Mechanics for Beginners: With Numerous Examples |
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Page 90
... displaced it will tend to return to its position of equilibrium or to re- cede from it according as the centre of gravity is above or below the fixed point . This may be taken as an experimental fact ; or it may be established thus ...
... displaced it will tend to return to its position of equilibrium or to re- cede from it according as the centre of gravity is above or below the fixed point . This may be taken as an experimental fact ; or it may be established thus ...
Page 152
... displacements , then the algebraical sum of the products of each force into its virtual velocity vanishes ; and conversely if this sum vanishes for all possible displacements the system of forces is in equilibrium . This proposition is ...
... displacements , then the algebraical sum of the products of each force into its virtual velocity vanishes ; and conversely if this sum vanishes for all possible displacements the system of forces is in equilibrium . This proposition is ...
Page 153
... displacements which the principle contemplates are such as do not destroy the connexion of the points of application of the forces with each other . Thus any rigid body must be conceived to be moved as a whole , without separation into ...
... displacements which the principle contemplates are such as do not destroy the connexion of the points of application of the forces with each other . Thus any rigid body must be conceived to be moved as a whole , without separation into ...
Page 154
... displacement of A resolved along AM = Aa cos MAa = Aa cos ( 90 ° —a — 0 ) = Aa sin ( a + 0 ) . = The displacement of B resolved along NB Therefore = Bb cos ( 180o —¿BC - CBN ) = Bb cos ( 90 ° -B + 0 ) = Bb sin ( 3-0 ) . Resolved ...
... displacement of A resolved along AM = Aa cos MAa = Aa cos ( 90 ° —a — 0 ) = Aa sin ( a + 0 ) . = The displacement of B resolved along NB Therefore = Bb cos ( 180o —¿BC - CBN ) = Bb cos ( 90 ° -B + 0 ) = Bb sin ( 3-0 ) . Resolved ...
Page 155
... displacement of its point of applica- tion . 236 . and Axle . To demonstrate the Principle for the Wheel Let two ... displacement of A resolved along the line of action of P is Ca sin A Ca ; the displacement of B resolved along the line ...
... displacement of its point of applica- tion . 236 . and Axle . To demonstrate the Principle for the Wheel Let two ... displacement of A resolved along the line of action of P is Ca sin A Ca ; the displacement of B resolved along the line ...
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Common terms and phrases
ABCD acceleration algebraical sum angular points axis balance beam bisects body or system centre of gravity circle coefficient of friction components conditions of equilibrium cos² couple cylinder denote described determine distance equi Euclid example feet find the centre fixed point fulcrum given heavy particles Hence horizontal plane impact inches inclined plane Law of Motion length line of action lower block magnitude and direction mechanical advantage middle point move moveable Pully P+Q+R parabola Parallelogram of Forces perpendicular point of application point of projection position Power preceding Article pressure proposition radius ratio Resolved displacement respectively rest right angles rigid body Screw shew sides single resultant smooth straight line string which passes system of forces System of Pullies Take moments round tension three forces tion triangle uniform vanishes velocity vertical weight Wheel and Axle
Popular passages
Page 260 - 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 210 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.
Page 327 - ... that the squares of the periodic times are proportional to the cubes of the mean distances of the planets from the Sun.
Page 16 - Conversely, if three forces act on a particle, and each force is proportional to the sine of the angle between the other two...
Page 10 - ... represented in magnitude and direction by that diagonal of the parallelogram which passes through the particle.
Page 134 - This proportion teaches us that, when in equilibrium, the power is to the weight as the height of the plane is to its length.
Page 13 - The nature of force is now, and always will be, unknown.' Force is known only by its effects: A point or particle at rest cannot give itself any motion since there is no reason why it should move in one direction rather than another. But if the particle is not forced to move upon a determinate curve, the curve which it describes possesses a singular property, which has been discovered by metaphysical considerations, ie between any two points is less than on every other curve, if the body be free,...
Page 74 - The intersection of the straight lines which join the middle points of opposite sides of any quadrilateral, is the middle point of the straight line which joins the middle points of the diagonals (I.
Page 290 - A ball is projected in a given direction within a fixed horizontal hoop, so as to go on rebounding from the surface of the hoop ; find the limit to which the velocity will approach, and shew that it attains this limit in a finite time, e being less than 1.
Page 264 - If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone...