Theoretical Mechanics: With an Introduction to the Calculus ; Designed as a Text-book for Technical Schools and Colleges, and for the Use of Engineers, Architects, Etc, Volume 1 |
Common terms and phrases
a₁ abscissas acceleration axle b₁ b₂ body C₁ centre of gravity co-ordinates coefficient of friction components compression consequently contrary cord corresponding couple cross-section curvature curve D₁ denotes determined direction distance equal equation equilibrium F₁ F₂ feet flexure forces P₁ formula G₁ G₂ girder h₁ hence horizontal inches inclined plane iron kilograms L₁ latter length lever limit of elasticity M₁ mechanical effect modulus of elasticity motion N₁ neutral axis obtain ordinates P₁ P₂ parabola parallel parallelogram perpendicular point of application portion pounds pressure proof load proof strength Q₁ r₁ radius resultant rope rotation S₁ S₂ space described substitute surface tang tangent tangential angle tension tion triangle uniformly V₁ variable velocity vertical W₁ whence width x₁ Y₁
Popular passages
Page 282 - ... when one of them is equal and opposite to the resultant of the other two (§ 87). In like manner the resultant R of the force P and of one of the tensions S, is equal and opposite to the second tension S*, etc.
Page 122 - ... formula more easy, assist the memory, protect us from many errors, and serve also directly for the determination of quantities which may be required, are of the greatest use in mechanics. In uniform motion, the space («) is the product (ct) of the velocity and the time, and in Geometry the area of a rectangle is equal to the product of the base by the altitude ; we can there-fore represent the space described (s) by a rectangle ABCD, Fig. 52, whose base AB is the time t, and whose altitude AD...
Page v - In his preface to the first edition of his work the author thus stated his design (we quote from the translation before us) : — " My principal effort has been to obtain the greatest simplicity in enunciation and demonstration, and to treat all the important laws in their practical applications without the aid of the higher mathematics. If we consider how many subjects a technical man must master in order to accomplish...
Page 304 - Hence, in a movable pulley, the force is to the load as the radius of the pulley is to the chord of the arc covered by the string. If a = 2 r, IE if the string covers a semicircle, Fig. 248, the force is a minimum and is P = $ R ; if « = r or if 60° of the pulley is covered by the string, we have P — R.
Page 187 - ... force of inertia ? Principle of the independence and composition of the effects of forces. Forces proportional to the acceleration which they produce on the same body. Composition of forces. Relation between the accelerating force, the pressure, and the mass. Definition of the work done by a force. The work done by the resultant is equal to the sum of the works done by the components. Moment...
Page 143 - ... directly as the square of the velocity, and inversely as the radius of curvature, or directly as the greatness of the curvature. EXAMPLE. — The radius of curvature of the parabolic trajectory produced...
Page 508 - ... the force P at the end A of the entire spring they are bent in arcs of circles of nearly or exactly the same radius. The force P bends the lowest triangular piece AA of the the entire spring ABH, Fig.
Page 269 - P would be moved a distance p along the axis. Assuming that there is no friction, the equation for the equality of the work at the handle and at the screw is: F27T/ =, Pp.
Page 256 - If two forces acting perpendicularly on a straight lever in opposite directions and on the same side of the fulcrum balance each other, they are inversely as their distances from the fulcrum ; and the pressure on the fulcrum is equal to the difference of the forces.
Page 157 - Prussian pound is also a nnit referred to the weight of water. A Prussian cubic foot of distilled water weighs at 15° R. in vacua 66 Prussian pounds. Now a Prussian foot is = 139,13 Paris lines = 0,3137940 meter; whence it follows that a Prussian pound = 467,711 grams. The Prussian new or custom-house pound weighs exactly .| kilogramm. The English pound is determined by the weight of a cubic foot of water at a temperature of 39°, 1 F. The pound is equal to 453,5926 grams. A cubic foot of water...