Tract 37.

Of guJSNERY.

28$

before the stroke; is equal to the momentum after it. Andthe velocity communicated will be the same, whatever bathe resisting force of the block, the weight being the same.

Again, by forces, it is u 2 = 4 ^- s , and — v l = ~ X (s + x),or rather, by correction, a 2 -

4»t. . v

= ir ( s + *)■

Hence the

penetration or x

b{a 2 — — 4 gTs

4«fr

And when v = u, by

substituting u for v, and B u 1 for 4 grs, the greatest penetra-

; and this again, by writing ab for

tion becomes

ba 11 — (b +4gr

its value (B + b)u, gives the greatest penetration x ~

•————= — x (1-—-). Which is barely equal to

when tlie block is fixed, or infinitely great; and is alwaysvery nearly equal to the same — when b is very great in re-spect of b. Hence then

* _ aH *

, _— W 1 . a (b + A)’. b* + 2b& a*4

s 4- .v — - b — - - b — ——— x —.

4^r 4gr (b + 6)* 4 gr

And therefore b + b : b + 2b : : x :.? -f- x,or B + b : b : : x : s,

, bx sb i a’ 1

and s = —— zz -— , ■■■

B + b 4gr( B + i) 4

159. Exam. When the ball is iron, and weigtis 1 pdund,it penetrates elm about 15 inches when it moves with a ve-locity of 1200 feet per second, in which case,

1200 4

= = 18000 nearly.

b 4gi 4 x 16 X il

When B = 400lb, and 5=1; then it =

ab

B + 6

feet nearly per second, the velocity of the block.

1200

401

= 3

Also s = —

*g T

400 x 9

4-x 16 x 18000 = 3K P art ° f a f ° 0t > ° r * ° f

an inch, which is the space moved by the block when the ballhas completed its penetration.

And / = — = ~— = <4- part of a second; or t =

u 320 X S 480 i Q

■2f + 0ac

_2_ 30

320 + 12

1+400

v 1200 1200.1600

the time of penetration.

vot. m- u

— = — part of a second nearly,

-.no 480 t •- »