1000000031

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a wineh; whieh wilI make ,he power of ,he eogine 'o

"exceed ,he power of the mao who works

¡t,

as much as

1he Dumber of

revolutions

of the winch exceerl lhore of

.he axle O, when multiplied by ,he e"eefs of ,he leng,h

the winch aboye the length of the femidiameter of the

."le, added 'o ,he femidiame'er or half·,hiekneCs of

,he rope K , by whieh ,he weigh' is drawn up. Thus,

fuppoCe ,he diame,er of ,he rope and axl< uken ,oge,her

to be

¡oches, and confequently haJf their diameters

10 be ',6 inehes; fo ,ha, Ibe weight W wilI hang a'

6 inehe. perpendicular dilhnee from below Ihe centre of

.he a"le. Now, let us fuppoCe the wheel AB, whieh is

fix, on ,he axle, ' o have 80 eogs, and to be lurned by

roeans of a

WiDCh

fix iDehes

long,

fixt on lhe axis of a

trundle

B llaves or rounds, working in the eogsof the

",heel.-Here i, is plaio, ,ha, ,he wineh and !ruodle

would make

revolu,ions for one of ,he whee! AB••nd

itl

axis

on whích the

rope

K winds in raiGng rhe

weigh' W; and ,he wineh

bei~

I~nger

,han Ihe Cum

of the femi,diame'ers of ,he grea'l xle and rope, ,he

tn,odle could have

more power o tbe

wheel, than

mao' could have by pulling i, round y ,he edge, beeauCe

,he wineh would have no ea'er ve!oei,y ,hao ,he

ed~

of ,be wheel has, ",hieh, e here fuppofe 'o be ten times

as great as lhe

velocity orthe

rifing wc:ight ; fa thar, in this

cafe, ,he power gained woold be as

10'0 l .

Bu,if,he

leog'h of,he wioeh be

inehes. ,he power gained will

be as

1 :

lBinehes (whieh is long enough for any

man

work by) ,he power gained would be as 30 ' o

1 ;

that is,

a,.

man could raife 30 times as much

fuch 'In

rngine. a. he eould do by his na,uralllreogth wi,hou, i"

beeauf. ,he veloei,y of ,he handle of the wineh would be

3<> time. a. great as <he veloci,y of ,he rifiog weigh' ; ,h.

abfolu,e force of any engine being in proportion of ,he

Teloei,y of ,he p0..,er

,he veloci,y of ,he weigh, raiCed

it.-But then, ju!l: as much power or advantage as is

gained

the engine. fo much time is 10Cl in wOlking it.

this fort of machines il is requilÍte to·have a ratchet·

wheel G on ooe end of ,he axle, wi,h a ca,eh H ' o faU

ioto its teeth ; which wiIJ at any time CuPPOrt [he weigbt,

.nd keep i, from defeending. if ,he workma. fhould,

,hrough inadvertency or earelefneCs. qui, his hold whilll the

1Veigh, is raifiog. And by ihis mean" the danger is pre–

ven,ed ",hieh migh, o'herwifehappen by ,he running down

of ,he weigh, when lef, a' liberty.

3. The ,hi.d ",echanical pOIVer or engine eonfill, ei–

,her of one

mov,oh/, pul/ey,

or a

Jjjl.m ofpu/lep;

fome

iD a block or caCe ",hieh is fixed. and o,hers in a block

whieh i. moveable. and rifes with ,he weigh' . For ,bo'

a ringle p\1J1ey, that only turos on its axis, and rifes Dot

Wilh the weight, may feTve to change the dire1..<):ion ofthe

power, yet it caD give no mechanical

advant3.ge

theTeto

but is onty

the beam of a balance, whore arms are of

equ.J leng,h and weigh'. Thus. if ,he equal weights

W and P (6g 7,) hang by ,he coro BS upon the pulley

A, whoCe block

i. 6xed 'o lbe beaOl HI, they \ViII

counterpoire e:.eh olher.

jun

iD the Carne manner asi frhe

coru were cut in the mlddle and its t\Vo cnd, hung upon

the hook. 6xt iD ,be pulley at A and A, equ.lly diflaD'

from its centre.

Bu' if a \Veighl W hanss a' lhe lower end of tbe more·

able block

of ,he pulley

and ,he cord GF goos

uoder ,he pulley, i, is plain lha! ,he half G of ,he cord

bears one half of ,he w<igb' W , and ,he hal f F ,he OIher ;

Cor

lhey bear the whole betweea them. Therefore, what.

ever holds ,he upper e,nd of ei,h« rope. fullains one half of

,he weigh'; and-if the eord

F be drawn up fo as

raife

,he pulley

,he eold will ,hen be ex,ended 'o in

whole leng,h, all bu, th .. part whieh goe, under ,he pul–

ley: and eonCequen,ly, ,he power ,ha, draws ,he eord

will have mov<d 'wice as fa r a. ,h. pulley

\Vi.h

it.

weight

rires: on which account, a power whofe in·

' enfi,y is equal 'o one

h.lf

of ,he weigh, \ViII be able

fuppor' i" beeaufe if ,he power moves (by means of a

fmall addi,ioo) its veloci,y

will

be double ,he veloei,y of

,he weigh' ; as may be

Ceen

by pulting ,he cord over ,he

fixt pulley

(whieh onlyehanges ,he direétion of ,he

power, without giving any advantage to

itJ

and hanging

on ,he weigh' P. whieh is equal only ' o one half of ,he

weigh ,

\V;

in whieh caCe ,herewill be..n equilibrium, and

a Jiltle .ddi,ion 'o P will cauCe i, tO deCeend. and raiCe W

through a fpaee equal ' o ono half of lh.. ,hrough whiell

P deCeends.-Hence, ,he ad.anuge gaioed will be

aI–

'way' equal lO twiee ,he

nllm~er

of pulleys in ,he move–

able or undermoll block. So ,ha" when ,he upper ar

fix' block

eontains ,wo pulleys, whieh only 'uro

the axes, and the lower or moveable block U conuins

two pulleys, which not only

turo

opon tbeir axes, but

alCo rife wi,h ,he block and IVeigh'; ,he advantage gained

by this is as 4 to the working power. Thus, ir one

ena

of ,he rope KMOQ..be 6xed 'o a hook

and ,he

rope palfe, over ,he pulley. N and

and under ,he pul–

ley. L aod P, and has a weigh, T , of one pound, hung

to its other cnd at T. this weigh, will balan« and Cup–

pon a weigh, W of four pounds hanging by a hook .,

,he moveable block

allowing ,he Caid block as a part

of ,he weigh"

And if as much more power be added as

is fufficieont to o\'crcome rhc: fti\'lion of the pulleys, the

power will defeend with four times as much velocity as

,he weigh, riCes, and eooCequco,ly ,hrough four ,imes as

mueh Cpaee.

The 'wo pulley, io ,he fi"ed block X, aod ,he ,"'o in

,he moveable block Y. are in ,he Carne eafe with ,hore laO:

mentioned

and thore in the lower block give the

[ame

advd.ntage to the power.

As a fyUem of pulley. has no, greal weigh, and lies

in a rmall compar" it is eafily carried aboul: and can be

applied, in a great

Olany

cares, for raifing weights. where

other t'ngines cannOt.

But they have a

gre:l.t

deal of

frie·

tion, on three accounfS:

Becaufc the diamcters of their

axes bear a

ver

Gonlid~rable

proportion to their own

di–

ameters;

2..

Becaufe in wurking they are-apt lo rub againfi:

one ano.her, or againlt the fide. of lhe block; 3. Be·

caufe oi ,he lI,ffneC. of ,be rope ,hat goes over and un–

der ,hem

4 . Tlle rourth mechanical power is Ihe

ilJdiJ1~d

¡.Jal1(:

and the ad'¡antage gí\ined by it is. as great as

lengt h

exceed, i.. ¡.erp,ndieular heigh!. Let

\6g. B.) be"

plaoe

p'".IIe1

to ,he horizon,

.nd·CD

a plan" inclined 'o .

it : and fuppofc the whote

J~ngtl1

to be three timcs

as great as lhe: perpendicular height G /F: in this cafe,

,he eylindcr E will be fupponed uRon ,he p.laoe

CD,

and

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