290

THEORY AND PRACTICE

TRACT 37.

For the circumstances relating to the motion of a block,suspended by, and vibrating on, an axis, when struck by aball, see Tract 3d, ai ts. 21 .... 31.

PROBLEM XIX.

1 60. To determine the Circumstances relating to a givenBall discharged from a Cannon , with a given Charge ofPowder.

Let the annexed figure re- „

b A R

present the bore of the gun ;abd being the part occupied D

■with the gunpowder. And putg = ab, the length at first occupied bj' the charge;i t= ae, the whole length of the gun bore;e — *7854, the area of a circle whose diameter is 1;d = bd, the diameter of the ball, or of the bore;e = the specific gravity of the ball, or weight of 1 cubicfoot;

g = ]6 T V or 16 feet, descended by a body in 1 second ;vi— 230 oz, the pressure of the atmosphere on 1 sq. inch ;

» to 1 the ratio of the first force of the fired powder, to thepressure of the atmosphere ;w= the weight of the ball; and let

x = AC, any variable distance of the ball from A, in movingalong the gun barrel. Then,

First, ed 1 is = the area of the circle bd of the ball;therefore mcd 1 is the pressure of the atmosphere on bd ;conseq. nincd 1 is the force of the powder on bd.

But thp force of the inflamed powder is supposed to be^proportional to its density, and the density is inversely as thespace it occupies; therelore the force of the inflamed pow-

is to ab ; that is , 1

der on the ball at b, is to the force oil the same at c, as ac

. . i ’

7 mriuia- |

x : a : : rnncdr : -- = f, the motive force a

7 mriuia- |

x : a : : rnncdr : ■—— = f, the motive force at c;corrseq. — = — —f, the accelerating force there..

1 u> ®

mnacd 9

mnacd 9