Un cube est posé sur un plan incliné et relié à un fil attaché à un poteau.
On représente ci-dessous la situation :
{"init": {"range": [[-9.0, 9.0], [-3.0, 12.0]], "scale": [20, 20]}, "line": [[[-8.0, -2.0], [8.0, -2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -1.0], [8.0, -1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 0.0], [8.0, 0.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 1.0], [8.0, 1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 2.0], [8.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 3.0], [8.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 4.0], [8.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 5.0], [8.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 6.0], [8.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 7.0], [8.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 8.0], [8.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 9.0], [8.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 10.0], [8.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 11.0], [8.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -2.0], [-8.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -2.0], [-7.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -2.0], [-6.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -2.0], [-5.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -2.0], [-4.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[-3.0, -2.0], [-3.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[-2.0, -2.0], [-2.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[-1.0, -2.0], [-1.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, -2.0], [0.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, -2.0], [1.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, -2.0], [2.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, -2.0], [3.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, -2.0], [4.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[5.0, -2.0], [5.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, -2.0], [6.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[7.0, -2.0], [7.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[8.0, -2.0], [8.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[-1.2480754415067656, 4.832050294337844], [-0.4160251471689219, 6.080125735844609], {"subtype": "segment"}], [[-0.4160251471689219, 6.080125735844609], [2.080125735844609, 4.416025147168922], {"subtype": "segment"}], [[2.080125735844609, 4.416025147168922], [1.2480754415067659, 3.1679497056621564], {"subtype": "segment"}], [[-6.0, 8.901387818865997], [-0.8320502943378438, 5.456088015091226], {"subtype": "segment"}], [[-6.0, 8.0], [-6.0, 10.0], {"subtype": "segment"}], [[6.0, 0.0], [-6.0, 8.0], {"subtype": "segment"}], [[-6.0, 0.0], [6.0, 0.0], {"subtype": "segment"}]], "arc": [[[6.0, 0.0], [1.5, 1.5], 146.30993247402023, 180.0, false, {}]], "circle": [[[0.4160251471689218, 4.624037720753383], 0.1, {"fill": "black"}]], "label": [[[4.0, -0.5], "\\alpha", "above", {}], [[-0.0839748528310782, 4.124037720753383], "G", "above", {}]]}
On considère à présent le solide comme un point pour effectuer le bilan des forces.
On représente la situation ci-dessous :
{"init": {"range": [[-5.0, 5.009615384615385], [-9.0, 7.0]], "scale": [40, 40]}, "line": [[[-4.0, -8.0], [4.0, -8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -7.0], [4.0, -7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -6.0], [4.0, -6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -5.0], [4.0, -5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -4.0], [4.0, -4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -3.0], [4.0, -3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -2.0], [4.0, -2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -1.0], [4.0, -1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, 0.0], [4.0, 0.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, 1.0], [4.0, 1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, 2.0], [4.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, 3.0], [4.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, 4.0], [4.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, 5.0], [4.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, 6.0], [4.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -8.0], [-4.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-3.0, -8.0], [-3.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-2.0, -8.0], [-2.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-1.0, -8.0], [-1.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, -8.0], [0.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, -8.0], [1.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, -8.0], [2.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, -8.0], [3.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, -8.0], [4.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 0.0], [2.769230769230769, 4.153846153846154], {"subtype": "segment", "arrow-end": "classic-wide-long"}], [[0.0, 0.0], [-2.769230769230769, 1.8461538461538456], {"subtype": "segment", "arrow-end": "classic-wide-long"}], [[0.0, 0.0], [0.0, -6.0], {"subtype": "segment", "arrow-end": "classic-wide-long"}]], "circle": [[[0.0, 0.0], 0.1, {"fill": "black"}]], "label": [[[0.0, 0.0], "G", "above", {}], [[1.8838455612180907, 1.7441029591879396], null], [[-1.7174355023505221, 0.4238467464742165], null], [[0.6, -3.0], null], [[1.0, -4.0], "\\overrightarrow{\\rm P}", "above", {}], [[4.384615384615385, 1.076923076923077], "\\overrightarrow{\\rm R}", "above", {}], [[-0.8846153846153846, 0.9230769230769228], "\\overrightarrow{\\rm T}", "above", {}]]}
Données
- - Accélération de la pesanteur : \( g = 9,81\:\text{m}\mathord{\cdot}\text{s}^{-2} \)
- - Masse du solide : \( m = 459\:\text{g} \)
En calculant graphiquement l'échelle des forces représentés, donner la valeur, en Newton (N), representée par 1
carreau.
On donnera la réponse avec \( 2 \) chiffres significatifs et suivie de l'unité qui convient.