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16 feet 3lbs action answer applied ascent axle body moving uniformly chap CHAPTER circumference consequently considered continued Coroll demonstrated descent described by gravity diagonal direction distance dividing double effect equal equilibrio Euclid EXAMPLE experiments expression falling feet per second fixed force of gravity forces acting formula four fulcrum given greater half Hence horizontal impelled impulse inches inclined plane increase initial velocity length less lever means momenta momentum motion moveable moving force obstruction opposite perpendicular Problem proportionals proposition pulley quantity ratio reaction rectangle remaining represent resistance rest resultant right angles right line Rule screw sides simultaneously Solution sought space described spiral square successive suspended sustain theorem theory third triangle uniform velocity acquired wedge weight wheel wherefore whole
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 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...