A Treatise on Elementary Statics |
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Page 7
... exerted by tangible means , but force is often manifested without any tangible means , as in the case of gravity , the name given to the force which causes any body near the earth to move towards it , STATICS OF A SINGLE PARTICLE . 7.
... exerted by tangible means , but force is often manifested without any tangible means , as in the case of gravity , the name given to the force which causes any body near the earth to move towards it , STATICS OF A SINGLE PARTICLE . 7.
Page 22
... exerted by the string . We have seen that the mechanical problem of compounding two forces into one is the same as the geometrical one of constructing the diagonal of a parallelogram , having given two adjacent sides : so also to ...
... exerted by the string . We have seen that the mechanical problem of compounding two forces into one is the same as the geometrical one of constructing the diagonal of a parallelogram , having given two adjacent sides : so also to ...
Page 37
... exerted on it , and similarly the latter was prevented from moving by the force which AP exerted on it . But we shall see in Art . 44 that these forces are equal to one another , and act in opposite directions along the lines joining ...
... exerted on it , and similarly the latter was prevented from moving by the force which AP exerted on it . But we shall see in Art . 44 that these forces are equal to one another , and act in opposite directions along the lines joining ...
Page 38
... exert , and if we try to transmit a force greater than this by means of the string , it will break . The above remarks apply to rods also if they are stretched , but the tension becomes a thrust , if the tendency of the forces on them ...
... exert , and if we try to transmit a force greater than this by means of the string , it will break . The above remarks apply to rods also if they are stretched , but the tension becomes a thrust , if the tendency of the forces on them ...
Page 39
... exerted by the plane and the particle will be in equilibrium . If , however , the resultant force is away from the plane , the particle will move , as the plane cannot exert a force to prevent motion away from itself . Smooth planes or ...
... exerted by the plane and the particle will be in equilibrium . If , however , the resultant force is away from the plane , the particle will move , as the plane cannot exert a force to prevent motion away from itself . Smooth planes or ...
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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.