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ABCD algebraical sum angle of friction angular points attached axis axle beam centre of gravity centre of mass circle coefficient of friction conditions of equilibrium cone couple cylinder diagonal direction distance ellipse equal external forces fixed point forces acting fulcrum given greatest slope Hence horizontal plane inclined plane indefinitely small lamina length line joining line of action line of greatest magnitude middle point motion move number of forces opposite P₁ parallelepiped parallelogram particle perpendicular placed polygon position of equilibrium Prop prove pulley radius represented resolved respectively rests resultant rhombus right angles rigid body ring rope scale-pan screw shew sides single force slide smooth peg sphere steelyard straight line string surface system of forces taking moments tangent tension three forces triangle ABC uniform rods velocity vertex vertical plane virtual displacement zero
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 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.