19. 2013P3Q7 (part)
(a) A tube, sealed at one end, has a uniform area of cross-section
. Some sand is placed in
the tube so that it floats upright in a liquid of density
as shown in the figure.
The total mass of the tube and the sand is
The tube floats with its base a distance
below the surface of the liquid.
Derive an expression relating
. Explain your working.
(b) The tube is displaced vertically and then released.
For a displacement
, the acceleration
of the tube is given by the expression
is the acceleration of the free fall.
Explain why the expression leads to the conclusion that the tube is performing
simple harmonic motion.
(ii) The tube has a total mass
of 32 g and the area
of its cross-section 4.2 cm
. It is
floating in liquid of density
of 1.0 x 10
Show that the frequency of oscillation of the tube is 1.8 Hz.
Since the tube is in equilibrium, net force = 0.
, g, A and m are constants, => a
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