Answer to Question #86814 in Mechanics | Relativity for Opopopo

Question #86814
Q1.A perfectly balanced weight and platform are supported by a steady water jet as shown in the figure below. If the total weight supported is 900 N, determine the jet velocity. Diameter of the water jet is 5 cm.

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Expert's answer
2019-03-27T05:48:23-0400

"F = 900N \\\\\nd = 5cm = 5 \\cdot 10^{-2}m\\\\\n\\rho = 1000 \\frac{kg}{m^3} \\\\\n\\pi \\approx 3.14"


"F_p = F_w = F"

Newton's second law => "F\\Delta t = mv" (*)

Where "m = V\\cdot\\rho", because of "V = S\\cdot h = S\\cdot v\\Delta t = \\pi\\cdot (\\frac{d}{2})^2 \\cdot v\\Delta t"


"F\\Delta t = v \\cdot \\rho \\cdot \\pi\\cdot (\\frac{d}{2})^2 \\cdot v\\Delta t"


"F = \\rho \\cdot \\pi\\cdot (\\frac{d}{2})^2 \\cdot v^2"

"v^2 = \\frac{F}{\\rho \\pi \\cdot (\\frac {d}{2})^2} = \\frac{900N}{1000\\frac{kg}{m^3} \\cdot 3.14 \\cdot (\\frac {5 \\cdot 10^{-2}} {2})^2m^2} = 458.5987 (\\frac{m}{s})^2"

Then the answer:

"v = 21.415 \\frac{m}{s}"


(*):

"F = ma \\\\\nF = m\\frac{v - 0}{\\Delta t} \\\\\nF \\Delta t = mv"

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