Category Archives: Physics

A volume of an iceberg’s tip

From the idiom “the tip of the iceberg” to the terrible disaster of the Titanic on the April 10th 1912 which was cause by the ship’s collision with the iceberg in the Atlantic Ocean. In this article a strict relation between the whole iceberg and its tip is calculated with application of the widely known Archimedes principle.

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An iceberg and its tip above water surface

The Archimedes principle describes the force which works on a material body which is submerged in other fluid. In general a value of this buoyancy force is equal to equivalent of the gravity force which was pushed out by the submerged material body; a direction of the buoyancy force is opposite to the gravity force.

\vec{F_{b}} = -\vec{g} \cdot d \cdot V

The iceberg presented above is in the static equilibrium, therefore, the vector of gravity force G is compensated by the vector of buoyancy force . Assuming that a chosen coordinate system shows that positive direction is upwards then:

\vec{F_{b}} - \vec{G}= \vec{0}

Previous equation, in scalar representation, can be written as

g \cdot d_{H_{2}O-LIQUID} \cdot (V - V') = \cdot d_{H_{2}O-ICE (SOLID)} \cdot V

After taking into account the numerical values for water’s density in solid and liquid state of condensation. It can be shown with quite good accuracy

V' = 0.0833 \cdot V

Thereby the tip of the iceberg constitutes less than the 90 percent of the iceberg. More detailed calculations are available at the Archimedes principle – example 1.

Physical pendulum

physical pendulum - motion equation

Physical pendulum is built with rigid body. One of rigid body ends is fixed to the ceiling. Rigid body is able to rotate around axis which is placed exactly in place where rigid’s end is fixed. Rotation axis is perpendicular to the plane of drawing. Rigid body has mass m and inertia I. Rigid body length is 2∙l. Note that inertia I is known for axis of rotations. If physical pendulum is in equilibrium position then it is not moving. In equilibrium position gravity force is balanced by rigid body’s reaction force. In a certain moment pendulum was deflected from its equilibrium and was inclined from vertical position by angle α. Pendulum is under gravity field, so gravity force works on it. Remember that physical pendulum is rigid body so gravity force is placed on rigid body’s gravity center C.

Physical pendulum – motion equation

Mathematical pendulum

mathematical pendulum - motion equation

Mathematical pendulum is built with massless rope with length l. One of rope’s ends is fixed to the ceiling. To the second end of rope is fixed to the material point with mass m. Material point is then hanged to the rope. When mathematical pendulum is in equilibrium material point is not moving. In equilibrium position gravity force is balanced by rope’s tension force. In a certain moment mathematical pendulum was deflected from its equilibrium and was inclined from vertical position by angle α. Mathematical pendulum is under gravity field, so gravity force works on it.

Mathematical pendulum – motion equation