## Key and Supplement to Elementary Mechanics |

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acceleration according action amount angle angular velocity answers to exercises applied Article attraction axis base cause centimetre centre of gravity centrifugal force centripetal force considered cubic centimetre cubic foot density diameter distance earth equal the weight equation of moments equilibrium fall feet per second force acting force of gravity friction given gives hence Infinitesimal Calculus inversely kinetic energy length less liquid measure ment metre miles per hour molecule momentum moon motion move nearly opposite orbit origin of moments oscillation overcome parabola pendulum plane point of application pounds pressure produce rotation pull quantity of matter radius rate of change resistance result side sin2 Sir Isaac Newton solutions of examples sphere stone stress string Substituting surface Take the origin temperature tension tion triangle uniform vibration wheel

### Popular passages

Page 187 - Pendulum vibrating Seconds of Mean Time in the Latitude of London in a Vacuum at the Level of the Sea...

Page 11 - To form some conception of the degree of coarse-grainedness indicated by this conclusion, imagine a rain drop, or a globe of glass as large as a pea, to be magnified up to the size of the earth, each constituent molecule being magnified in the same proportion. The magnified structure would be coarser grained than a heap of small shot, but probably less coarse grained than a heap of cricketballs.

Page 162 - Whence a sphere of one foot in diameter, and of a like nature to the earth, would attract a small body placed near its surface with a force...

Page 31 - 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...

Page 185 - At the centres of suspension and oscillation there were two triangular apertures to admit the knife edges on which the body rested while making its oscillations. Having thus the means of measuring the length L with accuracy, it remains to determine the time T. This is effected by comparing the vibrations of the body with those of a clock. The time of a single vibration or of any small arbitrary number of vibrations cannot be observed directly, because this would require the fraction of a second of...

Page 70 - Vis Viva, or Kinetic Energy, of a moving body is proportional to the mass and the square of the velocity, conjointly. If we adopt the same units of mass and velocity as before, there is particular advantage in defining kinetic energy as half the product of the mass into the square of its velocity.

Page 11 - The four lines of argument which I have now indicated lead all to substantially the same estimate of the dimensions of molecular structure. Jointly they establish with what we cannot but regard as a very high degree of probability the conclusion that, in any ordinary liquid, transparent solid, or seemingly opaque solid, the mean distance between the centres of contiguous molecules is less than the hundred-millionth, and greater than the two thousand-millionth of a centimetre.

Page 10 - ... (or six thousand million million million). The densities of known liquids and solids are from five hundred to sixteen thousand times that of atmospheric air at ordinary pressure and temperature ; and, therefore, the number of molecules in a cubic centimetre may be from 3 x 10M to 10* (that is, from three million million million million to a hundred million million million million).

Page 205 - But from this table it appears that the air, in proceeding upwards, is rarefied in such manner, that a sphere of that air which is nearest to the earth, of but one inch in diameter, if dilated with that rarefaction which it would have at the height of one semidiameter of the earth, would fill all the planetary regions as far as the sphere of Saturn, and a great way beyond; and at the height of ten semidiameters of the earth would fill up more space than is contained in the whole heavens on this side...

Page 184 - ... The period of this miniature pendulum was adjusted so as to be as nearly equal as possible to that of the sphere and wire. The influence on the period of the latter system is then negligible, and the knife-edge may be taken as the point of suspension. The second method above referred to is based on the principle of the convertibility of the centres of suspension and oscillation. A pendulum, whose precise form is unimportant, is constructed with two knife-edges facing one another, as nearly as...