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A Treatise on Analytical Statics: With Numerous Examples
I. (Isaac) Todhunter
No preview available - 2012
action angle application attached attraction axes axis base beam body centre of gravity circle co-ordinates components condition cone connected considered constant couple curve cylinder denote density determine direction displacement distance drawn element ellipsoid equal equation equilibrium example expression extremities face figure fixed point forces acting friction give given heavy Hence hold horizontal inclined integrate joining length limits magnitude mass moments move normal obtain opposite origin parallel particle passing perpendicular placed plane portion position pressure proportional proposition pully radius remain represented resolved respectively rest resultant right angles rigid rough round shell shew sides similar Similarly single smooth solid sphere straight line string suppose surface tangent tension tion triangle ultimately uniform vanish vertex vertical virtual velocities volume weight whole
Page 15 - ... the resolved part of the resultant is equal to the sum of the resolved parts of the components.
Page 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.
Page 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...
Page 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...
Page 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.
Page 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.
Page 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.
Page 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...
Page 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.
Page 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°.