A Treatise on Elementary Statics |
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Page 66
... cylinder ( W ) is placed with its axis horizontal on a smooth inclined plane : a weightless string is attached to a point in the plane and after passing over the cylinder supports a weight P , the straight portions of the string being ...
... cylinder ( W ) is placed with its axis horizontal on a smooth inclined plane : a weightless string is attached to a point in the plane and after passing over the cylinder supports a weight P , the straight portions of the string being ...
Page 91
... cylinder touches the other two along a generating line , the string is just not stretched : shew that if the system be placed on a smooth horizontal plane , the inclination ( 0 ) of the plane con- taining the axis of the upper cylinder ...
... cylinder touches the other two along a generating line , the string is just not stretched : shew that if the system be placed on a smooth horizontal plane , the inclination ( 0 ) of the plane con- taining the axis of the upper cylinder ...
Page 92
... cylinders is horizontal . If the pressure between the cylinders be equal to twice the weight of either of them ; prove that the length of the string the radius of either cylinder :: 4 ( 2 + tan - 1 2 ) : 1 . : 29. A homogeneous circular ...
... cylinders is horizontal . If the pressure between the cylinders be equal to twice the weight of either of them ; prove that the length of the string the radius of either cylinder :: 4 ( 2 + tan - 1 2 ) : 1 . : 29. A homogeneous circular ...
Page 94
... cylinder will not upset if the ratio of its weight to the weight of the upper sphere be greater than 2c - a - b : c , where a , b , c are the radii of the spheres and cylinder . 41. Three spheres of radius c are placed on a smooth ...
... cylinder will not upset if the ratio of its weight to the weight of the upper sphere be greater than 2c - a - b : c , where a , b , c are the radii of the spheres and cylinder . 41. Three spheres of radius c are placed on a smooth ...
Page 95
... cylinder in order that it may not be upset by the balls is given by = aW ' ( n - 1 ) ( a− r ) Wor according as n is ... cylinders , tied together STATICS OF SYSTEMS OF PARTICLES . 95.
... cylinder in order that it may not be upset by the balls is given by = aW ' ( n - 1 ) ( a− r ) Wor according as n is ... cylinders , tied together STATICS OF SYSTEMS OF PARTICLES . 95.
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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.