A tank, full of liquid of depth h, and top surface area A, is at rest on a frict
ID: 2278849 • Letter: A
Question
A tank, full of liquid of depth h, and top surface area A, is at rest on a
frictionless table. The liquid (density = ?) is pouring horizontally out of a
hole of radius r located at the bottom of the tank. The tank is pressing
against a spring of constant k, that is compressed a distance x, from equilibrium. A) . (a) Find the radius of the hole in terms of the h, k, ?, x, and g the acceleration of gravity. The hole is suddenly plugged by an object
from the inside of the tank. (b) Describe the subsequent motion. (c) What is the frequency of
this oscillation in terms of h, k, ?, and A. The object is then jarred from it
A tank, full of liquid of depth h, and top surface area A, is at rest on a frictionless table. The liquid (density = ?) is pouring horizontally out of a hole of radius r located at the bottom of the tank. The tank is pressing against a spring of constant k, that is compressed a distance x, from equilibrium. A) . (a) Find the radius of the hole in terms of the h, k, ?, x, and g the acceleration of gravity. The hole is suddenly plugged by an object from the inside of the tank. (b) Describe the subsequent motion. (c) What is the frequency of this oscillation in terms of h, k, ?, and A. The object is then jarred from it's position and water begins to flow again. d) describe the subsequent motion over time as the water level decreaseExplanation / Answer
a) F = kx
velocity of water coming out = sqrt(2gH)....toricelli's theorm
Force exerted by water = v*dm/dt = v* v* pi*r^2*row
v* v* pi*r^2*row = k * x
r^2 = k x/( v^2 * pi*row)
r= sqrt ( k x/( v^2 * pi*row))
b) subsequent motion is a shm(simple harmonic motion)
c) f = 1/2pi * sqrt( m/k)
d) The subsequent motion will be a damped simple harmonic motion. which finally comes to rest
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