A Treatise on Elementary Statics |
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Page 13
... passes through the point . 14. Prop . If a particle be in equilibrium under the action of a number of forces , any one of them is equal and opposite to the resultant of the rest . From the definition of a resultant , all the forces but ...
... passes through the point . 14. Prop . If a particle be in equilibrium under the action of a number of forces , any one of them is equal and opposite to the resultant of the rest . From the definition of a resultant , all the forces but ...
Page 21
... passes through the centre of the circle , and that its magnitude varies as the distance of the point from the centre . The centre of the circle is clearly the centroid of the points . Ex . 4. AOB and COD are chords of an ellipse ...
... passes through the centre of the circle , and that its magnitude varies as the distance of the point from the centre . The centre of the circle is clearly the centroid of the points . Ex . 4. AOB and COD are chords of an ellipse ...
Page 33
... passes through the point about which the moments are estimated , and in these two cases only . The student is recommended to accept the above definition of the moment of a force , and to follow the theorems concerning it , without ...
... passes through the point about which the moments are estimated , and in these two cases only . The student is recommended to accept the above definition of the moment of a force , and to follow the theorems concerning it , without ...
Page 35
... passes through both the points ; the latter cannot be the case as the line of action passes through the particle . Hence the forces are in equilibrium . 38. Def . If a force be resolved into two components respectively parallel and ...
... passes through both the points ; the latter cannot be the case as the line of action passes through the particle . Hence the forces are in equilibrium . 38. Def . If a force be resolved into two components respectively parallel and ...
Page 41
... passes through A. Draw AH the diameter of the circle ABC : join BH , CH : then the angle ABH is a right angle . By the triangle of forces the resultant of AP , PB is represented by AB , since the forces AP , PB , BA acting on a particle ...
... passes through A. Draw AH the diameter of the circle ABC : join BH , CH : then the angle ABH is a right angle . By the triangle of forces the resultant of AP , PB is represented by AB , since the forces AP , PB , BA acting on a particle ...
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Common terms and phrases
ABCD algebraical sum angle of friction angular points axis beam centre of gravity centre of mass circle coefficient of friction conditions of equilibrium cone couple cylinder diagonal displacement distance ellipse equal equation equi external forces Find the centre fixed point forces acting forces of constraint given Hence horizontal plane inclined plane indefinitely small lamina length line joining line of action middle point motion move number of forces original forces P₁ parallel forces parallelogram Parallelogram of Forces particle perpendicular polygon position of equilibrium Prop proportional prove pulley pyramid radius resolved respectively rests resultant rhombus right angles rigid body rope rough shew sides single force smooth peg sphere straight line string surface system of forces taking moments tension tetrahedron three forces triangle ABC uniform rod velocity vertex vertical plane virtual displacement weight zero
Popular passages
Page 9 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by forces to change that state.
Page 12 - Change of motion is proportional to the impressed force and takes place in the direction of the straight line in which the force acts.
Page 36 - Prove that the algebraic sum of the moments of two concurrent forces about any point in their plane is equal to the moment of their resultant about the same point.
Page 96 - Two strings of the same length have each of their ends fixed at each of two points in the same horizontal plane. A smooth sphere of radius r and weight W is supported upon them at the same distance from each of the given points. If the plane in which either string lies makes an angle a with Wa the horizon, prove that the tension of each is = -- - coseca; a being the distance between the points.
Page 90 - Show that the area of the triangle whose vertices are (4, 6), (2, —4), (—4, 2) is four times the area of the triangle formed by joining the middle points of the sides.
Page 227 - A uniform rod of length c rests with one end on a smooth elliptic arc whose major axis is horizontal and with the other on a smooth vertical plane at a distance h from the centre of the ellipse...
Page 185 - A body is supported on a rough inclined plane by a force acting along it. If the least magnitude of the force, when the plane is inclined at an angle a to the horizon, be equal to the greatest magnitude, when the plane is inclined at an angle /3, show that the angle of friction is J(a— /3).
Page 117 - Two equal beams AB, AC connected by a hinge at A are placed in a vertical plane with their extremities B, C resting on a horizontal plane ; they are kept from falling by strings connecting B and C with the middle points of the opposite...
Page 231 - These are usually accounted six in number, viz. the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Wedge, and the Screw.
Page 91 - A heavy equilateral triangle hung up on a smooth peg by a string, the ends of which are attached to two of its angular points, rests with one of its sides vertical — shew that the length of the string is double the altitude of the triangle.