A new treatise on mechanics, by the author of A new introduction to the mathematicsWhittaker, 1841 - 184 páginas |
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Página 14
... dividing each of these equals by v , they become Theorem 4 . S = t . v The velocity with which any body moving uniformly describes any space , is equal to the quotient of the space divided by the time in which it is described ; that is ...
... dividing each of these equals by v , they become Theorem 4 . S = t . v The velocity with which any body moving uniformly describes any space , is equal to the quotient of the space divided by the time in which it is described ; that is ...
Página 15
Joseph Denison. For by Theorem 2 , s vt ; wherefore , dividing both sides of the equation by t , S = v . t From these Theorems we collect the following formulæ : viz . ; by ditto . Coroll . 1 . ; by Theorem 1. Coroll . 1 . Ts 1 S = ; by ...
Joseph Denison. For by Theorem 2 , s vt ; wherefore , dividing both sides of the equation by t , S = v . t From these Theorems we collect the following formulæ : viz . ; by ditto . Coroll . 1 . ; by Theorem 1. Coroll . 1 . Ts 1 S = ; by ...
Página 22
... dividing the last two Hence , when the times are equal the spaces are directly as the velocities ; that is s : S ... dividing both sides by V , Sv V ; the value required . Problem 2. Given s , v , and V , to find S. Solution . Sv = sV ...
... dividing the last two Hence , when the times are equal the spaces are directly as the velocities ; that is s : S ... dividing both sides by V , Sv V ; the value required . Problem 2. Given s , v , and V , to find S. Solution . Sv = sV ...
Página 23
... dividing by s V = ; the value required . Ꮽ These four formulæ are collected in the following table for the sake of more ready reference . TABLE I. CHAPTER III . Table of Formula for finding the Spaces and Velocities of two bodies ...
... dividing by s V = ; the value required . Ꮽ These four formulæ are collected in the following table for the sake of more ready reference . TABLE I. CHAPTER III . Table of Formula for finding the Spaces and Velocities of two bodies ...
Página 24
... dividing by , ; G ; second value of t . Note . In this second solution , we use the second ex- pression , not the ... dividing both sides by V , T = Solution 2. Because , = (完) by dividing by ; T = ; 2nd value of T. Problem 3. Let t , T ...
... dividing by , ; G ; second value of t . Note . In this second solution , we use the second ex- pression , not the ... dividing both sides by V , T = Solution 2. Because , = (完) by dividing by ; T = ; 2nd value of T. Problem 3. Let t , T ...
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A New Treatise on Mechanics, by the Author of a New Introduction to the ... Joseph Denison Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 162 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Página 24 - In any proportion, the product of the means is equal to the product of the extremes.
Página 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,
Página 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.
Página 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...
Página 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....
Página v - Motion, or change of motion, is proportional to the force impressed, and is produced in the right line in which that force acts.
Página 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.
Página 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...
Página ix - ... as the distance between the threads to the circumference of the cylinder in which the spiral moves.