Book Description

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1897 edition. Excerpt: ... (32) to (40) can therefore be generalized by substituting a for g. One of the most important laws of dynamics is that constant or uniform forces, acting freely upon heavy bodies, impart to such bodies accelerations proportional to the intensities of the forces themselves. This law enables us to use terrestrial gravitation as a standard by which to measure the intensity of other forces, moving in any direction, under the influence of any other acceleration, a. The law is thus expressed: F W _ = _. (41) g In which F = any uniform force in lbs.; a = its acceleration in feet per second, per second, or the velocity imparted at the end of the first second; W = weight in lbs. of any heavy body freely acted upon by terrestrial gravitation, the coefficient of acceleration of which is g = 32.2. We have already seen that (32) may be generalized, thus: v = at. From this we deduce, a = v /1. Substituting this value of a, in (41), gives: WV Ft =. (42) g This is the formula of Momentum. Momentum, or "Quantity of Motion," is weight into time, and is expressed in second-pounds. The right-hand member of (42) shows that the momentum of a body moving with the velocity, V, is equal to its weight, IV, into the time during which it would have to fall under the influence of gravity in order to acquire that velocity. Momentum represents the stored or acquired energy of weight acting through time. Example 36.--A detached railway car of W = 10,000 lbs. is running away on a level track, with an initial velocity of 20 ft. per second. The train resistance is 30 lbs. per ton, or a total of 150 lbs. In how many seconds will it come to rest? 10000 X 20 150 / =. 32 t--41 seconds. Example 37.--Two weights, W = 100 lbs. and W' = 90 lbs., are suspended from...