A tank, full of liquid of depth h, and top surface area A, is at rest on a frict

ID: 2279301 • 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) 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

v = sqrt(2 g h)

Using conservation of momentum:

F = v (dM/dt)

F is "kx"; so

k x = v (dM/dt)

==> k x = v (rho v (pi r^2))

==> k x = v^2 (rho pi r^2)

==> k x = (2 g h) (rho pi r^2)

==> r = (k x)/(2 g h rho pi)

The tank will have a simle harmonic motion.

M = rho h A

w = sqrt(k/m) = sqrt(k/(rho h A))

f = w/2pi

==> f = (sqrt(k/(rho h A)))/(2 pi)

At first the tank will be damped and finally it will have a motion a one direction with a decreasing acceleration.

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