A Treatise on Analytical Statics: With Numerous ExamplesMacmillan, 1866 - 364 من الصفحات |
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angular points attracted particle axes beam centre of gravity circle co-ordinates coefficient of friction cone constant couple curve cylinder denote density displacement distance ds ds elastic string element ellipsoid equal equation equi find the centre fixed point forces acting formulæ frustum Hence horizontal plane inclined plane indefinitely integrate lamina latus rectum law of attraction length librium mass middle point origin P₁ parallel forces passing perpendicular point of application polygon portion position of equilibrium pressure proposition pully radius resolved rest resultant attraction right angles rigid body round the axis shell shew shewn sides Similarly single force single resultant smooth solid sphere spheroid suppose surface system of forces tangent tension tetrahedron tion triangle uniform vanish vertex virtual velocities weight ΣΧ
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الصفحة 15 - ... the resolved part of the resultant is equal to the sum of the resolved parts of the components.
الصفحة 283 - ... 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.
الصفحة 225 - ... 54. Motion on a surface. We shall next proceed to consider the motion of a particle which is free to move on a smooth surface, and is acted on by any forces. Let (X, Y, Z) be the components, parallel to fixed rectangular axes, of the external force on the particle, not including the pressure of the surface: let (x, y, z) be the coordinates and v the velocity of the particle, s the arc and p the radius of curvature of its path, ^ the angle between the principal normal to the...
الصفحة 41 - Hence the moment of the resultant couple is equal to the sum of the moments of the original couples. If one of the couples, as...
الصفحة 252 - ... c is the length of a portion of the chain whose weight is equal to the tension at the lowest point, and h the length of the end that hangs down vertically.
الصفحة 88 - ... at the top of the inclined plane, hangs vertically and supports a weight; the portion of the string between the cylinder and the pully is horizontal.
الصفحة 362 - A pack of cards is laid on a table ; each projects in the direction of the length of the pack beyond the one below it; if each projects as far as possible, prove that the distances between the extremities of the successive cards will form an harmonic progression.
الصفحة 298 - It may he shewn also that two such spheres attract each other in the same manner as if each were condensed at its centre. For consider any element of mass forming part of the first sphere; the attraction of this on the second sphere will...
الصفحة 166 - Five pieces of a uniform chain are hung at equidistant points along a rigid rod without weight, and their lower ends are in a straight line passing through one end of the rod; find the centre of gravity of the system.
الصفحة 61 - One end of a string is fixed to the extremity of a smooth uniform rod, and the other to a ring without weight which passes over the rod, and the string is hung over a smooth peg. Determine the least length of the string for which equilibrium is possible, and shew that the inclination of the rod to the vertical cannot be less than 45°.