Problem 3.125 - Problem*3.125[Difficulty 3 Pail is swung in...

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Problem *3.125 [Difficulty: 3] V = 5 m/s d d R = 1 m r T Given: Pail is swung in a vertical circle. Water moves as a rigid body. Point of interest is the top of the trajectory. Find: (a) Tension in the string (b) Pressure on pail bottom from the water. Solution: We will apply the hydrostatics equations to this system. a g p G G ρ = + Governing Equations: (Hydrostatic equation) r r a g r p = + (Hydrostatic equation radial component) Assumptions: (1) Incompressible fluid (2) Rigid body motion (3) Center of mass of bucket and water are located at a radius of 1 m where V = r ω = 5 m/s Summing the forces in the radial direction: T M b M w + () g M b M w + a r = where a r V 2 r = Thus the tension is: TM b M w + V 2 r g = where: M b 15 N s 2 9.81 m × kg m Ns 2 × = M b 1.529 kg = and: M w ρ V = ρ π 4 d 2 h = M w 999 kg m 3 π 4 × 0.4 m 2 × 0.2 × m = M w 25.11 kg = Now we find T: T 1.529 25.11 + k g 5 m s
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