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The range and the maximum height of the projectile do not depend upon its mass. Hence range and maximum height are equal for all bodies that are thrown with the same velocity and direction. The horizontal range d of the projectile is the horizontal distance it has traveled when it returns to its initial height (=).
Jurin's law, or capillary rise, is the simplest analysis of capillary action —the induced motion of liquids in small channels [1] —and states that the maximum height of a liquid in a capillary tube is inversely proportional to the tube's diameter. Capillary action is one of the most common fluid mechanical effects explored in the field of ...
Brunt–Väisälä frequency. In atmospheric dynamics, oceanography, asteroseismology and geophysics, the Brunt–Väisälä frequency, or buoyancy frequency, is a measure of the stability of a fluid to vertical displacements such as those caused by convection. More precisely it is the frequency at which a vertically displaced parcel will ...
The first equation shows that, after one second, an object will have fallen a distance of 1/2 × 9.8 × 1 2 = 4.9 m. After two seconds it will have fallen 1/2 × 9.8 × 2 2 = 19.6 m; and so on. On the other hand, the penultimate equation becomes grossly inaccurate at great distances. If an object fell 10 000 m to Earth, then the results of both ...
The data is in good agreement with the predicted fall time of /, where h is the height and g is the free-fall acceleration due to gravity. Near the surface of the Earth, an object in free fall in a vacuum will accelerate at approximately 9.8 m/s 2 , independent of its mass .
[19] [20] David Gregory wrote a treatise on the catenary in 1697 [12] [21] in which he provided an incorrect derivation of the correct differential equation. [20] Euler proved in 1744 that the catenary is the curve which, when rotated about the x-axis, gives the surface of minimum surface area (the catenoid) for the given bounding circles. [1]
The metacentric height (GM) is a measurement of the initial static stability of a floating body [1]. It is calculated as the distance between the centre of gravity of a ship and its metacentre. A larger metacentric height implies greater initial stability against overturning. The metacentric height also influences the natural period of rolling ...
Euler's critical load or Euler's buckling load is the compressive load at which a slender column will suddenly bend or buckle. It is given by the formula: [1] where. P c r {\displaystyle P_ {cr}} , Euler's critical load (longitudinal compression load on column), E {\displaystyle E} , Young's modulus of the column material, I {\displaystyle I ...