# A Treatise on Elementary Dynamics, for the Use of Colleges and Schools

Deighton, Bell, 1889 - 320 páginas
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### Contenido

 ON THE GEOMETRY OF A MOVING POINT AND THE FUNDAMENTAL 1 Acceleration 7 Parallelogram of Accelerations 15 Areal Velocity 21 Second Law of Motion 28 Independence of Forces 34 HorsePower and Energy 43 Examples on the Laws of Motion 54
 Examination 145 48 154 CHAPTER III 155 Range 158 Range on Inclined Plane 165 Envelope of System of Trajectories 171 Problems on Projectiles 177 CHAPTER IV 188

 Evidence for Laws of Motion 62 7 63 Examples of Change of Units 68 Unit of Length 78 Unit of Work 84 9 88 Transmission of Power by Belts 91 12 95 Examination 97 25 103 29 103 31 104 CHAPTER II 107 Space described during a Given Interval 114 Pressure of Shot on Target 122 Time of describing a Given Path 132 Examples of HorsePower 139
 Direct Impact of Smooth Spheres 194 Forces of Compression and Restitution 200 Continuous Impact 211 Kinetic Energy after Impact 218 Energy dissipated by Sudden Changes of Motion 224 51 237 CHAPTER V 243 Properties of the Cycloid 249 Cycloidal Pendulum 254 Centrifugal Force 261 Velocity of a Transverse Wave in a Stretched String 267 Initial Actions 273 Examination 279 CHAPTER VI 286 Velocity of Mean Square 293 Cooling produced by Expansion 299 ANSWERS 313

### Pasajes populares

Página 25 - 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.
Página 47 - Now it has been shewn that the product of a force into the velocity of its point of application in the direction of the force, is the rate at which it works.
Página 141 - The total energy of any material system is a quantity which can neither be increased nor diminished by any action between the parts of the system, though it may be transformed into any of the forms of which energy is susceptible.
Página 85 - It is therefore of precisely the same nature as the unit of work, and we have seen (Art. 77) that when work is done on a free particle, an equivalent amount of energy is always given to it ; this could not be the case were work and energy of different natures, that is, of different dimensions in the three fundamental mechanical units. The numerical measure of the kinetic energy of a moving particle will of course vary inversely as the unit of mass, inversely as the square of the unit of length, and...
Página 88 - A numerical value - will vary inversely as /, and directly in the duplicate ratio of t. In other words, the unit of acceleration varies directly as the unit of length, and inversely as the square of the unit of time ; and the numerical value of a given acceleration varies inversely as the unit of length, and directly as the square of the unit of time. It will be observed that these have been deduced as direct consequences from the fact that [the numerical value of] an acceleration is equal to [the...
Página 306 - A ball is projected from the middle point of one side of a billiard-table, so as to strike in succession one of the sides adjacent to it, the side opposite to it, and a ball placed in the centre of the table ; shew that, if a and...
Página 5 - A denote a concrete acceleration such that the velocity V is gained in the time T, and let a denote the unit of acceleration. Then, since the numerical value of the acceleration A is the numerical value of the velocity V divided by the numerical value of the time...
Página 30 - The unit of force in this case is that force which acting on the mass of a pound for one second generates in it a...
Página 181 - A plane is inclined at an angle of 30° to the horizon: a particle is projected from a point in it in a direction making an angle of 60° with the horizon.
Página 67 - ... directly as the unit of length, and inversely as the unit of time — a property which is also characteristic of the unit of velocity.