A Treatise on Analytical Statics with Numerous Examples |
Other editions - View all
Common terms and phrases
attracted particle axes beam centre of gravity circle co-ordinates coefficient of friction cone constant cos² couple curve cylinder denote density diagonal displacement distance ds ds dx dy dy dz elastic string element ellipsoid equal equation equi find the centre fixed point forces acting frustum Hence horizontal plane inclined plane integrate lamina latus rectum law of attraction length librium mass middle point obtain origin P₁ parallel forces passing perpendicular point of application polygon portion position of equilibrium proposition pully radius resolved rest resultant attraction right angles rigid body round the axis shell shew shewn sides sin² single force smooth sphere straight line suppose surface system of forces tangent tension tetrahedron three forces tion triangle uniform vanish vertex virtual velocities weight y₁
Popular passages
Page 15 - Art. 26, shews that the resolved part of the resultant in any direction is equal to the sum of the resolved parts of the components...
Page 72 - To find the conditions of equilibrium of any number of forces acting upon a particle.
Page 10 - If a moving point possess simultaneously velocities which are represented in magnitude and direction by the two sides of a parallelogram drawn from a point, they are equivalent to a velocity which is represented in magnitude and direction by the diagonal of the parallelogram passing through the point.
Page 65 - Forces P, Q, R act along the sides of a triangle ABC, and their resultant passes through the centers of the inscribed and circumscribed circles. Prove that P _ Q _ R cos B — cos C cos C — cos A cos A — cos B 5.
Page 289 - ... the percussive action is the same as if the whole mass of the body were concentrated at that point, is called the center of percussion. This point is located at the same point as the center of oscillation. CENTER REAMERS. A " center reamer " is a reamer the teeth of which meet in a point.
Page 60 - Neglecting the weight of the rod, find the tension of the string and the action at the hinge. 4. A uniform heavy rod AB has the end A in contact with a smooth vertical wall, and one end of a string is fastened to the rod at a point C, such that...
Page 258 - ... the sphere may be divided into two equal portions by means of a vertical plane without disturbing the equilibrium. 29. Shew that if a chain exactly surrounds a smooth vertical circle, so as to be in contact at the lowest point without pressing, the whole pressure on the circle is double the weight of the chain, and the tension at the highest point is three times that at the lowest. 30. Two strings without weight of the same length have each of their ends fixed at each of two points in the same...
Page 203 - AB is a rod capable of turning freely about its extremity A, which is fixed ; CD is another rod equal to 2AB, and attached at its middle point to the extremity B of the former, so as to turn freely about this point; a given force acts at C in the direction CA, find the force which must be applied at D in order to produce equilibrium.