Problem 1.8[Difficulty: 2]Given:Small particle accelerating from rest in a fluid. Net weight is W, resisting force is FD= kV, where V is speed. Find:Distance required to reach 95 percent of terminal speed, Vt. Solution:Consider the particle to be a system. Apply Newton's second law. Basic equation: ∑Fy= mayAssumptions: 1. W is net weight. 2. Resisting force acts opposite to V. Then, dVWdVdtgdyFWkV = mamVyy=−==∑or V dVkWgdy1V−=At terminal speed, ay= 0 and WtkVV==. Then gVdV
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