A spring with spring constant 34N/m is attached to the ceiling, and a 4.6-cm-dia

Question

A spring with spring constant 34N/m is attached to the ceiling, and a 4.6-cm-diameter, 1.4kg metal cylinder is attached to its lower end. The cylinder is held so that the spring is neither stretched nor compressed, then a tank of water is placed underneath with the surface of the water just touching the bottom of the cylinder. When released, the cylinder will oscillate a few times but, damped by the water, quickly reach an equilibrium position.

When in equilibrium, what length of the cylinder is submerged?

Explanation / Answer

in eqb.

kx + d*V*g = 1.4 g        V = pi*(.023)^2 *x = .00166x           and d = density of water =1000

34x + 1.66x *9.8 = 1.4*9.8

x = 27.3 cm

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