Principles of the Mechanics of Machinery and Engineering Volume 1

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1848 Excerpt: ...by a directrix, Fig. 273, to describe its circular orbit, this directrix would act, by its rigidity, as a centripetal force, and opposed to the centrifugal force of the body. If, lastly, the revolving body be connected by a thread or by a rod with the centre of revolution, the elasticity of the rod will then be in equilibrium with the centrifugal force of the body, and thereby act as a centripetal force. Let G be the weight of the revolving body, therefore its mass G the radius of the circle in which it revolves = r, and the velocity of revolution = v; from the last § we have the centrifugal force:. /--"if z.r.'ca/u.U-r Jf-'f Cu&i x.tt /: r rrv.' ' 7--' '944 lbs. and the modulus of l = 7000. f; hence inches, and its radius threefold security # 2. From the earth's of a day T--24 h. le earth's equator is t were the length of ldbel7=2S9timee I the equator, there md the body would its centrifugal force lit of the moon, r its ifugal force of this n Mv2 Gv% n V2 G.,, n n o « P = = = 2.--.--, therefore also P: G = 2.--: r, r gr 2g r 2g i. e., the centrifugal force is to tfie weight of the body as double the height due to the velocity is to the radius of revolution. If the motion be uniform, which always, takes place if no other feee (tangential force) fana the centripetal,'act upon the body, the velocity v = c may be expressed by the time of revolution T, if we put c =-?--=-----, and hence we shall obtain for the centrifugal time T force: T ) r T gT Since 4J = 39,4784, and for the measure in feet-= 0,031, we g then have more conveniently for calculation p= 39,4784 1)224.Gr The number n of revolutions per minute is often given, and therego" fore T is replaced by, whence it follows: n P = 39'4784 n Mr = 0,010966 n2 Mr = 0,000331 n2 Gr. 3600' ...