| University of Cambridge, Sir Thomas Gery Cullum - 1830
...attractive or repulsive force, the tension at any point is inversely as the perpendicular from the center **of force upon the tangent at that point. 8. Find the...the square of the velocity, find the equation to the** carve described ; and when the resistance vanishes, shew that it is the equation to a parabola. TUESDAY... | |
| Miles Bland - Trigonometry - 1830 - 374 pages
...moving in directions making equal angles with the horizon, then will t 2 "* = 1 + 2ns'. 85. If a body **be projected in a medium, the resistance of which varies as the** velocity, and be acted on by gravity ; and another be projected in vacuo, at the same angle, and with... | |
| Samuel Earnshaw - Attractions - 1832 - 185 pages
.../?, v = 0, 197. To determine the motion of a body descending in a circular arc, acted on by gravity **in a medium, the resistance of which varies as the square of the velocity.** Using the notation of Art. 113, and putting v for the velocity at P, we have the accelerating force... | |
| Mathematics - 1836
...upon its circumference ; find the velocity of the chain at the end of a given time. 118. If a body **be projected in a medium, the resistance of which varies as the** velocity, and be acted on by gravity, and another be projected in vacua at the same angle, and with... | |
| William Walton - Mechanics - 1842 - 451 pages
...differential equation to the curve in x and r. Euler; Mechan, torn. п. р. 246. (4) To find the tautochrone **in a medium the resistance of which varies as the square of the velocity,** the particle being acted on by gravity. Let 0 (fig. 150) be the point to which the particle is always... | |
| Samuel Earnshaw - Attractions - 1844 - 372 pages
...the velocity of the body. Hence the ultimate value of PT is . 302. A heavy body descends from rest **in a medium, the resistance of which varies as the square of the velocity,** toJlnd the space described in a given time. Let a be the space descended in the time t ; \/~kdfs Vg... | |
| William Walton - Fluid mechanics - 1847 - 230 pages
...— 437. 4. To find the centre of resistance on a semicircular plate, revolving about its diameter **in a medium, the resistance of which varies as the square of the velocity.** Let ft> denote the angular velocity of revolution, a the radius of the circle, x the distance of the... | |
| University of Cambridge, Sir Thomas Gery Cullum - 1849
...the motion of a material particle which falls from rest under the action of a constant force, through **a medium the resistance of which varies as the square of the velocity.** Shew that the velocity of the particle never exceeds a certain limiting value, to which it approximates... | |
| Bartholomew Price - Calculus - 1856
...particle projected with a given velocity in a line inclined at a given angle to the horizon, and moving **in a medium the resistance of which varies as the square of the velocity.** In this case the equations of motion are, as in Art. 302, dx _ ,dsdx ~w = ~ dtdi (70) rf**~ dt dt If... | |
| 1865
...moves being uniform, and the resistance varying as the square of the velocity. (10) If one particle **be projected in a medium, the resistance of which varies as the** velocity, and be acted on by a constant force parallel to a given line, and another be projected in... | |
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