A Treatise on Elementary Statics |
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Page vii
... ropes used in machines , as well as a description of Weston's Differential Pulley . Many errors in Examples have been corrected , and it is hoped that very few now remain . April , 1888 . CONTENTS . CHAPTER I. ON THE STATICS OF A SINGLE ...
... ropes used in machines , as well as a description of Weston's Differential Pulley . Many errors in Examples have been corrected , and it is hoped that very few now remain . April , 1888 . CONTENTS . CHAPTER I. ON THE STATICS OF A SINGLE ...
Page xi
... ropes Single pulley First system of pulleys CHAPTER VII . ON MACHINES . PAGE 164 · 165 . 169 172 • • 173 185 198 199 202 205 206 207 208 210 • 215 216 225 231 232 • 235 235 · 237 239 · 240 Second system of pulleys . Third system of ...
... ropes Single pulley First system of pulleys CHAPTER VII . ON MACHINES . PAGE 164 · 165 . 169 172 • • 173 185 198 199 202 205 206 207 208 210 • 215 216 225 231 232 • 235 235 · 237 239 · 240 Second system of pulleys . Third system of ...
Page 37
... rope or chain . Now when a string AB is stretched by the application of forces it is a matter of everyday expe- rience that if it be cut at any point P , the two ends on either side of P separate : what then prevented the portion AP ...
... rope or chain . Now when a string AB is stretched by the application of forces it is a matter of everyday expe- rience that if it be cut at any point P , the two ends on either side of P separate : what then prevented the portion AP ...
Page 66
... rope is passed several times round a fixed rough post , the tensions exerted at the ends of the two parts of the rope not in contact with the post , are 3 lbs . and 2/2 lbs . respectively , and these two parts make an angle of 45 ° with ...
... rope is passed several times round a fixed rough post , the tensions exerted at the ends of the two parts of the rope not in contact with the post , are 3 lbs . and 2/2 lbs . respectively , and these two parts make an angle of 45 ° with ...
Page 100
... rope composed of several fibres be taut , though we may know the tension of the rope itself , i.e. the sum of the tensions of the different fibres , we cannot say how it is distributed among them . This can only be ascertained when the ...
... rope composed of several fibres be taut , though we may know the tension of the rope itself , i.e. the sum of the tensions of the different fibres , we cannot say how it is distributed among them . This can only be ascertained when the ...
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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.