A Treatise on Analytical Statics with Numerous Examples |
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applied attracted particle axes beam centre of gravity circle co-ordinates coefficient of friction component cone constant curve cylinder denote density diagonal distance ds ds dx dy dy dz element equal equation equi find the centre fixed point forces acting frustum given forces Hence horizontal plane inclined plane integrate lamina latus rectum length line of action m₁ mass middle point motion normal opposite P₁ P₂ parabola parallel forces passing point of application polygon portion position of equilibrium proposition pully radius ratio rectangular represented resolved rest resultant attraction resultant force right angles rigid body round the axis shell shew shewn sides single force smooth sphere straight line suppose surface system of forces tangent tension tetrahedron three forces tion triangle uniform vanish vertex weight work-rate Y₁ ΣΧ
Popular passages
Page 15 - ... the resolved part of the resultant is equal to the sum of the resolved parts of the components.
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 301 - ... 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 194 - ... animal economy. The limbs of animals are generally levers of this description. The socket of the bone is the fulcrum ; a strong muscle attached to the bone near the socket is the power; and the weight of the limb, together with whatever resistance is opposed to its motion, is the weight.
Page 185 - Shew that the centre of gravity of a segment of an arc, subtending an angle, 20, at the centre, C, of a circle of radius, r, lies on the line of bisection of the angle, at a distance from the centre equal to rsin*° 3 0 — sin.0co8.0 1 1. Find the centre of gravity of the area contained between the curves, y- = ax, and, y* = 2ax — x2, lying above the axis of x.
Page 39 - 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 98 - ... 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 68 - A flat semicircular board with its plane vertical and curved edge upwards rests on a smooth horizontal plane, and is pressed at two given points of its circumference by two beams which slide in smooth vertical tubes; find the ratio of the weights of the beams that the board may be in equilibrium.
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 69 - 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°.