5,
      "question_title": "Un objet de \\\\( 4{,}0 \\\\, \\\\mathrm{kg} \\\\) est posé sur un plan incliné de \\\\( 25^\\\\circ \\\\). Quelle est la valeur de la réaction normale du support ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La réaction normale est \\\\( R = m g \\\\cos(\\\\alpha) = 4{,}0 \\\\times 9{,}8 \\\\times \\\\cos(25^\\\\circ) = 39{,}2 \\\\times 0{,}906 = 35{,}5 \\\\, \\\\mathrm{N} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 35{,}5 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 39{,}7 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 16{,}6 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 9{,}8 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 6,
      "question_title": "Un solide de \\\\( 0{,}5 \\\\, \\\\mathrm{kg} \\\\) est posé sur un plan incliné de \\\\( 40^\\\\circ \\\\), sans vitesse initiale. Quelle est la vitesse du solide à l’arrivée en bas du plan de \\\\( 1{,}2 \\\\, \\\\mathrm{m} \\\\) ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La vitesse à l’arrivée est \\\\( v = \\\\sqrt{2 a L} \\\\) avec \\\\( a = 6{,}3 \\\\), donc \\\\( v = \\\\sqrt{2 \\\\times 6{,}3 \\\\times 1{,}2} = \\\\sqrt{15{,}12} \\\\approx 3{,}89 \\\\, \\\\mathrm{m/s} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 3{,}89 \\\\, \\\\mathrm{m/s} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 2{,}40 \\\\, \\\\mathrm{m/s} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 6{,}30 \\\\, \\\\mathrm{m/s} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 1{,}20 \\\\, \\\\mathrm{m/s} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 7,
      "question_title": "Un bloc de \\\\( 2{,}0 \\\\, \\\\mathrm{kg} \\\\) est lâché sans vitesse initiale du haut d’un plan incliné de \\\\( 2{,}5 \\\\, \\\\mathrm{m} \\\\) de long, incliné à \\\\( 20^\\\\circ \\\\). Quelle est la vitesse du bloc à l’arrivée en bas du plan ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La vitesse finale est \\\\( v = \\\\sqrt{2 g h} \\\\) avec \\\\( h = 2{,}5 \\\\times \\\\sin(20^\\\\circ) = 0{,}855 \\\\), donc \\\\( v = \\\\sqrt{2 \\\\times 9{,}8 \\\\times 0{,}855} = \\\\sqrt{16{,}77} \\\\approx 4{,}1 \\\\, \\\\mathrm{m/s} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 4{,}1 \\\\, \\\\mathrm{m/s} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 2{,}5 \\\\, \\\\mathrm{m/s} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 6{,}3 \\\\, \\\\mathrm{m/s} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 3{,}0 \\\\, \\\\mathrm{m/s} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 8,
      "question_title": "Sur un plan incliné de \\\\( 15^\\\\circ \\\\), un bloc de \\\\( 3{,}0 \\\\, \\\\mathrm{kg} \\\\) est lâché sans vitesse initiale. Quelle est l’accélération du bloc ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "L’accélération est \\\\( a = g \\\\sin(15^\\\\circ) = 9{,}8 \\\\times 0{,}2588 = 2{,}54 \\\\, \\\\mathrm{m/s^2} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 2{,}54 \\\\, \\\\mathrm{m/s^2} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 3{,}0 \\\\, \\\\mathrm{m/s^2} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 9{,}8 \\\\, \\\\mathrm{m/s^2} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 1{,}50 \\\\, \\\\mathrm{m/s^2} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 9,
      "question_title": "Un objet de \\\\( 2{,}0 \\\\, \\\\mathrm{kg} \\\\) est posé sur un plan incliné de \\\\( 60^\\\\circ \\\\). Quelle est la composante parallèle du poids ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La composante parallèle est \\\\( P_{\\\\parallel} = m g \\\\sin(60^\\\\circ) = 2{,}0 \\\\times 9{,}8 \\\\times 0{,}866 = 16{,}97 \\\\, \\\\mathrm{N} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 16{,}97 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 9{,}8 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 19{,}6 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 8{,}49 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 10,
      "question_title": "Un objet de \\\\( 1{,}5 \\\\, \\\\mathrm{kg} \\\\) est lancé vers le haut d’un plan incliné à \\\\( 25^\\\\circ \\\\) avec une vitesse initiale de \\\\( 3{,}0 \\\\, \\\\mathrm{m/s} \\\\). Le plan mesure \\\\( 1{,}8 \\\\, \\\\mathrm{m} \\\\) de long. L’objet atteint-il le sommet du plan ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "L’énergie initiale est insuffisante pour atteindre le sommet, car \\\\( E_{c,0} = 6{,}75 \\\\mathrm{J} \\\\) et \\\\( E_{p,f} = 11{,}18 \\\\mathrm{J} \\\\).",
      "answers": [
        {
          "answer_title": "Non, il n’atteint pas le sommet.",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "Oui, il atteint le sommet avec une vitesse nulle.",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "Oui, il atteint le sommet avec une vitesse de \\\\( 1{,}2 \\\\, \\\\mathrm{m/s} \\\\).",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "Oui, il atteint le sommet avec une vitesse de \\\\( 2{,}0 \\\\, \\\\mathrm{m/s} \\\\).",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 11,
      "question_title": "Un bloc de \\\\( 2{,}0 \\\\, \\\\mathrm{kg} \\\\) descend un plan incliné de \\\\( 1{,}5 \\\\, \\\\mathrm{m} \\\\) de long, incliné à \\\\( 30^\\\\circ \\\\), sans vitesse initiale. Quelle est la hauteur verticale descendue ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La hauteur est \\\\( h = L \\\\sin(\\\\alpha) = 1{,}5 \\\\times 0{,}5 = 0{,}75 \\\\, \\\\mathrm{m} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 0{,}75 \\\\, \\\\mathrm{m} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 1{,}5 \\\\, \\\\mathrm{m} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 1{,}0 \\\\, \\\\mathrm{m} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 0{,}50 \\\\, \\\\mathrm{m} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 12,
      "question_title": "Un objet de \\\\( 0{,}8 \\\\, \\\\mathrm{kg} \\\\) est posé sur un plan incliné de \\\\( 35^\\\\circ \\\\). Quelle est la valeur de la réaction normale du support ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La réaction normale est \\\\( R = m g \\\\cos(35^\\\\circ) = 0{,}8 \\\\times 9{,}8 \\\\times 0{,}819 = 6{,}43 \\\\, \\\\mathrm{N} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 6{,}43 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 7{,}84 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 4{,}57 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 9{,}8 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 13,
      "question_title": "Un bloc de \\\\( 1{,}0 \\\\, \\\\mathrm{kg} \\\\) est posé sur un plan incliné de \\\\( 60^\\\\circ \\\\). Quelle est la composante du poids perpendiculaire au plan ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La composante perpendiculaire est \\\\( P_{\\\\perp} = m g \\\\cos(60^\\\\circ) = 1{,}0 \\\\times 9{,}8 \\\\times 0{,}5 = 4{,}9 \\\\, \\\\mathrm{N} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 4{,}9 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 8{,}5 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 9{,}8 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 0 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 14,
      "question_title": "Un objet de \\\\( 2{,}5 \\\\, \\\\mathrm{kg} \\\\) est posé sur un plan incliné de \\\\( 45^\\\\circ \\\\). Quelle est la composante parallèle du poids ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La composante parallèle est \\\\( P_{\\\\parallel} = m g \\\\sin(45^\\\\circ) = 2{,}5 \\\\times 9{,}8 \\\\times 0{,}707 = 17{,}32 \\\\, \\\\mathrm{N} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 17{,}32 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 24{,}5 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 9{,}8 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 12{,}25 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 15,
      "question_title": "Un bloc de \\\\( 4{,}0 \\\\, \\\\mathrm{kg} \\\\) descend un plan incliné de \\\\( 2{,}0 \\\\, \\\\mathrm{m} \\\\) de long, incliné à \\\\( 45^\\\\circ \\\\), sans vitesse initiale. Quelle est la vitesse du bloc à l’arrivée en bas du plan ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La hauteur est \\\\( h = 2{,}0 \\\\times 0{,}707 = 1{,}414 \\\\), donc \\\\( v = \\\\sqrt{2 \\\\times 9{,}8 \\\\times 1{,}414} = \\\\sqrt{27{,}7} \\\\approx 5{,}26 \\\\, \\\\mathrm{m/s} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 6{,}26 \\\\, \\\\mathrm{m/s} \\\\)",
          "is_correct": false,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 4{,}43 \\\\, \\\\mathrm{m/s} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 2{,}83 \\\\, \\\\mathrm{m/s} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 5{,}26 \\\\, \\\\mathrm{m/s} \\\\)",
          "is_correct": true,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 16,
      "question_title": "Un objet de \\\\( 3{,}0 \\\\, \\\\mathrm{kg} \\\\) est posé sur un plan incliné de \\\\( 30^\\\\circ \\\\). Quelle est la composante du poids parallèle au plan ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La composante parallèle est \\\\( P_{\\\\parallel} = m g \\\\sin(30^\\\\circ) = 3{,}0 \\\\times 9{,}8 \\\\times 0{,}5 = 14{,}7 \\\\, \\\\mathrm{N} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 14{,}7 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 25{,}5 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 9{,}8 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 19{,}6 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 17,
      "question_title": "Un bloc de \\\\( 2{,}0 \\\\, \\\\mathrm{kg} \\\\) est posé sur un plan incliné de \\\\( 45^\\\\circ \\\\). Quelle est la valeur de la réaction normale du support ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La réaction normale est \\\\( R = m g \\\\cos(45^\\\\circ) = 2{,}0 \\\\times 9{,}8 \\\\times 0{,}707 = 13{,}86 \\\\, \\\\mathrm{N} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 13{,}86 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 19{,}6 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 9{,}8 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 8{,}49 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 18,
      "question_title": "Un objet de \\\\( 1{,}2 \\\\, \\\\mathrm{kg} \\\\) est posé sur un plan incliné de \\\\( 20^\\\\circ \\\\). Quelle est la composante du poids perpendiculaire au plan ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La composante perpendiculaire est \\\\( P_{\\\\perp} = m g \\\\cos(20^\\\\circ) = 1{,}2 \\\\times 9{,}8 \\\\times 0{,}94 = 11{,}05 \\\\, \\\\mathrm{N} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 11{,}05 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 9{,}8 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 3{,}6 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 4{,}03 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 19,
      "question_title": "Un bloc de \\\\( 3{,}0 \\\\, \\\\mathrm{kg} \\\\) est posé sur un plan incliné de \\\\( 15^\\\\circ \\\\) et de \\\\( 3{,}0 \\\\, \\\\mathrm{m} \\\\) de long. Quel est le travail du poids lors de la descente complète du plan ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "Le travail du poids est \\\\( W = m g h \\\\) avec \\\\( h = 3{,}0 \\\\times \\\\sin(15^\\\\circ) = 0{,}776 \\\\), donc \\\\( W = 3{,}0 \\\\times 9{,}8 \\\\times 0{,}776 = 22{,}8 \\\\, \\\\mathrm{J} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 75{,}1 \\\\, \\\\mathrm{J} \\\\)",
          "is_correct": false,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 44{,}1 \\\\, \\\\mathrm{J} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 29{,}4 \\\\, \\\\mathrm{J} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 22{,}8 \\\\, \\\\mathrm{J} \\\\)",
          "is_correct": true,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 20,
      "question_title": "Un objet de \\\\( 2{,}0 \\\\, \\\\mathrm{kg} \\\\) est posé sur un plan incliné de \\\\( 30^\\\\circ \\\\). Quelle est la composante du poids perpendiculaire au plan ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La composante perpendiculaire est \\\\( P_{\\\\perp} = m g \\\\cos(30^\\\\circ) = 2{,}0 \\\\times 9{,}8 \\\\times 0{,}866 = 16{,}97 \\\\, \\\\mathrm{N} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( 16{,}97 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( 9{,}8 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( 19{,}6 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( 8{,}49 \\\\, \\\\mathrm{N} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    }
  ]
}