Problem 3.122 - Problem*3.122[Difficulty 3 Given...

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Problem *3.122 [Difficulty: 3] Given: Rectangular container of base dimensions 0.4 m x 0.2 m and a height of 0.4 m is filled with water to a depth of d = 0.2 m. Mass of empty container is M c = 10 kg. The container slides down an incline of θ = 30 deg with respect to the horizontal without friction. Find: (a) The angle of the water surface relative to the horizontal. (b) The slope of the free surface for the same acceleration up the plane. θ y x α Solution: We will apply the hydrostatics equations to this system. a g p G G ρ = + Governing Equations: (Hydrostatic equation) a M F G G = (Newton's Second Law) Assumptions: (1) Incompressible fluid (2) Rigid body motion x a x p = x a x p = y a g y p = () y a g y p + = Writing the component relations: dy y p dx x p dp + = We write the total differential of pressure as: Now along the free surface of the water dp = 0. Thus: y x a g a y p x p dx dy + = = and α atan dy dx = To determine the acceleration components we analyze a free-body diagram:
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