A Treatise on Elementary Statics |
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Page 18
... four forces of 5 , 6 , 9 , 10 lbs . acting on a particle and represented in direction by OA , OB , OC , ` OD , re- spectively , where O is the point of intersection of the diagonals of a square ABCD . Ans . 4/2 lbs . , in the direction ...
... four forces of 5 , 6 , 9 , 10 lbs . acting on a particle and represented in direction by OA , OB , OC , ` OD , re- spectively , where O is the point of intersection of the diagonals of a square ABCD . Ans . 4/2 lbs . , in the direction ...
Page 22
... four sides of a parallelogram : find the magnitude and direction of the resultant of the forces represented by these four straight lines . Ans . The direction is along the line joining the point with the centre of the parallelogram ...
... four sides of a parallelogram : find the magnitude and direction of the resultant of the forces represented by these four straight lines . Ans . The direction is along the line joining the point with the centre of the parallelogram ...
Page 47
... four forces , its weight W which acts vertically downwards , the tension T of the string AC , T ' , that of BC , and the pressure of the inclined STATICS OF A SINGLE PARTICLE . 47 Second system of pulleys Third system of pulleys ...
... four forces , its weight W which acts vertically downwards , the tension T of the string AC , T ' , that of BC , and the pressure of the inclined STATICS OF A SINGLE PARTICLE . 47 Second system of pulleys Third system of pulleys ...
Page 51
... Four particles A , B , C , D are attached to the ends of strings whose other ends are tied in a knot at O. Any two particles repel one another with a force which varies directly as the distance and the product of their masses . Shew ...
... Four particles A , B , C , D are attached to the ends of strings whose other ends are tied in a knot at O. Any two particles repel one another with a force which varies directly as the distance and the product of their masses . Shew ...
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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.