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ABCD algebraical sum applied attached axis balance base beam body called centre of mass circle conditions of equilibrium cone connected corresponding couple cylinder direction displacement distance Draw drawn equal equation equilibrium exerted external forces fixed forces acting four given greatest Hence horizontal horizontal plane inclined indefinitely joining jointed length line of action magnitude means middle point moments motion move obtained opposite parallel particle passes perpendicular placed plane position position of equilibrium pressure produced proportional prove pulley radius reaction represented resolved respectively rests resultant right angles rigid ring rope rough scale-pan screw shew sides single slide smooth sphere square straight line string supported suppose surface tension triangle turn vertical virtual weight zero
Page 7 - 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 34 - 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 94 - 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 88 - 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 225 - 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 183 - 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 115 - 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 229 - These are usually accounted six in number, viz. the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Wedge, and the Screw.