Mechanics for Beginners: With Numerous Examples |
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Page 233
... projected vertically upwards with a velocity u it rises for a time , u2 " reaches the height falls to the ground in the same 2g ' time as it took to rise , and strikes the ground with the velocity u downwards . EXAMPLES . IV . 1. A ...
... projected vertically upwards with a velocity u it rises for a time , u2 " reaches the height falls to the ground in the same 2g ' time as it took to rise , and strikes the ground with the velocity u downwards . EXAMPLES . IV . 1. A ...
Page 238
... projected in any direction not vertical and acted on by gravity will describe a parabola . Let a body be projected from the point A in any direction which is not vertical ; let AT be the space which would be de- scribed by the body in ...
... projected in any direction not vertical and acted on by gravity will describe a parabola . Let a body be projected from the point A in any direction which is not vertical ; let AT be the space which would be de- scribed by the body in ...
Page 239
... projected in any manner and acted on by gravity is called a Projectile ; thus we have shewn that the path of a Projectile is in general a parabola , and is a straight line in the particular case in which the body is projected vertically ...
... projected in any manner and acted on by gravity is called a Projectile ; thus we have shewn that the path of a Projectile is in general a parabola , and is a straight line in the particular case in which the body is projected vertically ...
Page 240
... projection is u2 u2 2g ' where u is the velocity of projection ; and is equal to the vertical 2g space through which a body must fall from rest under the action of gravity in order to acquire the velocity u . Now any point of the ...
... projection is u2 u2 2g ' where u is the velocity of projection ; and is equal to the vertical 2g space through which a body must fall from rest under the action of gravity in order to acquire the velocity u . Now any point of the ...
Page 241
... projection makes with the horizon . The distance of the focus from the point of projection u2 is by Art . 51. By the nature of the parabola the tan- 2g gent at any point makes equal angles with the focal dis- tance of that point and the ...
... projection makes with the horizon . The distance of the focus from the point of projection u2 is by Art . 51. By the nature of the parabola the tan- 2g gent at any point makes equal angles with the focal dis- tance of that point and the ...
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Common terms and phrases
ABCD acceleration algebraical sum angular points axis balance beam bisects body or system centre of gravity circle coefficient of friction components conditions of equilibrium cos² couple cylinder denote described determine distance equi Euclid example feet find the centre fixed point fulcrum given heavy particles Hence horizontal plane impact inches inclined plane Law of Motion length line of action lower block magnitude and direction mechanical advantage middle point move moveable Pully P+Q+R parabola Parallelogram of Forces perpendicular point of application point of projection position Power preceding Article pressure proposition radius ratio Resolved displacement respectively rest right angles rigid body Screw shew sides single resultant smooth straight line string which passes system of forces System of Pullies Take moments round tension three forces tion triangle uniform vanishes velocity vertical weight Wheel and Axle
Popular passages
Page 260 - Change of motion is proportional to the impressed force and takes place in the direction of the straight line in which the force acts.
Page 210 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.
Page 327 - ... that the squares of the periodic times are proportional to the cubes of the mean distances of the planets from the Sun.
Page 16 - Conversely, if three forces act on a particle, and each force is proportional to the sine of the angle between the other two...
Page 10 - ... represented in magnitude and direction by that diagonal of the parallelogram which passes through the particle.
Page 134 - This proportion teaches us that, when in equilibrium, the power is to the weight as the height of the plane is to its length.
Page 13 - The nature of force is now, and always will be, unknown.' Force is known only by its effects: A point or particle at rest cannot give itself any motion since there is no reason why it should move in one direction rather than another. But if the particle is not forced to move upon a determinate curve, the curve which it describes possesses a singular property, which has been discovered by metaphysical considerations, ie between any two points is less than on every other curve, if the body be free,...
Page 74 - The intersection of the straight lines which join the middle points of opposite sides of any quadrilateral, is the middle point of the straight line which joins the middle points of the diagonals (I.
Page 290 - A ball is projected in a given direction within a fixed horizontal hoop, so as to go on rebounding from the surface of the hoop ; find the limit to which the velocity will approach, and shew that it attains this limit in a finite time, e being less than 1.
Page 264 - If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone...