A Treatise on Statics: Containing the Fundamental Principles of Electrostatics and Elasticity |
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angle of friction attraction axes axis beam centre of gravity centre of mass centroid circle co-ordinates coefficient of friction components conductor cone constant couple curve cylinder denote density distance dx dy dy dz element element plane ellipse ellipsoid elongation equation of virtual example extremity find the position fixed point forces acting funicular given Hence inclined plane integral internal forces intersection length line of action m₁ middle point motion normal P₁ P₂ particle perpendicular polygon portion position of equilibrium potential pressure quadric radius rectangular resultant right line rigid body rope rotation rough round shearing shearing stress sides smooth sphere strain stress string suppose surface system of forces tangent tension Theorem three forces total resistance triangle uniform vertex vertical plane virtual displacement weight zero
Popular passages
Page 400 - that every particle of matter in the universe attracts every other particle, with a force whose direction is that of the line joining the two, and whose magnitude is directly as the product of their masses, and inversely as the square of their distances from each other.
Page 209 - A frustum of a solid right cone is placed with its base on a rough inclined plane, the inclination of which is gradually increased ; determine the nature of the initial motion of the body.
Page 147 - 2r" £>" 2 € 'tvo e • 3. Find the position of equilibrium of a uniform heavy beam, one end of which rests against a smooth vertical plane, and the other against the internal surface of a given fixed smooth sphere. Let the length of the beam...
Page 94 - Prove that the algebraic sum of the moments of two concurrent forces about any point in their plane is equal to the moment of their resultant about the same point.
Page 283 - Ox intersects the revolving figure, the theorem still applies with the convention that the volumes generated by the portions of the figure at opposite sides of Ox are affected with opposite signs.
Page 251 - The lines joining the middle points of the opposite sides of a quadrilateral bisect each other.
Page 107 - COR. 1. Whatever be the path described by the pole, the point of intersection of the extreme sides of the funicular describes a fixed right line. This is the line of action of the resultant of the given system of forces. COR. 2. The point of intersection of any two sides of a funicular describes a fixed right line, when the pole varies in any manner. Thus the sides flmf2 a,ndftf6 will always intersect on the line of action of the resultant of the forces P2, P3, P4.
Page 340 - The tension at. any point of the catenary is equal to the weight of a portion of the string whose length is equal to the ordinate of the point.
Page 133 - Condition of Equilibrium of a Body under the Action of three Forces in one Plane. If three forces maintain a; body in equilibrium, their lines of action must meet in a point, or be parallel. For, take moments round the point of intersection of two of them, P and Q. The sum must (Art.
Page 383 - A machine may be defined either from a statical or from a kinematical point of view. Regarded statically, it is any instrument by means of which we may change the direction, magnitude, and point of application of a given force ; and regarded kinematically, it is any instrument by means of which we may change the direction and velocity of a given motion.