Manual of Mechanics |
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adhesion angle of friction applied beam calculate centre of gravity centrifugal force circle described circumference coefficient of elasticity components constant force cord cos² cubic inch denote diameter distance equal equation equilibrate equilibrium EXAMPLES feet per second find the ratio Find the velocity foot-tons force of gravity forces acting forces meeting forces OA friction fulcrum heavy body horizontal inclined plane inversely kilogram-metres kilos labour law of motion length lever machine miles per hour moveable pulleys Oolite parallel forces parallelogram parallelogram of forces passing perpendicular point of application Power and Resistance pressure Principle of Moments produced proof Prop PROPOSITION quantity of matter radius rection represented in magnitude respectively resultant right angles screw seconds pendulum space described specific gravity surface threads tion tons triangle Twist velocity acquired velocity of projection vertical weight wheel and axle
Popular passages
Page 49 - The resultant of two forces acting at right angles is double the lesser of the components ; find the angles it makes with the components. 3. A body is supported on a smooth inclined plane by a force parallel to the plane. Show that the power is to the resistance as the height of the plane is to its length. 4. A uniform bar 4 ft.
Page 47 - ... evidently the same as a windlass, in which the Resistance is applied by means of cogged wheels instead of by means of a rope or chain ; the mechanical effect of both instruments is the same. EXAMPLES. 1. What force will be required to work the handle of a windlass, the Resistance to be overcome being 1156 Ibs., the radius of the axle being 6 inches, and of the handle 2 feet 8 inches ? Ans. 216.75 Ibs. 2. A weight of 17 Ibs. just balances a weight of 79 Ibs. on a wheel and axle. What will be the...
Page 55 - Ans. 143 tons, 5 cwt. 1 qr. 8 Ibs. 7. The Pulley. — A force may be transmitted from one point to another by means of a cord, and if there were no friction, this force might be transmitted undiminished in any direction. In order to diminish friction in thus transmitting a force from one point to another, by means of a cord, we make the cord pass over a wheel with a groove cut in its circumference, which turns with the cord, and so diminishes the friction. This wheel is called the sheaf, and the...
Page 46 - Then the proportion teaches us that the power and weight will be in equilibrium when the power is to the weight as the radius of the axle is to the radius of the wheel.
Page 2 - Force. 1 . Direction of a Force. — In estimating the effects of a given force, there are two things to be considered: — first, its direction; and secondly, its magnitude. By the direction of a force, we mean the line in which it tends to produce motion, and the force may be conceived to act at any point of this line : as experience fully shows that the effect of a force, whether in producing pressure or motion, is the same at whatever point in the line of its direction it is applied. If, for...
Page 33 - YD' and cut it at Z, in the inverse ratio of the sum of AA', BB', CC', to the force DD' ; the resultant of the first four forces AA', BB', CC', DD', which is equal to their sum, passes through this point, and so on. The point V, which is found last, is the point of application of the resultant of all the forces ; and the magnitude of the resultant VO is the sum of all the forces AA', BB', &c. The point V which has just been found is called the centre of the system of parallel forces, for as it was...
Page 18 - Four forces represented by 1, 2, 3 and 4, act in the same plane on a point. The directions of the first and third are at right angles to each other ; and so are the directions of the second and fourth ; and the second is inclined at an angle of 60° to the first. Find the magnitude and direction of the resultant.
Page 35 - P, Q ; the weights of the three sides respectively may be conceived as concentrated in these three points. The question is thus reduced to Example (4). It is not difficult to prove that the centre of gravity is the centre of the circle inscribed in the triangle OPQ.
Page 129 - A stone is thrown vertically upwards from the bottom of a tower 300 ft. high, with a velocity of 100 ft. per second ; after what time should another stone be projected downwards from the summit of the tower, with the same velocity, in order that they may meet at the middle point of the tower? Ans. 1.25 seconds. 1 1. A stone is dropped from a height of 400 ft., and, when it has fallen through 50 ft., a second stone is projected after it, so that both stones reach the ground together ; find the velocity...
Page 133 - The force is proportional to the square of the velocity and inversely proportional to the radius of turn during radial acceleration.