A new treatise on mechanics, by the author of A new introduction to the mathematics |
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Page vi
... problems , in which the use of the different formulæ is manifested . In chap . iv . part i . the author has , in like manner , treated of the Gravitation of Bodies near the surface of the earth ; in chap . v . Gravitation augmented by ...
... problems , in which the use of the different formulæ is manifested . In chap . iv . part i . the author has , in like manner , treated of the Gravitation of Bodies near the surface of the earth ; in chap . v . Gravitation augmented by ...
Page 16
... Problem 1. If a body moving uniformly has described 4 feet in 3 " , in what time will the body describe 18 feet ? Here s is given = 4 feet ; t , is given = 3 ′′ ; and S , is given 18 feet ; and T , the time in which the greater space ...
... Problem 1. If a body moving uniformly has described 4 feet in 3 " , in what time will the body describe 18 feet ? Here s is given = 4 feet ; t , is given = 3 ′′ ; and S , is given 18 feet ; and T , the time in which the greater space ...
Page 17
... Problem 3. To find the time in which any given space is described with a given velocity . Let a railway train pass over a line of 100 miles , at the rate of 30 miles per hour when it is in motion ; and let the train stop at five ...
... Problem 3. To find the time in which any given space is described with a given velocity . Let a railway train pass over a line of 100 miles , at the rate of 30 miles per hour when it is in motion ; and let the train stop at five ...
Page 18
... Problem 5. With what velocities will a body moving uniformly describe 64 feet in 2 " , 144 feet in 3 " , 256 feet in 4 " , 400 feet in 5 " , and 576 feet in 6 " ? In each of these cases s and t are given , and v , the velo- city , is ...
... Problem 5. With what velocities will a body moving uniformly describe 64 feet in 2 " , 144 feet in 3 " , 256 feet in 4 " , 400 feet in 5 " , and 576 feet in 6 " ? In each of these cases s and t are given , and v , the velo- city , is ...
Page 19
... problem we should use the third formula ST t = representing the quantities S ' 18 x 3 4 ; as before . But our object is to render the subject as intelligible as possible to beginners , by giving a distinct formula in the table for its ...
... problem we should use the third formula ST t = representing the quantities S ' 18 x 3 4 ; as before . But our object is to render the subject as intelligible as possible to beginners , by giving a distinct formula in the table for its ...
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A New Treatise on Mechanics, by the Author of a New Introduction to the ... Joseph Denison No preview available - 2016 |
A New Treatise on Mechanics, by the Author of a New Introduction to the ... Joseph Denison No preview available - 2016 |
Common terms and phrases
16 feet 2lbs 32 feet 4lbs abscissa acquired by gravity acquired velocity acting simultaneously action body falling body impelled body moving uniformly chap circumference contiguous threads Coroll cylinder demonstrated descent describe a space described by gravity diagonal distance dividing equal velocity equilibrio Euclid falling from rest feet per second find the space fixed pulley force applied force of gravity forces acting formula fulcrum gravitating body heavier weight heavy body height of ascent Hence hypothenuse inches inclined plane length lever momenta momentum moveable pulleys moving body moving force obstruction parallelogram perpendicular Problem proposition quantity ratio reaction rectangle repre represents the space required to find resistance right angles right line right-angled triangle Scholium screw sides Solution sought space described spiral square theorem uniform velocity velo velocity acquired WABC wedge weight of 3lbs wheel and axle wherefore
Popular passages
Page 162 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 24 - In any proportion, the product of the means is equal to the product of the extremes.
Page 180 - ... we substitute the causes which produce them, it may be said that the accelerative force is as the moving force directly, and the quantity of matter moved inversely,
Page 157 - THE WEDGE. The wedge is a double inclined plane, consequently its principles are the same : Hence when two bodies are forced asunder by means of the wedge in a direction parallel to its head, — Multiply the resisting power by half the thickness of the head or back of the wedge, and divide the product by the length of one of its inclined sides ; the quotient is the force equal to the resistance.
Page 33 - ... passed over in the 4th second is seven times that passed over in the 1st ; that the space of the 5th second is nine times that of the first ; and the space of the 6th second eleven times that of the first. Hence, we arrive at the important conclusion that the spaces described in the succeeding seconds increase in the ratio of the odd numbers 1, 3, 5, 7, 9, 1 1, 13, &c. &c. Fig. 9. 15. "We shall now consider the spaces passed over, not in the seconds taken singly, but in any number of them taken...
Page 143 - ... The movable pulley changes its position with that of the weight, and effects a saving equal to half the power. An equilibrium is preserved between the power and weight, when the weight is equal to the product of the power and twice the number of movable pulleys. RULE. Divide the weight to be raised by twice the number of pulleys in the lower block ; the quotient will give the power necessary to raise the weight. EXAMPLE. Required the power to raise 600 Ibs. when the lower block contains six pulleys....
Page v - Motion, or change of motion, is proportional to the force impressed, and is produced in the right line in which that force acts.
Page 130 - So that the length of the winch doubles the power gained by each trundle. As the power gained by any machine, or engine whatever, is in direct proportion as the velocity of the power is to the velocity of the weight ; the powers of this crane are easily estimated, and they are as follows.
Page 1 - FIRST LAW.—A body continues always in a state of rest, or of uniform rectilinear motion, until by some external force, it is made to change its state.—This law contains the doctrine of INERTIA, expressed in four particulars. First, that unless put in motion by some external force, a body always remains at rest; secondly, that when once in motion it continues always in motion, unless stopped by some force; thirdly...
Page ix - ... as the distance between the threads to the circumference of the cylinder in which the spiral moves.