M

342

MISCELLANEOUS

TRACT 38.

Again t or — = x ■■■ ; the correct fluent of

which is t — xX—; x log. J -—, the time for any

length x. And when x = l = 100, it is £ = X log.

- v - = 2 69676 seconds, the time when the last of the

chain just quits the plane.

PROBLEM XVIII.

To find the Time and Telocity of a Chain, of very smallLinks, quitting a Pulley, by 'passingfreely over it: the wholeLength being 200 Inches, and the one End hanging 2 Inchesbelow the other at the beginning.

Put a — 2, l = 200, and x = bd any variabledifference of the two parts ab, ac. Then7 " =/, and vv or 2 gfs = 2g. ~ . \x —

- a*

Hence the correct fluent is if — g X

-, and

v ■— </{g x x -~)y the general expression for the

velocity. And when x = l, or when c arrives at a, it is»= X ^)= ^(193 X ^i*)= V(386x^)=,

,386 x 9999

✓ -

100

l j ’ \*-r •• 200 ' ' ' ”” " 100

= 196*45902 inches, or 16*311585 feet for the

greatest velocity when the chain just quits the pulley.Again,# or — = -~ = x —;• And t^ e cor -

o 3 w 4& ./{x 1 — a* >

rect fluent is # = x log. the general ex-

pression for the time. And when x — l, it becomes # =

* lo S- ~~—■ = An x log.--=

v/ 1 — x log. - 100 * v ^ - 99 = 2*69616 seconds, the whole timewhen the chain just quits the pulley.

So that the velocity and time at quitting the pulley in thisprob. and the plane in the last prob. are the same; the dis-