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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 capillary length or capillary constant is a length scaling factor that relates gravity and surface tension. It is a fundamental physical property that governs the behavior of menisci, and is found when body forces (gravity) and surface forces (Laplace pressure) are in equilibrium. The pressure of a static fluid does not depend on the shape ...
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 height to which the column is lifted is given by Jurin's law: [8] = where h is the height the liquid is lifted, γ la is the liquid–air surface tension, ρ is the density of the liquid, r is the radius of the capillary, g is the acceleration due to gravity,
[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]
Escape speed at a distance d from the center of a spherically symmetric primary body (such as a star or a planet) with mass M is given by the formula [2] [3] = = where: G is the universal gravitational constant (G ≈ 6.67×10 −11 m 3 ·kg −1 ·s −2)