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abscissa angular points attracted particle axes axis of x beam centre of gravity circle co-ordinates coefficient of friction cone constant couple curve cylinder denote density determine displacement distance element ellipsoid equi find the centre fixed point forces acting forces which act forces with respect frustum Hence horizontal plane inclined plane integrate lamina latus rectum law of attraction length lever librium magnitude and direction mass middle point moments normal obtain opposite origin parabola parallel forces parallelogram passing point of application polygon portion position of equilibrium pressure proposition pully radius ratio rest resultant attraction resultant force right angles rigid body rough round the axis shell shew shewn sides Similarly single force single resultant smooth solid sphere spheroid suppose surface system of forces tangent tetrahedron three forces tion triangle vanish vertex vertical plane virtual velocities weight
Page 71 - we repeat two definitions already given in arts. 54 and 67. Moment of a force with respect to a point. The moment of a force with respect to a point is the product of the force into the perpendicular from the point on the direction of the force. Moment of a force with respect to a plane. The moment
Page 285 - If the particles of a body attract with a force varying as the product of the mass into the distance, the resultant attraction of the body is the same as if the whole mass of the body were collected at its centre of gravity. Take the centre of gravity of the attracting
Page 43 - of the couple corresponding to the direction of the force and the moment of the couple to the intensity of the force. Hence for example, by Art. 29, the resolved part of a resultant couple in any direction is equal to the sum of the resolved parts of the component couples in the same direction. CHAPTER IV. RESULTANT
Page 64 - magnitude and direction of the resultant of any number of parallel forces acting on a rigid body, and to determine the centre of parallel forces. Let the points of application of the forces be referred to a system of rectangular co-ordinate axes. Let m 1 , m 2 ,... be the points of application; let
Page 9 - AD. Hence the resultant is represented in magnitude as well as in direction by the diagonal of the parallelogram. Thus the proposition called the Parallelogram of Forces is completely established. 18. Hence if P and Q represent two component forces acting at an angle a on a particle, the resultant
Page 173 - 49. Apply Guldinus's theorem to find the volume of the frustum of a right cone in terms of its altitude and the radii Result. o 50. Find the surface and the volume of the solid formed by the revolution of a cycloid round its base.
Page 234 - is acted on by a tension at P along the tangent at P, a tension at Q along the tangent at Q, and the resistance of the smooth curve which will be ultimately along PO. Let s be the length of the curve measured from some fixed point up to P, and PQ
Page 167 - coincides with the centre of the circle inscribed in DEF. 7. A piece of wire is formed into a triangle; find the distance of the centre of gravity from each of the sides, and shew that if x, y, z be the three distances, and r the radius of the inscribed circle, then ixyz
Page 267 - if it be taken hold of at a point P, between A and B, and pulled in the direction AB, shew that it will begin to slip round A and B at the same time if 18. An elastic string without weight of variable thickness is extended by a given force ; find the whole extension.
Page 324 - 7. Find the locus of a point such that its resultant attraction on a fixed straight line may always pass through, a fixed point in the straight line. Result. A sphere. 8. Find the attraction of a segment of a paraboloid of revolution, bounded by a plane perpendicular to its axis, on a particle at the focus. Result.