A Treatise on Elementary Statics |
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Page 9
... Weight : hence the weights of different bodies are proportional to their masses , since the change of velocity ... weight , and would , if it acted alone , produce in the body the same change of motion upwards that its weight does ...
... Weight : hence the weights of different bodies are proportional to their masses , since the change of velocity ... weight , and would , if it acted alone , produce in the body the same change of motion upwards that its weight does ...
Page 10
... weight the force would statically support . Ans . 9.3 lbs . nearly . Ex . 2. During what time must a constant force equal to the weight of one ton act upon a train of 100 tons to generate in it a velocity of 40 miles an hour ? Ans . 3 ...
... weight the force would statically support . Ans . 9.3 lbs . nearly . Ex . 2. During what time must a constant force equal to the weight of one ton act upon a train of 100 tons to generate in it a velocity of 40 miles an hour ? Ans . 3 ...
Page 47
... weight W is supported on a smooth inclined plane by means of two strings of given lengths , which are attached to the particle C and to fixed points A , B in a horizontal line in the plane and at a given distance apart . It is required ...
... weight W is supported on a smooth inclined plane by means of two strings of given lengths , which are attached to the particle C and to fixed points A , B in a horizontal line in the plane and at a given distance apart . It is required ...
Page 51
... weights W and W ' , connected by a string , slide upon two fixed wires , the former of which is vertical , and the other inclined at an angle a to the horizon . A weight P is tied to the string , prove that in the position of ...
... weights W and W ' , connected by a string , slide upon two fixed wires , the former of which is vertical , and the other inclined at an angle a to the horizon . A weight P is tied to the string , prove that in the position of ...
Page 52
... weight attached by a cord to a fixed point O , rests against a frictionless curve in the same vertical plane with 0 : shew that ( 1 ) if the pressure on the curve is to be independent of the position of the weight on it , the curve must ...
... weight attached by a cord to a fixed point O , rests against a frictionless curve in the same vertical plane with 0 : shew that ( 1 ) if the pressure on the curve is to be independent of the position of the weight on it , the curve must ...
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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.