A Treatise on Elementary Statics |
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Page 50
... ring slides on a smooth arc of a circle and rests in equi- librium under the repulsion of three forces P , Q , R , directed from points dividing the circumference into three equal parts : if its position of equili- brium lie on the ...
... ring slides on a smooth arc of a circle and rests in equi- librium under the repulsion of three forces P , Q , R , directed from points dividing the circumference into three equal parts : if its position of equili- brium lie on the ...
Page 51
... rings 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 ...
... rings 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
John Greaves. 27. Two small heavy rings slide on a smooth wire , in the shape of a parabola , whose axis is horizontal : they are connected by a light string which passes over a smooth peg at the focus : shew that in the position of ...
John Greaves. 27. Two small heavy rings slide on a smooth wire , in the shape of a parabola , whose axis is horizontal : they are connected by a light string which passes over a smooth peg at the focus : shew that in the position of ...
Page 89
... ring at C , and also through a ring at the end B of the rod , the free end of the string supporting a weight P ; if the system be in equilibrium prove that AC : BC :: 2P + W : W. 8. A horizontal rod , the ends of which are on two ...
... ring at C , and also through a ring at the end B of the rod , the free end of the string supporting a weight P ; if the system be in equilibrium prove that AC : BC :: 2P + W : W. 8. A horizontal rod , the ends of which are on two ...
Page 90
... ring which slides on the rod ; and the bar rests on the sphere . Shew that in equili- brium the angle ( a ) the bar makes with the horizontal is given by a sin a = b cos3 a . 15. Forces P , Q , R act along the sides BC , CA , AB of a ...
... ring which slides on the rod ; and the bar rests on the sphere . Shew that in equili- brium the angle ( a ) the bar makes with the horizontal is given by a sin a = b cos3 a . 15. Forces P , Q , R act along the sides BC , CA , AB of a ...
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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.