The pull recorded on the diagram includes the resistances due to acceleration and to the gradient on which the train is moving.
The acceleration therefore remains the same, and the velocity is unaltered.
Since the difference between the acceleration of gravity at the pole and at the equator is about 2%, the correction for latitude will be quite sensible in an instrument which might be used at various times in high and low latitudes.
By using a formula that takes into account the acceleration of gravity, you calculate the time it takes for an object to fall to the ground.
The acceleration of a falling body is naturally attributed to the presence of the earth; and, though the body approaches the earth in the course of its fall, it is easily recognized that the conditions under which it moves are only very slightly affected by this approach.
The alternate delay and acceleration of the eclipses are then merely apparent; they represent the changes in the length of the light-journey as the stars perform their wide circuit.
- If W 1 is the weight of the train in pounds and a the acceleration in feet per second, the force required to produce the acceleration is f = Wi a / g (19) And if V is the average speed during the change of velocity implied by the uniform acceleration a, the rate at which work is done by this force is fV= W1Va /g (20) or in horse-power units Time occupied in the change - 13 - 0 113.
When the service is frequent enough to give a good power factor continuously, the steam locomotive cannot compete with the electric motor for the purpose of quick acceleration, because the motors applied to the axles of a train may for a short time absorb power from the central station to an extent far in excess of anything which a locomotive boiler can supply.
Hence the elementary arc divided by the element of time is the rate of change of velocity of the moving-point, or in other words, the velocity in the hodograph is the acceleration in the orbit.
The rapid variation of certain groups of animals or the acceleration of certain organs is also not evidence of the sudden appearance of new adaptive characters.
During some revolutions there was evidence of a slight acceleration of the return, and during others there was not.
As a rule these equations are established immediately by determining the component acceleration of the fluid particle which is passing through (x, y, z) at the instant t of time considered, and saying that the reversed acceleration or kinetic reaction, combined with the impressed force per unit of mass and pressure-gradient, will according to d'Alembert's principle form a system in equilibrium.
The term "weight" denotes a magnitude of the same nature as a force; the weight of a body is the product of the mass of the body by the acceleration of gravity; in particular, the normal weight of a body is the product of the mass of the body by the normal acceleration of gravity.
Galileo proceeded to measure the motion of a body on a smooth, fixed, inclined plane, and found that the law of constant acceleration along the line of slope of the plane still held, the acceleration decreasing in magnitude as the angle of inclination was reduced; and he inferred that a body, moving on a smooth horizontal plane, would move with uniform velocity in a straight line if the resistance of the air, and friction due to contact with the plane, could be eliminated.
The year 1787 was rendered further memorable by Laplace's announcement on the 19th of November (Memoirs, 1786), of the dependence of lunar acceleration upon the secular changes in the eccentricity of the earth's orbit.
" When I say," says Mach, " that a body A exerts a force on a body B, I mean that B, on coming into contraposition with A, is immediately affected by a certain acceleration with respect to A."
The principal condition operating in the design of locomotives intended for local services with frequent stops is the degree of acceleration required, the aim of the designer being to produce an engine which shall be able to bring the train to its journey speed in the shortest time possible.
Sometimes, as on the Central London railway, the acceleration of gravity is also utilized; the different stations stand, as it were, on the top of a hill, so that outgoing trains are aided at the start by having a slope to run down, while incoming ones are checked by the rising gradient they encounter.
The acceleration of the departure of the Japanese is shown by the fact that in the eighteen months (July 1904 to January 1906) occurred 19,114 of the 42,313 departures in the sixty-six months from July 1900 to January 1906.1 After 1906, owing to restrictions by the Japanese government, immigration to Hawaii greatly decreased.
It has since been discovered, however, that the magnitude of the acceleration in question is not exactly the same at different places on the earth, the range of variation amounting to about 2%.
In addition to the foregoing list, various special locomotive types have been developed for suburban service, where high rates of acceleration and frequent stops are required.
Since high average speed on a line with frequent stops depends largely on rapidity of acceleration, the tendency in modern equipment is to secure as great an output of power as possible during the accelerating period, with corresponding increase in weight available for adhesion.
Motion is obtained from a continuous-current generator driven by an alternating motor with a very heavy fly-wheel, a combination known as the Ilgner transformer, which runs continuously with a constant draught on the generating station, the extremely variable demand of the winding engine during the acceleration period being met by the energy stored in the fly-wheel, which runs at a very high speed.
The reader should, however, notice that what is generally called electric force is the analogue in electricity of the so-called acceleration of gravity in mechanics, whilst electrification or quantity_of electricity is analogous to mass.
This view involves the denial of force as a cause, and the assertion that all we know about force is that the acceleration of one mass depends on that of another, as in mathematics a function depends on a variable; and that even Newton's third law of motion is merely a description of the fact that two material points determine in one another, without reciprocally causing, opposite accelerations.