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QUESTIONS AND PROBLEMS
ELEMENTARY PHYSICS,
C ON T A IN IN G
N UM EROUS PR A C T IC A L EXA M P L E S A N D EXE R C I SE S FOR
USE OF PUP IL S IN H IGH S C HOOL S AN D A C ADEM IES .
O . L . H O T ! E,
T EACHE R OF N AT URAL S C I E N C E S IN T H E C L EVE LA N D HIGH S C HOOL ;A utlzor cf First L esson: in P bysics,
” “ F irst L esson:
in P fiysz’
ology,”(16.
S T . L O U I ST HE CEN TR AL PUBL ISH IN G COMP A N Y .
C H A S . T . DI L L IN GHA M , N EW YORK.
J. L . H AM M ET T , BOSTON .
T H E N I’
W ‘
x
’
i R K
1 57020A S T OR . L E N OX A N D
T I LDE N FOUN DAT ION S .
1 899 .
Entered ac cording to A c t ofCongress, in the year 1878, by
W . B. C H IT T E N DEN ,
In the Office ofthe Librarian ofCongress, at Washington.
PRE FACE .
Every teacher appreciates the value of a comprehensive
series of questions and problems in Elementary Sc ience.
Next to the experiment, they are the only prac tical means of
testing the student’s acc urac y, and , at the same time, of
extending his knowledge. In the minds of some theremay be a doubt as to the importanc e of questions ; therec an be none in regard to problems, for these are as ih
dispensable in P hysic s as they are in Arithmetic .
This volume claims comprehensiveness so far as c on
c erns instruction in the Elements ofNatural Philosophy or
P hysics in the lowest, or next to the lowest,grade ofour
High S chools. I t may‘
be used as an auxiliary to any textbook . Most of the problems require only so muc h knowledge of' Mathematics as every young person is supposed to
possess on entering the High S c hool. Solutions of problems have oc c asionally been inserted in the text. T he
metric system has, throughout the entire w olume, gregoiig'
éd4 4 3‘
the attention due to its importance.
T he answers to the problems will shortly he pubhshed ,and may be obtained by teac hers updn applicationgtoth epublishers.
C leveland , 0ȣ0, April, 1877
REM ARK S .
Each example or question has its own number. At theclose ofa sechon a few numbers are left blank for any example or question that the student maywish to-add .
For prac tical purposes as well as for the sake of con
venienc e, fractions may be considered as units, when theydiffer from a unit by only a minute quantity ; thus,may, in nearly all c ases, be takenT he sign ofmultiplication adopted in the problems is the
period because the usual sign (x ) is, in writing, easilyconfounded with x. Thus, 2 3 6.
Unless stated otherwise, the term velocity means velocityper second Ofmean solar time.
All objects are considered as moving without friction or
resistance. Any exception to th is is distinctly indic ated. In
solving problems, the young learner is cautioned against writing his answer without addmg its denomination.
Questions or Problems marked S . K.
”
(South Kensington) have been selected from Examination Papers for Sc hence Schools and Classes, London.
” Those marked “ T.
”
are Prof. Tyndall’s. M .
”refers to Magnus, Elem. Mechan
ic s B .
”to Burbach , P hysikal. Aufgaben “ T o. to T od
hunter, Mechanics for Beginners ; A .
”to Atkinson, P rob .
and Examples in P hysics ; C . 8: M .
”to Chevall ieret Muntz ,
Problemes de P hysique ; “ D .
”to Day, Numerical Examples
inHeat.
MATHEMATICAL DATA.
7? ratio of circumferenc e ofcircle to diameterCirc umferenc e ofa c ircle (d=diameter) 7: d .
A rea of circle r’
square ofdiam. XSurface ofa sphere = square of diam. x
C ap. or vol. ofa sphere f'
T
z f cube ofdiam . x
C ap. or vol. of cylinder zrr‘l : area ofbase X by height.
Area ofretangle, square, rhombus, rhomboid base x height.
Fric tion
C O NTENT S .
M M ymunios.
ofH u t—M ach. Equiv
d
M im l'neousQuestion: (H eat)
R efrac tion ofL ight
INTRODUCTION.
(METRIC SYSTEM.)
(See Taéle in Appendix .)
and is
1 . H ow y cm timeters in a meter? In a decimeta
In five decime2 . H ow m ymillimeters in a cm timeter? In a decime
fiac tion of a meter is ten centimeters T en
One decimeterfrw fion ofa meter is the sum oftwo decimeters,
7. What fifac tion ofa centimeter is a millimeter ? Fourmillimeters
8. What frac tion of a kilometer is 1 25 meters ?
9. Disn'
nguish between a decameter and a decimera '
.
Express the difierenc e in c entimeters.
(7)
8 QUE S T ION S u rn 11110a a t m ans .
1 0 . T he veloc ity ofa man walking rapidly is meters,
nearly. Convert this into feet.(T ake 1 meter inches, then m.
inch 5 it. inch , answer.)1 1 . T he veloc ity ofa horse galloping h from 4to 5me
ters. Express this in feet.1 2 . T he veloc ity ofa railway train is from 8 t0 18 meters.
Express this in feet.13. T he veloc ity ofsteam vessels is from 3 to 7 meters.
Express this in feet.
14. T he veloc ity ofa rifle ball is 500 meters, nearly. Express this in feet.
15. T he velocity ofa 24-p0und ball is 80 0 meters, nearly.
16. T he velocity ofsound is 333meters, nearly. Reduc ethis to feet.
1 7. Reduce to inc hes the diameter ofa nic kel five c ent
18. H ow many c entimeters in a yard P(Take 1 ft. m. , then3it. 1 yd.) 3
m. meter c entimeters.)19. H ow many meters in a mile ?20 . Reduce an inc h to c entimeters.
2 1 . Assuming the height of the atmosphere to befeet, what is it in kilometers
22 . T he mercury in a barometer stands 30 inches ; howmany millimeters is this
23. Reduce 25 pounds (avoir. ) to kilograms.
(Take 1 pd. kilo. , then 25 pds. 25
kilograms.)24. Reduc e 1 ounc e (avoir.) to grams.
M E T R I C SYS T EM . 9
25. A cubic foot ofwaterweighs 62% pounds,nearly. R e
duce this to kilograms.
26. T he weight ofone hundred c ubic inc hes ofair is 31 '
grains, nearly. Reduce this to grams.
27. A cubic foot ofbrickwork weighs about 1 cwt. R e
duce this to kilograms.
28. T he pressure ofair is nearly 1 5 pounds to the squareinch . Reduc e this to kilograms.
29. T he weight ofa traction engine is 6 tons. Reducethis to kilograms.
30 . H ow many pints in c. 0 . (cubic c entim.) P31 . What is the unit of length in the Metric system, and
what its approximate value in the English system P32 . H ow is the meter divided ? Give the names of the
principal multiple and sub-multip le divisions.
33. What is meant by a liter? H ow many liters in a
cubic meter P34. Give the equivalent ofa liter in English cubic inc hes.
35. H ow many cubic c entimeters (c . c . ) in a c ube,each.
edge ofwhic h is meter long P36. H ow many liters in the same P37. In liters how many c . c . P
38. Find the area (in sq. cent .) ofa nickel five cent piece.
39. S tate what is meant by a meter40 . S tate what is meant by a gram
M O T I O N .
U N I F O R M M O T I O N .
43. What is motion? What is uniform motion?44. What is meant by velocity ? By acceleration?45. A body pw ca 0ver840 feet in
its velocity .
46. A point in the c irc umference ofa grindstone is r foot
d istant from the centre ; it revolves 3 times in 2 1 seconds ;
find the velocity ofthe point.(T he diameter 2 . 1 ft. = 2 ft, and the
the grindstone 2 1
revolves 5 times in 2 1 seconds, it passes ovft. it. in 2 1 seconds, and
R. per second, answer. )
47. A carrier pigeon traveled 200 miles in4hours, 4363sec . Find its velocity.
48. T he length ofthe minute-hand ofa watch is 2 1meters. Required the veloc ity ofits point.49. Assum ing the length ofthe equator to be 24000 miles,
what is the velocity ofany point on the equator?50 . What diameter must a wheel have in order to make
90 revolutions a m inute, and that the veloc ity ofany point atits circumference may be 9 meters (Take 7t
'
51 . H ow many revolutions must eac h of the drivingwheels ofa locomotive make in an hour, ifthe diameter ofeach is 6 ft., and ifthe veloc tty of the train is 54it. (Takei t 3
norms . 1 1
52 . Distinguish between motion of trnnslation, rotation
53. A body passes over 1 00 feet in 1 0 seconds, while an
other body passes over z o feet infseconds. Find the ratios
the piston in a steam
minute, each 1 meter long?
LY ACCELERATED AND RETARDEDM OTION .
is meant by variable motion ; by uniformly acon
,and retarded motion P
per second .
360 sec . a , hence c H, ft.)what time will a body, moving from rest wi th an
of 25 ft. per second , acquire a velocity of500 ft.
44ft. per second. N ow v
t space will a body pass over in 6 seconds, ifitacc eleration of80 yards perminute P
38yds 4ft. I ts velocity(1 24ft. henc e its mean veloc ity per
14ft., and in 6 seconds the space passed
ft. )
pac e will a body describe in 1 0 seconds ifan ac c eleration of5 meters per second ?
motion?body is 6 feet per
been moving for 6
f 30 miles an hour.
12 QUE S T ION S A N D P R OBL E M S I N P H Y S I C S .
62. With what veloc ity per sec ond must a body start ifitsvelocity be retarded 6 ft. every sec ond and ifit c omes to restin 6 seconds P63. With what veloc ity will a body move after 5 seconds
ifit started from rest with an ac c eleration of1 2 ft. per second P64. What are the chiefimpediments to motion P
FIRST LAW OF MOTION .
66. S tate the first law Ofmotion.
67. H ow does a body tend to move when set in motion P68. A stone is tied to a string and whirled round ; if the
stone free itselffrom the string, inwhat direc tion will itmove P69. What is meant by inertia P70 . Mention three fac ts that serve to verify Newton’s
first -law Ofmotion.
71 . Why c an we drive the head ofa hammer by strikingthe end ofthe handle ?72 . Explain why a running jump is longer than a
standing one?
SECOND LAW OF MOTION .
73. S tate the second law ofmotion.
‘
74. What is the direction of a stone dropped from the
masthead ofa vessel in motion
75. Ifa person is walking in a straight line, inwhat direction must he throw a ball upward that it may return into hishand P76. Ifa ball be held out of the window ofa railway c ar
riage in rapid motion, and then be dropped, in what direction will it seem to fall , a , to a passenger? b, to an observeron the ground? c , in what direction will it really fall ? (Illustrate by a drawing.)
M OT ION . 13
77. What is meant by the parallelogram ofmotion, or offorces P
78. What is meant by resultant motion P
79. Given a fixed point a on a vessel , and the directionin which the vessel moves. A ball is assumed to be thrownfrom a to a fixed point on the shore. Show by a diagram the
d irection ofthe path ofthe ball (gravity neglected).80 . A column of smoke tends to rise vertic ally from a
chimney, with a velocity equal to 6, but the prevailing windis horizontal, and has a velocity of 2 c . What is the path ofthe smoke.
81 . A man crosses a river in a row-boat at right angles tothe current. T he current is assumed to be 4miles an hour
,
the velocity imparted to the boat by the oars 3 miles anhour. Draw a parallelogram, and give the length of the
resultant. 5miles. )
82 . A body while mov1ng vertic ally downward , with a
uniform velocity of 1 0 feet, is urged horizontally w ith an
acceleration of 5 feet . Find its distanc e from the startingpoint after 2 seconds.
83. A body tends to move horizontally with a uniformvelocity of 1 2 feet, and also vertic ally downward with a uni
form velocityof8 feet. Determ ine its position after3sec onds.
84. Iftwo forces of5 and 7 units ac t on a point in directions at right angles to each other, show by a diagram the
direc tion in which the point begins to move.
85. A balloon is carried along by a current of air movingfrom east to west, at the rate of60 miles an hour, having no
motions ofits own through the air, and a p ith ball is dropped
from the balloon. What sort of a path will it appear to de
scribe as seen by a man in the balloon What will be its actual path P (Illustrate by a diagram.)
14 QUE S T ION S A N D P BOBL E M S I N P H YS I C S .
86. A ball, having a velocity of 180 0 feet, strikes the s ideofa vessel in motion. T he vessel is 50 feet wide ; the plumat the other side ofthe vessel
,where the ball passes out, lies
4inches farther to the rear than the place where the ballstruc k first. Find the velocity '
ofthe vessel (retardation ofthe ball neglected) .87. A ship is 1560 meters from the shore, and travels
parallel to the shore with a speed of 1 0 meters. A cannonball is fired with the assumed velocity of 780 meters from
the ship against the shore. T he ship at this instant is sup
posed to c ease moving. H ow far in the d irection of the pre
vions motion ofthe ship will the ball strike the shore P88. A body is subjected to two forces
,of 90 and 1 1 2
pounds respec tively, ac ting upon it at a right angle. Findthe resultant forc e by whic h the body is propelled.
89. A steamer moves due north with a certam velocity,the wind blowing from the west with the same veloc ity. In
what direc tion will a streamer on the vessel point ? (Illustrateby a diagram . )
90 . A steamer is going north with a veloc ity of 1 2 mi lesan hour; the wind is blowing from the west with a velocity of3miles perhour. What will be the d irec tion ofa streameron
the masthead of the vessel P, (Illustrate by a diagram. )
9 1 . A vessel is sail ing northeast with a c ertain velocity ;the wind is blowing from the south-southwest at the same
rate ofspeed. Find the direction ofa streamer on the masthead ofthe vessel . (Illustrate by a diagram . )
THIRD L AW OF MOT ION .
92 . S tate the third law ofmotion, and show how it holdsin case ofa stone falling to the earth .
93. What is meant by tension P H ow does it illustratethe third law ofmotion P M .
M OT ION . 16
94. Show the application of the third law ofmotion inhammering a nail into the wall ; in the fall ofa heavy body tothe earth ; in the driving ofpiles into the ground. M .
95. Ifa shot weighing 20 pounds leave a gun weighing 3tons w ith a velocity of 1 20 0 feet, find the velocity Of the
rec oil ofthe gun.
96. Explain the terms force,” “ weight and pressure.
’
97. Fourmen ofequal strength are in a boat on a lake.
They all have oars, but only one of them is rowing, giving’
the boat a veloc ity of2 miles per hour. What would be the
velocity ofthe boat ifthe other three men helped row1ng98. T wo spring balances are fastened together at their
fixed ends, and are then pulled horizontally, in oppositedirec tions, by two men, one at each end . With what forcewill each pull P99. T wo spring balances are so connected with each
other that the fixed end ofthe one is fastened to the movableend ofthe other; two persons then pull at Opposite ends, in a
horizontal direc tion. What is the eftec t ofthe pull ?1 0 0 . T he pairofSpring balanc es Ofthe prec eding example
are now held vertic al, the movable end being below. Whatdo the balances indic ate when the free end is pulled down ?
1 0 1 . A man standing on shore pulls in a rope, part of
which is on a vessel at some distanc e trom the shore. If,
now, a man on the vessel also begins to pull rope into the
vessel, w ill the vessel then move faster toward the shore thanbefore P
1 0 2 . Suppose that the man on shore had been pullingwith all his strength when the other person c ommenc ed to
pull rope into the vessel, would the vessel then move fastertoward the shore than before P
16 QUE S T ION S A N D P R OBL E M S I N P H YS I C S .
GR A V I T Y
1 07. Mention the points that must be specified in order
that a torce may be considered as known.
1 08. What is meant by universal gravitation, and why isit called universal P
1 09. What is Gravity P1 1 0 . What is the direction ofgravity, and how may this
be illustrated P
F A L L I N G B O D I E S .
(Unless otherwise indicated, take g 32 ft. , or 1 0
meters.)FOR M ULIE .
(I ) v= t g (4)
(2 ) v V”g s (s) t(3) s l g t
’
1 1 1 . Give formula for the falling bod ies.
T o find 1)
1 1 2 . A body falls freely for five seconds ; what is its velocity at the end ofthe time P(5 32 ft. 1 60 ft. Or 5 1 0 meters 50 meters. )1 I 3. What was its velocity at the end ofthe fourth sec ond P1 14. What was its veloc ity at the end of3% seconds 0 1
its fall P1 15. A body falls Ireely for one-fourth ofa second, what
is its velocity per second at the end ofthat time.
18 QuE S T IoN s A N D P R OBL EM S I N P H YSI C S .
Find space passed over1 24. A stone dropped from the top ofa tower struck the
ground in4sec onds. H ow high is the tower P
(s g. t’
1 6 4’
256
1 25. What spac e did the stone describe in the last second P
(Space desc ribed in4sec . 256 ; space described in 3sec .
(16 ft. 144ft. N ow,256 144 1 1 2 ft.
,answer. )
1 26. What spac e did it pass over in the first 254secondsofits fall P
(s 16 ft, (16$3i“) 1 0 0 ft. , answer.)
1 27. A body was fall ing freely for one-halfsec . Throughwhat height did it fall ?
1 28. H ow deep is a well with 20 feet ofwater, into whicha stone is dropped which reaches the surface of the water in154seconds P
1 29 . A body falls freely during 1 0 seconds; suppose gravity to cease acting upon it at the end of the seventh second ,what is the entire height ofthe fall ofthe body P
130 . T wo balls are dropped into a mine, one of them 3
seconds before the other. What space are they apart 5 secouds after the first was let fall ?
131 . Ifa body, having fallen 3 seconds, breaks a pane ofglass, and thereby loses one-third ofits veloc ity
, find the en
tire space passed over at the end ofthe fourth second.
132 . A balloon rises uniformly with a velocity of 1 0 feetper second, when a man drops a stone, which reaches the
ground in 3seconds after it was dropped. Find the height ofthe balloon,first, when the stone was dropped ; secondly,
whenthe stone reached the ground.
133. A t the instant offalling vertically a body is impelledby a force which causes it to move (vertic ally) three feet per
FAL L IN G BODIE S . 19
second ; how far is the body from the starting point after twosec onds
(Space described under gravity (16 64ft. Spacedescribed by virtue of the impulse 6 ft. 64 6
70 ft. )
134. A ball is dropped from the top ofthe mast ofa ship,which is sailing at the rate of 18 miles an hour. If the mast
be 64feet high, how far will the ship have sailed during the
passage ofthe ball.I35. Through what space must a body fall vertically to
acquire a velocity of 96 feet per second ? T o acquire a
velocity of40 m. per second P2 2
I . s—:g 22 144ft. Or,
I I : t—v 96 Hence s 16 3
’
g 32
2
Also, s— v2 — 40 —80 m.
28 29
136. A freely falling body strikes the ground with a velocity of1 meter. From what height has it fallen?
137. A falling body is precipitated vertically with a veloc
ity of 14feet per second, and reaches the ground with a
velocity of46 feet per second ; required, the space passedover.
138. A body falls vertically from a certain height ; threeseconds after it started another body descends vertically froma height of784feet. From what height must the first bodyfall, if both bodies are to reach the ground at the same in
stant.139. A body has been falling under gravity with an initial
veloc ity of 5m. per second. What is the space passed overin ten seconds P
so QUE S T ION S A N D P R OBL EM S I N P H YS IC S .
140 . A body falling freely from rest struck the groundwi th a velocity of85m. per second . For how long had itbeen moving , and what space did it describe in the lastsecond of its fall ?
Find the velocity.
142 . A body has been falling freely 576 feet. What is It:
velocity at the end ofits descent?V
143. A body has been falling freely 55 m. What it itsvelocity at the end ofits passage P
144. A body falls vertIc ally from a height of320 meters.
Find the time spent, and the velocity acquired.
145. A body was 554seconds in falling vertically R e
quired the height offall, and the velocity acquired.
146. With what veloc itv must a body be projected vertically downward to describe 206 feet In4seconds?
Find the time, 5 being known.
147. A body falls through a spac e of1 296 feet. Find thetime required .
(1 296= 54g t’ 1 296 t"
148. In what time would a body fall verticallyheight ofa mile P
P R OJEC T I L E S . 21
149 . In what time will a body fall vertically Irom the
height ofa kilometer P1 50 . A body falls several seconds during one of them it
passes over 528 feet which one is it ?
P R O JE C T I L E S .
(In these examwes bodies are supposed to move in vacuo
that is, without resistance. )1 55. Prove that in vacuo a body projected vertically up
ward c onsumes the same amount of time in rising that it doesin falling from the same height.
1 56. Show that in vac uo a body projected vertically up
ward returns to its starting point with the same velocity withwhich it was projected.
157. Show by a diagram the pa‘h ofa projectile thrownhonzontally, and moving during 4seconds with a horizontalveloc ity of1 0 0 feet per sec ond.
158. Explain the path ofa projectile thrown obliquely.
159. A ball is thrown vertically upward with a velocity of96 feet, how high will it rise P
v2
962
1st Solution. s . .-
2g 64144ft.
2d Solution. First find the time : t v 963seconds.
8 32
N ow, s 16 3’
144ft.160 . A n mronaut (in a balloon at rest in the air) projects
a body vertically downward with a velocity of60 meters persecond. Afterwhat time will the velocity ofthe body be 1 0 0
22 QUES T ION S A N D P R OBL E M S I N P H YS I C S .
meters, and what spac e will it have then described ?(100 m.=60 + g t ; that is, 1 00 = 60 + 1 0 t) whenc e t=4
seconds.
T he spac e desc ribed is r (60 4) (5 whenc e r
320 m.)161 . A body is projected vertically upward with aveloc ity
of 1 00 meters ; how high will it rise P162 . A body is projected vertically upward with an initial
velocity of10 0 m. After a time x, another body, is projectedvertically upward with the same velocity, and , after rising 8.5
seconds, meets the first. Find x, the time wh ich elapsed
between the two starts. (Take g
Solution—In redescending, projectiles have at every insul toftheir downward course the same velocity that theyhad whenrising . Both projectiles having had the same initial veloc ities,their velocities at the instant ofmeeting are also the same.
According To form. v t g, the velocity of the ris1ng bodyat the instant ofmeeting 1 00 (1 0 8. T he veloc ityofthe descending body at the instant ofmeeting also t g,where t is the time employed in rising and descending to thepoint where both meet . This t x and y
x find“) 1 0 ; hence 1 0 0 (1 0
1 0 , whence x 3seconds.
163. H ow long will a body continue to rise ifit is projec ted vertically upward with a velocity of48 feet P
164. H ow long will a body continue to rise if projec tedvertically upward and attaining a height of96 feet ? H ow
long will it be in the air P165. H ow long will a body rise if thrown vertically up
ward with a velocity of 1 5meters, and how long will it be inthe air P
166. A body is projected vertic ally upward with a velocity
om vrrr. 23
of80 feet ; give space passed over, rst, during first second ofits ascent ; 2d, during last second ofits descent.
167. A body is projected vertically upward with a velocityof35meters ; give space passed over 1 st, during first secondofits ascent 2d, during last second ofits descent.
168. A projectile was impelled vertically upward, and rose
to a height of605 meters. Find the velocity with which itrose.
1 1 0 m. )169 . With what velocity must a body he projected verti
cally upward to return to the starting place in 6 seconds P1 70 . A body is thrown vertically upward, and reaches the
highest point of its flight in 5 seconds. Whatmust havebeen its velocity two seconds before this point was attained P
171 . A body was projected vertically upward , and passeda certain point with a velocity of 80 feet per sec ond . H ow
much higher did it rise P (This question is equivalent to the
following one172 . A body was projected with a velocity of80 feet per
second. H ow high did it rise 7173. In its vertical upward flight a body passed a certain
point with a veloc ity of 18 meters per second . H ow muchhigher did it rise P
1 74. A body projected vertically downward with a velocityof 20 feet a sec ond, passes through 1 0 0 feet in a certain sec
ond . Find overwhat space it passed in the preceding second.
175. A body projected vertic ally downward with a veloc ityof4meters a sec ond, passes through 39 metres in a c ertainsecond. What space did it desc ribe in the sec ond prec eding P
176. A ball is projected upward with a velocity of160 feetper second, and two sec onds afterward another ball is projec ted vertically upward with a velocity of 20 0 feet per sec
was gt1 .ri
double the w lucmr qf the 011115; H ow m ny fimes as highas the latter will che firrm rise ?
179. A tu iy projec ted horiz onmlly fim tbe wp ofa c lifl‘
,
I ith a veloc ity ofao t‘
eet per seconi snikes tbe ground after
point ofprojex tiun.
180 . lt g m me m is i ma m mem how high
could a boy leap vemc l ly on the moon, 1f on tbe earth he
FA LL OF BODIES ON T H E IN C LIN ED P LAN E .
_l
h
z: 1: h ! z?
28 l , ls/ g
(In these examples friction is neglected.)18 1 . A ball rolls down an incline for 3 seconds, and
passes over 7 feet the first second. Find the velocity ac
quired at the end .
26 00 1131 1033 u p room u m ean.
W E I G H T .
188. Define theM or weight ofa body.
189 . What is meant by mass ?190 . Distinguish between the gravity and the mass ofa
hod r.
19 1 . H ow do you find the gravity of bodies at a point
below the surfac e ofthe earth Psurface ofthe earth ?
192. If a stone weighs 1 0 pounds at the level of the
oc ean. how muc h would it weigh 1 00 0 miles below the sur
face P('
l‘
he proposed place below the surface is 300 0 miles hourthe earth’s c entre. Take this distance as a new radius.
Then, by proportion, 400 0 mi. 3000 mi. 1 0 x, whence x
7} lbs.,answer.
Or, for every mile that the distance from the objec t to the
centre ofthe earth is diminished diminish the weight by “ in .
N ow, 1 0 lbs. (iggsof1 0 ) 1 0 z } 7} lbs.)1 93. H ow far below the surface Ofthe ocean must I plac e
the stone, in the previous example, that it mayweigh onlyone-fourth Ofa pound P
194. H ow far below the level Of the ocean must a roc kweighing a ton be placed in order that it may weigh onlyone-sixteenth ofa ton P
195. H ow do you find the weight Of bodies imagined to
be placed above the surface ofthe earth P
WE IGH T . 27
196. A body weighs 180 0 pounds at the earth’s surface.
What would be its weight 20 00 miles above the surface P(T he proposed place being 200 0 miles distant from the sur
face, we have a new imaginary radius (of the earth ) of60 00m iles. N ow, g varies inversely as the square ofthe distance ;henc e
,by proportion
, 400 0’ 60 0 0 ’ x 180 0 lbs. ,
whencex 80 0 lbs.)
1 97. What would be itsweight 50 miles above the surface P1 98. A meteorite was found, after striking the earth, to
weigh 20 pounds. What was its weight 1 0 miles above the
surfac e P1 99 . A body weighs 50 kilos. at the earth’s surface. What
would be its weight 20 0 0 kilometers above the surface P (Takethe radius ofthe earth 6367kilometers. )
20 0 . H ow far above the surfac e Ofthe earth must a poundweight be placed in order to have the gravity ofone ounce(avoir.) P20 1 . S tate the law and formula ofthe intensity ofgravity.
20 2 . H ow does the intensity of gravity vary at differentplaces on the earth ’s surface P
203. I suddenly jump off a platform with a 20 poundweight in my hand. What will be the pressure upon my arm
while I am desc ending through the air? Explain your an
swer.
204. Define the c entre ofgravity.
205. What is meant by equilibrium P206. Explain the different kinds of equilibrium, and illus
trate each .
207. Define stability, and tell how it may be increased .
208 Must the c entre ofgravity ofa body always be withinthe substanc e ofthe bodv P
209 . Illustrate stable and unstable equilibrium by the c ase
ofa loaded sphere plac ed upon an horizontal plane.
28 QUE ST ION S A N D P R OB L EM S IN P H YS I C S .
2 10 . Why is it easier to roll a round body than a squareone ?
2 1 1 . Where is the centre ofgravity ofa triangle situated?2 1 2 . T wo balls ofuniform density, eac h 6 inches in radius,
are placed side by side in c ontac t ; one weighs 1 2 lbs.,the
other36 lbs. Find how far the c entre of gravity of the twoballs is from the centre ofthe heavier.
THE P E N DULUM.
t : T VT: I/ij , or t’: l z L
,in which t
the time which pendulum 1 requires to make one oscillation and
'
l‘
the time which pendulum L requires to make
one oscillation.
2 15. What is meant by a physic al pendulum P What ismeant by a mathematic al pendulum P
2 16. What is meant by the c entre ofsuspension, and the
centre ofosc illation P2 17. S tate the laws ofthe pendulum.
2 18. Illustrate the first two laws.
2 1 9. Illustrate the third law .
2 20 . Express formula in the fourth law in ordinary language.
2 2 1 . T wo pendulums are respectively 4feet and 9 feet
long ; the shorter uses two units of time (that is, a time of2)for making one osc illation. What is the time used by the
otherformaking one oscillation PSolufion.
—T he shorter the pendulum, the shorter the timeit requires for one oscillation ; the longer the pendulum, the
longer the time required for one oscillation ; and their lengthsare to eac h other as the sqnares oftheir time. H enc e 4z 9 z z
2' x’
,whence x 3units oftime.
2 2 2 . One pendulum is4times as long as another. WhatIs their relative time ofoscillation P
2 23. T wo pendulums are respec tively 49 centimeters and
64 c entimeters long. What is their relative time ofoscillation P224. A pendulum 16 inches long makes an oscillation in a
unit of time. In what time will a pendulum 25 inc hes longmake one oscillation at the same place P
2 25. I t a pendulum 39 inches long oscillates seconds,what will be the time of its osc illations when it is lengthenedone inch ? (When lengthened, it is another pendulum
, 40inches long ; whereas the former pendulum had a length of
39 inches. )2 26. Ifa pendulum 1 meter long oscillates seconds, what
will be the time ofits osc illations when it is shortened 1 c en
timeterP
227. In N ew York City how long must a pendulum be tooscillate once in 3 seconds P(Take the length of the second pendulum in N ew YorkW 39 1 inches.)228. T wo pendulums malte respectively 7 and 8 Oscilla
tions 2 minute. Find their relative lengths.
(Solution to problem 2 2 1 shows that the pendulum making8 oscillations aminute is shorter than the onemaking 7osc illa~
so QUE S T ION S A N D P R OBLE M S I N P H YS IC S .
140 . A body falling freely from rest struck the groundwith a veloc ity of85m . per second . For how long had itbeen moving
,and what spac e did it describe in the last
sec ond of its fall ?
Find the velocity.
142 . A body has been falling freely 576 feet. What is It:
velocity at the end ofits descent ?V
143. A body has been falling freely 55 In. What is itsvelocity at the end ofits passage P
144. A body falls vertic ally from a height of320 meters.
Find the time spent, and the veloc ity acquired.
145. A body was 5% seconds in falling vertically R e
quired the height offall, and the velocity acquired.
146. With what veloc itymust a body he projected vertically downward to describe 206 feet In4secondsP
Find the time,5 being known.
147. A body falls through a space of1 296 feet. Find thetime required.
1 296_ t, ,
148. In what time would a body fall vertically from theheight ofa mile P
P R OJEOT I L E S . 21
149 . In what time will a body fall vertically trom the
height ofa kilometer P1 50 . A body falls several seconds ; during one of them it
passes over 528 feet which one Is it ?
P R O JE C T I L E S .
(In these examples bodies are supposed to move in vacuo
that is, without resistanc e. )1 55. Prove that in vacuo a body projected vertically up
ward c onsumes the same amount of time in rising that it doesin falling from the same height.
1 56. Show that in vac uo a body projected vertic ally up
ward returns to its starting point with the same velocity withwhich it was projected.
1 57. Show by a diagram the path ofa projectile thrownhorizontally
,and moving during 4seconds with a horizontal
velocity of1 0 0 feet per sec ond.
1 58. Explain the path ofa projec tile thrown obliquely.
159. A ball is thrown vertically upward with a velocity of96 feet, how high w ill it rise P
v2
962
1 1! Solution. s__2g 64
144ft.
2d Solution. First find the time : t v 963seconds.
8 32
N ow, s 16 3’
144it.
1 60 . An a ronaut (in a balloon at rest in the air) projec tsa body vertically downward with a velocity of60 meters persecond. After what time w ill the veloc ity ofthe body be 1 00
28 QUES T ION S A N D P R OBL E M S IN P H YS IOS .
meters, and what space will it have then described ?(100 that ia, 1 0 0 = 6o+ 1 0 t) whenc e t= 4
seconds.
T he space described is r (60 4) (5 whence I
320 m .)161 . A body is projected vertically upward with aveloc ity
of 1 00 meters ; how high will it rise ?162 . A body is projected vertically upward with an initial
velocity of1 00 m. After a time 11, another body, is projectedvertically upward with the same veloc ity, and , after rising 8.5
seconds, meets the first. Find x, the time which elapsedbetween the two starts. (Take g
Solution—In redescending. projectiles have at every instantoftheir downward course the same velocity that theyhad whenrising. Both projectiles having had the same initial velocities,their velocities at the instant ofmeeting are also the same.
A c cording
\'
to form. v t g, the velocity of the rismg bodyat the instant ofmeeting 1 00 (I o T he velocityofthe descending body at the instant ofmeeting also t g,where t is the time employed in rising and descending to thepoint where both meet. This t : x 31159 ; d
x 1 0 ; henc e 1 00 (1 0
x 1 0,whence x 3seconds.
163. H ow long will a body continue to rise ifit is projec ted vertically upward with a veloc ity of48 feet P
164. H ow long will a body continue to rise if projectedvertically upward and attaining a height of96 feet ? H ow
long will it be in the air P165. H ow long -will a body rise if thrown vertically up
ward with a velocity of 1 5meters, and how long will it be inthe air P
166. A body is projected vertically upward with a velocity
24 QUE S T ION S A N D P R OB LE M S IN P H YS IOS .
ond. Find their distance apart 5 seconds after the first ballwas projected.
177. T wo bodies are projected vertically upward, one withdouble the velocity ofthe other. H ow many times as highas the latter will the former rise?
178. A body is projected vertically upward with a velocityof40 meters. H ow many seconds, and how high, will itrise P
179. A body projected horizontally from the top ofa c lifi'
,
with a velocity of40 feet per second, strikes the ground after
8 seconds. Find the distance of the point offall h'
om the
point ofprojection.
1 80 . Ifg on the moon is i that on the earth, how highcould a boy leap vertically on the moon, if on the earth he
c an leap two feet high P
FALL OF BODIES ON THE INCLINED PLANE .
v = t g . ll
l
; Vz g ss s= i g t’o -
l
i
l
Y: E h J ET
2g 1 n(In these examples friction is neglected.)181 . A ball rolls down an incline for 3 seconds, and
passes over 7 feet the first second. Find the velocity ao
quired at the end .
P A LL IN o BODI E S ON I N OL IN E . 25
Solution—Since the spac e passed over under gr. during thefirst sec ond i g, the velocity at the close of this secondg, or twic e the space desc ribed in the first second. Hence v
182 . A ball was ascending the same inclined plane in 3
seconds. What velocity had it when starting P183. A body rolling down an inclined plane in 1 0 seconds
acquired a velocity of 20 feet at the end of the first second.
Find the final velocity.
184. What space did the same body desc ribe in the firstsecond, and what was the length ofthe iod ine P
185. T he length ofan inc line is 80 0 feet a body requires1 0 seconds to descend it. What velocity does it acquire at
the c lose ofthe first second P186. A body desc ended an inclined plane of64feet verti
cal height and 256 feet in length . In what time, and withwhat velocity did it reach the base P
26 QUES T tON S A N D P ROBLEII S IN P R Y S IG .
W E I G H T .
188. Define the grow'
ly or weight ofa body.
189. What is meant by mass ?190 . Distinguish between the gravity and the mass ofa
body .
1 9 1 . H ow do you find the gravity of bodies at a pointbelow the surface ofthe earth Psurfac e ofthe earth ?
1 92. If a stone weighs 1 0 pounds at the level of theoc ean, how much would it weigh 1 0 0 0 miles below the sur
face(T he proposed place below the surface is 300 0 miles from
the earth’s centre. T ake this distance as a new radius.Then
,by proportion, 40 0 0 mi. 30 0 0 mi. 1 0 x, whence x
7} lbs.
,answer.
Or, for every mile that the distance from the object to the
centre ofthe earth is diminished, diminish the weight by solosN ow, 1 0 lbs. (1838of1 0 ) 1 0 2 } 7} lbs.)
193. H ow far below the surface ofthe ocean must I plac ethe stone, in the previous example, that it may weigh onlyone-fourth ofa pound
194. H ow far below the level of the ocean must a rockweighing a ton be plac ed in order that it may weigh onlyone-sixteenth ofa ton P
195. H ow do you find the weight of bodies imagined to
be plac ed above the surface ofthe earth P
WE IGH T . 27
196. A body weighs 180 0 pounds at the earth’s surface.
What would be its weight 20 00 miles above the surface P(T he proposed place being 200 0 miles distant from the sur
face, we have a new imaginary radius (of the earth ) of60 00miles. N ow,
g varies inversely as the square ofthe distance ;hence, by proportion, 40 0 0 ’ 60 0 0’ x 180 0 lbs.,
whenc eX 80 0 lbs.)
1 97. What would be its weight 50 m iles above the surface P1 98. A meteorite was found, after striking the earth, to
weigh 20 pounds. What was its weight 1 0 miles above the
surfac e P1 99 . A body weighs 50 kilos. at the earth’s surface. What
would be its weight 20 0 0 kilometers above the surface P (Takethe radius ofthe earth 6367kilometers. )
20 0 . H ow far above the surfac e ofthe earth must a poundweight be placed in order to have the gravity ofone ounc e
(avoir.) P20 1 . S tate the law and formula ofthe intensity of gravity.20 2 . H ow does the intensity of gravity vary at different
places on the earth ’s surface P203. I suddenly jump off a platform with a 20 pound
weight in my hand . What will be the pressure upon my arm
while I am descending through the air? Explain your an
swer.
204. Define the c entre ofgravity .
20 5. What is meant by equilibrium P206. Explain the different kinds of equilibrium, and illus
trate each .
207. Define stability, and tell how it may be increased .
208 Must the c entre ofgravity ofa body always be withinthe substanc e ofthe body
209 . Illustrate stable and unstable equilibrium by the caseofa loaded sphere placed upon an horizontal plane.
28 QUE S T ION S A N D P R OB L EM S IN P R Y S IOS .
2 10 . Why is it easier to roll a round body than a squareone P
2 1 1 . Where is the c entre ofgravity ofa triangle situated ?2 1 2 . T wo balls ofuniform density, eac h 6 inches in radius,
are placed side by side in contac t ; one weighs 1 2 lbs., the
other36 lbs. Find how far the c entre of gravity of the twoballs is from the centre ofthe heavier.
THE PE N DULUM.
Formula : t : T : : VT: VI; or t’: l z L , in which t
the time whic h pendulum 1 requires to make one oscillation ; and
'
l‘
the time which pendulum L requires to makeone oscillation.
2 1 5. What is meant by a physical pendulum ? What ismeant by a mathematic al pendulum P
2 16. What is meant by the c entre ofsuspension, and the
centre ofosc illation P2 17. S tate the laws ofthe pendulum.
2 18. Illustrate the first two laws.
2 1 9. Illustrate the third law .
2 20 . Express formula in the fourth law in ordinary language.
P E N DULUM . 29
22 1 . T wo pendulums are respectively 4feet and 9 feet
long ; the shorter uses two units of time (that is, a time of2)for mak ing one oscillation. What is the time used by theotherfor making one oscillation PM urrow—T he shorter the pendulum, the shorter the time
it requires for one oscillation ; the longer the pendulum, the
longer the time required for one oscillation ; and their lengthsare to eac h other as the sqnares oftheir time. Hence 4: 9 ::
2’1 x
’, whence x 3units oftime.
2 2 2 . One pendulum is 4times as long as another. WhatIs their relative time ofoscillation P
2 23. T wo pendulums are respectively 49 centimeters and
64 c entimeters long. What is their relative time ofoscillation P
2 24. A pendulum 16 inches long makes an oscillation in a
unit of time. In what time will a pendulum 25 inches longmake one oscillation at the same plac e P
2 25. I t a pendulum 39 inc hes long oscillates seconds,what will be the time ofits oscillations when it is lengthenedone inc h ? (When lengthened, it is another pendulum, 40
inc hes long ; whereas the former pendulum had a length of
39 inc hes )2 26. Ifa pendulum 1 meter long oscillates seconds, what
w ill be the time ofits oscillations when it is shortened 1 cen
timeter?
2 27. In N ew York City how long must a pendulum be toosc illate once in 3seconds P(Take the length of the second pendulum in N ew York
inches.)228. T wo pendulums make respectively 7 and 8 oscilla
tions a minute. Find their relative lengths.
(Solution to problem 2 2 1 shows that the pendulum making8 oscillations aminute is shorter than the onemaking 7oscilla
30 QUE ST ION S A N D P ROBLn S I N P R Y S IOS
tions in the same time. T heretore, its time for one osc illation
must also be shorter than the time used by the other. N ow,
the time ofoscillation oftwo pendulums ofunequal lengths isinversely as their respective numbers of oscillations. H enc e
ac cording to form, t‘ T’ l L, and ass uming the length to
be I , we have 7’ 8’ I x, whence x 23. H enc e the
answer : A s 1 Is to
2 29 . A pendulum 1 meter long makes 40 oscillations in a
given time. H ow long must a pendulum be to make 60
oscillations in the same time and at the same place P230 . In N ew York City how long must a pendulum be to
oscillate in i second P231 . A pendulum feet long makes 45 oscillations in a
given time. H ow long must a pendulum be to mak e 60 osc illations in the same time and at the same place P
232 . A pendulum meters long makes 400 osc illations
in a given time. H ow many oscillations will it make duringthe same time, if the rod has expanded min of its former
length P233. A small, heavy ball is suspended by a thread from a
point, and makes small oscillations. T he thread is shortenedby two feet, and now the number ofoscillations per minute isincreased in the ratio of4to 3. Find the original length of
the thread. (S . K.)234. A pendulum clock loses two seconds each day. H ow
much must it be shortened to keep correc t time?235 A pendulum, the length ofwhich is m., makes
82 commons A N D rm nm s m Pum ice.
F O R C E
(Formula for General E quation ofForce F m c , in
whic h F stands for anyforce acting for one sec ond upon a
mass m ; and c the velocity generated (in feet per second).Since the mass ofa body its weight W d ivided by g, the
Wgravity at-the place, we also have F g c.)
250 . What are the ways inwhich torce maybe measured ?251 . Define work.
252 . What is a footpound A kilogrammeter253. Distinguish between the mass and the weight ofa
body.
254. What is the magnitude ofa force which in one sec
ond c an generate in a mass of40 a velocity of6feet per sec . ?
Solution—F m c 40 6 240 , answer. That is, theforce exerts the same vertical pressure as a mass of240 .
255. What is the magnitude ofa force which in one sec
ond c an generate in a body weighing 40 lbs. a velocity of6
feet per second Solution—F (1260 (33) 6 lbs.
256. Required the force producing motion, if a weight of25 ounces be caused to move through 320 feet in 1 0 seconds.
(According to formula 3 g) t’, we have 320 (Kc )whence c feet, the acceleration per second. N ow,
FW c
5 oz . , answer.)8 32
257. Required the magnitude of a force which in one
FORC E . 83
second c an give a body weighing 1 1 2 lbs. a velocity of1 0 feetper second.
258 A force of8 ounces causes a certain mass to movefrom rest w ith a veloc ity of4feet per sec ond ; required the
weight ofthe mass.
259 . A body is started from a state of rest by an ac celer
ating force of1 2 meters per sec ond, and passes over a spaceof3750 meters. Find the time.
(L et g the accelerating forc e ; then, ac c ording to for
mula s g t’, we have 3750 t’
,whence t 25sec . )
2
260 . Given a forc e of lbs. ,ac ting on a mass whose
weight 40 lbs. For how long a time must the forc e ac t
upon the mass to produce a veloc ity of48 feet per second261 . A loc omotive moves at the rate oi 30 miles an hour
when the steam is shut off; the fric tion ah the weight ofthe locomotive. Find the time that will elapse before it steps.
262 . T wo bodies, whose masses are m and 3m,are moved
by forces 3 p and p respec tively . Compare the Spac es theydescribe in t sec onds.
F g henc e mass mW
and mass 3m That is, the velocities of both
masses are to each other as 3_p E,or as 3 1 . Henc e the
c c
spac es described are to eac h other as 32 that is, as 9 1 .
263.A body starting from a state ofrest is ac ted upon by
an ac c elerating forc e, whic h impressess upon it an ac c eleration of5 m . per second. What will be the spac e it desc ribesin 1 0 sec onds
264. Ifa forc e of1 0 pounds in a c ertain time gives a body3
34 QUE S T ION S A N D P R OBL E M S I N P H YS IC S .
a velocity of9 feet per sec ond, what veloc ity will a force of
25 pounds impart to the same body in the same time ? R .
265. Ifa forc e of36 pounds imparts a veloc ity of 5 feetto a mass of 1 0 0 pounds, what mass will in the same time,
plac e and c irc umstanc es rec eive a veloc ity of 6 feet from a
mass of45 pounds266. If a forc e of 6 pounds gives to a certain mass a
veloc ity of 20 feet per sec ond in 4sec onds, what vel. w illa forc e of4pounds give to twic e the mass in 6 seconds (M .)
267. A body is subjec ted to the action ofan acceleratingforc e of 1 0 meters per sec ond. What will be its veloc ityat the end offifteen minutes (60 1 5 1 0 90 0 0 m . )
268. A body under the influenc e ofan acc elerating force(ofc onstant ratio) passes over a spac e of360 m . in 6 seconds.
Required the 1ntensity ofthe ac c elerating force.
whenc e g 20 m . per second.)2
269. What was the Spac e passed over by the body in theprevious example during the last second(Ifin 6 sec onds it describes 360 m,
it will in five seconds
desc ribe ff 52
250 m. ,and in the sixth sec ond it will pass
2
over 360 250 1 1 0 meters. )270 . A canon ball was projec ted vertic ally upward with a
veloc ity of50 0 meters per sec ond . After how many secondswas its veloc ity reduc ed to 30 0 m . (under the retarding influenc e ofgravity) , and what spac e had it passed over (g1 0 m . )
271 . A body impressed w ith an initial velocity, whoseamount or
‘
intensity is unknown, is ac ted upon by a retardingforc e of20 m . per second in the Opposite direc tion,
in conse
quenc e ofwhic h it c omes to rest at the end of30 seconds.
Find the intensity ofthe initial veloc ity.
" ’ m '
E N E R GY . 35’
E N E R G Y .
(Formula ofKinetic Energy %mv’
, in wh ic h m the
mass (or Y ) of the moving body, v its veloc ity per sec .)g280 . S tate what is meant by energy, by kinetic energy, and
by potential energy.
28 1 . Explain the great natural principle from which flywheels derive their efiic iency. (S . K. )
282 . S tate briefly how a fly-wheel equaliz es the motion of
mac h inery. (S . K .)283. H ow is the energy ofa fly-wheel affec ted by
(1 ) Giving it tw ice the weight ?(2) By giving it twic e the diameter(the weight and
number ofrevolutions remaining the same)?(3) By giving it twic e the number of revolutions in
a given timeA nswers—(Friction neglected) T he energy becomes
twic e as great. (2 ) T he energy becomes four times as great.(3) T he energy becomes four times as great.Explain eac h answer.
284. Required the kinetic energy, or vis viva,” ofa bodywhose mass 1 0
,and whose v 1 0 0 0 feet per second.
Soluti'
on. m) v’ 5 1 0 0 0’
50 0 0 0 0 0
1 56250 footpounds.
285. Required the vis viva ofa body weighing 96
pounds, moving with a velocity of1 0 00 feet per second.
36 ounsrmN s A N D P R OBL E M S I N a eros.
286. Find the kinetic energy ofa 24pound ball, movingat the rate of 200 0 feet per second.
287. Find the kinetic energy of5c ub. meters ofwater thatflow every second through a channel with a veloc ity of3meters.
288. Find the kinetic energy or striking forc e ofa 96
pound cannon ball, flying with a velocity of 1 50 0 feet.
289. What would be the kinetic energy ofa pebble weighing one
-halfounce, and striking the earth after falling twoseconds
290 . If a gun with a certain charge of powder cause a
hundred-pound shot to ascend vertically for three seconds,through what height will a fifty pound shot ascend with threetimes as great a c harge ? (M .)
Ammer.—5184feet high . (T he height towhich a body c an
be projected varies directly as the square of the projectingforce, and inversely as the square of the mass projected.)
29 1 . Ifa shot weighing one ounc e, and projected with nounc es of powder, rises 20 0 feet high, how high will a shotrise that weighs three ounces, and is projected with 22: ounc es
ofpowder292 . An arrow shot from a bow starts offwith a veloc ity
of 1 20 feet per second. With what veloc ity will an arrow
twic e as heavy leave the bow,if sent offwith three times the
force (M . )
293. Ifa ball fired from a gun rise to a height of150 feet,to what height will a ball halfagain as heavy rise iffired withtwic e the charge ofpowder? (M
294. T wo balls weighing 8 and 6 ounces respectively aresimultaneously projected upward. T he former rises to a
height of324feet, and the latter to one of256 feet ; comparethe forces ofprojection. (M .)
WORK . 87
W O RK .
30 0 . Define Work .
30 1 . What is a unit ofwork, and what a horse power30 2 . H ow do you measure work, or mechanical energy303. C an you destroy work by any combination ofma
c hines304. Point out the absurdity ofperpetual motion.
305. H ow much work is done per hour, if 1 00 pounds beraised 3feet high perminuteSolution. T o raise 1 00 pounds one foot high 1 0 0 foot
pounds ofwork perminute ; to raise 1 0 0 pounds three feethigh 30 0 footpounds ofwork per minute, and in one hour60 30 0 1 8000 footpounds ofwork.
306. H ow many units ofmechanical work will be ex
pended in raising 1 0 c ub. feet ofwater 1 0 0 feet high ? (Ac ub. ft. ofwaterweighs lbs.)
307. Five hundred cubic feet of water per minute are
raised by pumping to a height of 200 feet. Find the workdone perminute in footpounds and the rate ofdoing work inh rses-power. (S . K. )308. H ow many gallons orwater would a steam engine of
lo-hOl’
S C -pOWC l’
raise from a depth of1 00 0 feet in an hour?
(A gallon ofwater weighs 1 0 pounds.) (8. K.)
309. What power ofsteam engine will be required to raise1 0 tons of coal per hour from a mine whose depth is 60 0feet K )
38 QUE S T ION S A N D P R OB L E M S I N Pnrsros.
31 0 . A weight of3 tons is raised through 50 feet. H ow
many units ofwork must be done by the agent31 1 .
oIfthe weight 15 raised m one fourth ofaminute, whatmust be the horse-power ofthe agent?31 2 . A man works on a mac hine in suc h a manner as to
do units of useful work in a day of 8 hours. T he
mac hine is so arranged that he c an lift a mass of5 c wt. H ow
long will it take him,working at his daily average rate
, to liftthat weight through a height of1 0 0 feet ? (S . K .)
313. A bricklayer’s laborer with his hod weighs 1 70 lbs
he puts into the hod 20 bric ks weighing 7 pounds eac h ; hethen walks up a ladder to a vertic al height of 30 feet. H ow
many units ofwork does he do And ifhe c an do
units ofwork per day, how many bricks will he tak e up the
ladder in a day (S . K.)
40 QUE S T ION S A N D P ROBL EM S I N P H YS I C S .
320 . An inelastic body weighing 25 kilos. moves with a
velocity Of meters. I t is struck by another inelastic bodyweighing 40 kilos. , whose veloc ity 7m. , and whose motionis Opposite to that Of the first. With what velocity and inwhat direction will both bodies move after impact (B.)32 1 . Find the momenta and kinetic energies of the two
bodies. in the previous example, both before and after impact.32 2 . With what veloc ity and in what direction w ill bothbodies move after c ontac t if their motions originally have thesame direc tion
323. Find the kinetic energies of the two bodies after
impac t,ifthe conditions are the same as in example 32 2 .
324. T wo inelastic bod ies, weighing together 80 0 pounds,move against eac h other. One has a velocity of40 feet, theother a velocity of 60 feet. After impac t both move on witha velocity of25feet. Find the weight ofeac h body. (B.)325. T wo inelastic bodies, respec tively weighing 1 8 and
24pounds, move in the same direc tion. After impact bothhave a velocity of8 feet ; the original veloc ity ofthe first bodywas to that ofthe sec ond as 2 is to 3. Find the veloc ity eachhad before impac t. (B. )
326. I twill be observed that the pavior employs a woodenram wherewith to imbed stones. Those who break stones atthe roadside use a small, elongated hammerwith a long, supple handle or shaft. Will you explain the natural principlesthat are involved in these and similar devic es tS . K.)
OE N TBI FUGA L roses . 41
C ENTRIFUGAL FORCE .
2
inwhic h m mass ofthe revolving body
v its velocity ; r the radius ofthe circ le,)
330 . What is meant by centrifugal forc e What,by c en
tripetal force331 . Find the c entrifugal force Ofa two-ounc e leaden ball
at the end of a string 3 feet in length , and rotating around
the other end ofthe string with a velocity of50 feet.W
the mass of the ballg
5232 , 028. answer.
S olution. S ince mass
hencem v’ 50
,
r3
332 . A body weighs40 kilos. ; it moves in a c ircle Of
m. radius, with a velocity of22 In. Find its centrifugal force.
333. A pail filled with water is whirled in a horizontal c irc le of 38 inches radius, so as to perform two revolutions a
second. I ts c ubic contents cubic foot. S tate w ithwhat force the water is forc ed against the bottom ofthe pail.334. An appleweighing two ounc es is tied to one end ofa.
string 3feet in length , and whirled round three times a sec ond .
R equired its centrifugal force.
335. A t the equator the c entrifugal forc e is 259 of the
intensity ofqgravity. What must be the velocity ofrotationof the earth in order that the c entrifugal forc e may equal theforce ofgravity (Solution on next page. )
42 common A N D P ROBLE I S IN P ursrc s.
(L et v the actual veloc ity, and v’ the unknown ve
loc ity, then, as centrifugal forc e varies d irectly as the square ofthe velocity
v’ v g 289 g,whenc e v
” g v’ 289 g,or v"289 v’,and v
’ v J 2891 7 v.
the rotary velocity Of the earth must
F R I C T I ON .
336. What is fric tion ? What is the difl'erenc e betweenrolling and sliding fric tion
337. What kind of friction between the ground and the
feet ofa person walking P338. Explain fully the nature Of the resistance termedfriction, and state the laws by which it is governed, so far
as they apply to mac hinery ; and likewise mention some of
the means that are employed to diminish its effec t so far as
may be practicable. (S . K.)
339. What is the object ofhaving bronz e or other peculiarmetal as the bearings or bushes ofmachinery for iron axles torun or work upon (S . K .)
340 . A body weighing 1 0 0 pounds is mous e. on a hori
zontal plane by a force of 1 2 pounds. Find the coefficient offric tion. Answer,
FR I C T ION . 43
341 . A body weighing 20 kilos.,and moving on a hori
ziontal plane, requires a force of50 0 grams to keep it in motion. Find the coefficient offric tion.
342 . A sleigh containing two persons, weighs450 pounds,and moves on an horizontal trac k. T he coed'
. of frict1on
being find the force required to keep the sleigh inmotion.
Solution—450 36 pounds .
343. A cast iron plate having a weight of 200 0 poundsis nicely p laned and smoothed upon its undersurface, In orderthat it may slide easily on c arefully prepared brass or gun
metal bearings, whic h are properly lubricated with good oil.What amount offric tion
,expressed in pounds, will have to be
ovc rc ome in giving it a slid ing motion (Coeffic ient offriction
,
344. A body is moving with a veloc ity of 1 0 0 feet. A s
suming that the resistanc e of the air amounts to 1 5 pounds,what will be the resistanc e if the same body moves with a
veloc ity of1 20 feet ?(T he two resistanc es are to eac h other direc tly as the squares
ofthe veloc ities. )
345. T he front end of a railway c ar has a surfac e of90
square feet. When the c armoves with a veloc ity of 25 feet,
the resistanc e ofthe air in front is 1 0 pounds for every squarefoot. What will the resistanc e be when the c ar moves with aveloc ity of40 feet ?346. T he resistanc e ofthe air tends to c onvert the motion
ofa freely falling body into uniform motion. Explain this.
44 QUE S T ION S A N D P R OBLE M S I N P H Y S IC S .
M A C H I N E S .
350 . What is a machine351 . Define the terms power and weight.
352 . Tell what is meant by “ internal resistance,illustrate by the steam engine.
353. S tate the general law ofmachines in equilibrium, and
give equation.
354. M ention the simple mec hanic al powers.
355. S tate the general law Of mec hanic al powers, and
illustrate by means ofthe movable pulley.
356 H ow do you find the mec hanic al advantage of a
machine, or the power gained by it357. Show that no mac hine ever creates power or energy.
358. What is meant by the amount of useful work ofa
machine359. What is meant by the entire effec t ofa machine
L E V E R S .
(W P L 1, where W weight ; P force required tobalanc e W L distance between P and the fulc rum ; 1distance betweenW and fulcrum. )
360 . What is a lever? H ow are the difl'
erent orders of
levers distinguished from one another
361 . S tate the rule for finding how one weight will balanceanoth :r on a straight lever.
L EVE R S . 45
362 . H ow do you find the advantage gained by a lever363. A small weight at one end of a lever raises a big
weight at the other end . S how that there is, nevertheless, noenergy created by a lever.
364 Classify the following objec ts ac c ording to the orderoflevers to whic h they belong
Knife, Pincers, Spade, Oar ofrow-boat,Shears, T weez ers, A x , H ammer,
A uger, L emon-squeez er, Bow , H uman arm,
Wheel-barrow, Sugar-tongs, C rowbar, C hisel,
Key, Fork, C hopping-knife, N ut-cracker.
LEVERS .
(Remember: When there is a slight excess offorce on eitherside
, the lever will c ommence to turn. In this c ase the workdone is the same on either side minus the surplus ofworkproduc ed by that slight exc ess, which, in these examples, isneglec ted. Illustrate every example by a drawing.)
370 . T he F (fulcrum ) ofa lever 1 0 feet long is 2 feet from
one end at this end hangs aW (weight) of80 pounds. Whatforc e (P ) at the other end will balance it(W P L l
,
80 x 8 2 , whenc e x 20 pounds. )
371 . T he F of a lever is I foot from one end and 4feet
from the other. What is the advantage gained What is theeffect ifthe P applied 1 pound372 . Find the power required to raise the weight in ex
ample 370 , ifthe friction at the fulc rum amounts to one-fourthofthe advantage gained.
373. Find the weight ofa rock lifted by means ofa crowbar 8 feet long ; F 1 foot from one end , P 30 pounds.
46 QUE S T ION S A N D P R OBL EM S I N P H YS IC S .
374. T wo weights of6 and 8 pounds respectively are to
be suspended from the ends of a lever 7feet long. Wheremust the F be placed so that the weights may balanc e375 Length of lever, m. At its ends are two forc es,
respec tively of40 and 30 kilograms. Find position ofF.
376. A heavy rod 1 2 inc hes long balanc es at a point 3inc hes from the end . Will it continue to balanc e about thatpoint ifequal weights be attached to both ends377. If 16 pounds balance 20 ounc es at the ends of a
lever 8 feet long, where is the F (neglec ting the weight ofthelever) ? (S . K . )
378. A force of35pounds at one end ofa lever is inequilibt ium with a weight of50 c wt. at the other end . If I w ish to
raise the weight one inch, through what spac e w ill the powerparts in the same time ?379. T he F ofa lever 3 meters long is 60 c entimeters
from one end at this end is a forc e of 40 kilograms.
What force, ifapplied at the other end , will balance the lever?
380 . A crowbar 2 meters long is supported 25 c entimeters
from one end . H ow great a weight maybe lifted by means
ofa power of15kilograms?381 . T wo weights, 3 and 5 kilograms respectively, are
to be suspended from the ends ofa lever meters long.
Where must the F be placed so that the weights balance
382 . A and B carry a heavy objec t on a rod betweenthem, eac h holding one end of the rod . T he rod is 1 1 feet
long,and A
’s S trength is I % that of B: Where should the
objec t be suspended
(L et x distanc e between A and W (the object) ; then1 1 x) distance between B and W . N ow, 1 1% x1 1 x), whenc e x 4feet from A . )
383. T wo horses, one of 80 0 pounds, the other of 90 0
48 QUE S T ION S A N D P R OBL E M S I N P H YS IC S .
392. Where must the F in example 381 be placed it theweight ofthe lever, 1 kilogram, be taken into account393. A lever is in equilibrium under the action of the
forc es P and Q, and is also in equilibrium when P is trebledand Q increased by 6 pounds. Find themagnitude ofQ . (T o.)
394. A plank weighing 1 0 pounds rests on a single propat its middle point ; ifthe prop be replaced by two others on
each side of it, 3feet and 5feet from the middle point, findthe pressure on each. (M395. A lever 7feet long is supported in a horiz ontal posx
tion by props placed at its extremities. Find where a weightof 28 pounds must be placed so that the pressure on one of
the prommay be 8 pounds. (T o. )
396. A plank weighing 5 kilograms rests on a singleprop at its middle point. If this prop be replaced by twoother props, one on eac h side of it, and respectively and
m . from the middle point, what will be the press ure on
eac h prop ?
397. T wo weights of1 2 a nd 8 pounds respectively,balance
at the ends ofa horizontal lever 1 0 feet long. Find how farthe fulc rum ought to be moved for the weights to balancewhen eac h is increased by 2 pounds. (T o. )
398. A B C is a straight lever ; the length ofA B is 7
inc hes, that ofB C is 3 inches ; weights of 6 and 1 0 poundshang at A and B, and an upward pressure of6 pounds acts atC . Find the position of a fulc rum about which the lever soacted upon would balanc e . (T o. )
399. T he short arm ofa lever is two feet long, and at its
end hangs a weight of50 0 pounds. What must be the entirelength of the lever, if a P of 20 0 pounds at the other end isto raise the weight40 0 . What is the advantage gained by a compound lever
LEVE R S . 49
whose short arms 1 , 2 and 3 feet respec tively, and whoselong armS are 6, 7 and 8 feet respectively. Loss by friction
ofthe advantage gained.
40 1 . Three levers, each having a short arm 1 foot long,and a long arm 4feet long, are made into a compound lever.What force at the end of the last short arm c an be balancedby a force of1 pound acting at the free end ofthe long arm40 2 . Find the advantage gained by a compound lever
whose short arms are 30 , 40 and 50 centimeters respectively,and whose long arms 3, 4and 5meters respectively. LOSSby friction of the advantage gained .
403. A substance is plac ed in one pan of a balanc e, andrequires 3262 grams to hold it in equilibrium. I t is thenplac ed in the other pan, and now requires 3140 grams tobalance it. What is the actual weight of the body (rejec tingsmall remainders) ?
41 0 . What force must be applied at the free end ofa lever
4feet long to balance a weight of 1 0 0 pounds hung up 1 rootfrom the other (fixed) end
(P W l : L ; hence x : 1 0 0 whence x 25 pds.)
41 1 . What forc e will balance a weight of 20 0 kilogramssuspended m . from the end ofa fixed lever4m . long
41 2 . A lever is 4feet long ; 6 inc hes from one end (F)4
60 QUES T ION S A N D P R OBL EM S I N P H YS IC S .
hangs a weight which is balanced by a force of30 pounds atthe other end . Required the amount ofthe weight.413. A lever is m . long, and 60 centimeters from its
fixed end hangs a weight balanced at the other end by a
force ofone-halfkilogram. Find the weight.414. A lever 8 feet long, w ith its fulc rum at one end is
maintained in a horizontal position by two forc es of 1 0
pounds and 160 pounds respectively. H ow far fiom the
fulcrum may the latterbe A nd what is the pressure upon thefulcrum (P lace the smaller weight at the free end . )415. A lever 6 feet long is held horiz ontal by two forc es
whose sum 40 0 pounds ; one of them is applied at one
end of the lever, the other at a distanc e of3 inches fromthe other end (F) . Find the amount ofeac h force.
416. T he sum oftwoforces is 50 0 kilograms ; one ofthemOperates at the end ofa lever m . long
, the other 45 c entimeters front the other end . Find the amount ofeach forc e.
417. T he weight ofa uniform rod 8 feet long is 1 pound ;a weight of 1 0 pounds is suspended two feet from the fixedend . Find what forc e at the other end w ill balanc e the lever.
418. A rod 4tn. long is inserted 0 .5 m . deep in a wall ;a weight of80 kilograms hangs from the free end of the rod .
Find the pressure on the edge ofthe opening in the wall.
419. A chopping knife 15 inches long is acted upon bv a
powerof1 0 pounds. T he resistanc e is equivalent to a weIght
of pounds ; how far from the fulc rum should it be
plac ed
420 . A man is rowing a boat ; eac h oar is 1 0 feet long,and fastened to the boat 7% feet from the immersed end of
the oar ; the power he exerts at eac h oar 25 pounds.
What resistance does the boat meet with42 1 . A nut is placed in a pair ofnut c rackers at a distance
L EVER S . 51
ofone inch from the joint ; 8 pressuI e of6 pounds applied toeach lever 5 inches from the joint is just sufficient to crackit. What resistance does the nut ofl
'
er
422 . A horiz ontal rod has a length of4feet ; one ofits
ends is fastened to awall, the other bears a large, woodenwatch S ign weighing 25 pounds. What must be the leastbearing capac ity of a wire that upholds the rod 1% feet fromthe sign (T he weight ofthe rod neglected.)
423. T he safety-valve ofa steam boiler is required to Openwhen the steam pressure reaches 50 pounds per square inch.
What weightwill be required upon the extremity ofthe safetyvalve lever, the valve being 3 inc hes in diameter, the entirelength of the lever 24 inches, and the distanc e between thefulcrum and the center ofthe valve being 3 inches (S . K.)
63 QUES T I ON S A N D P R OBL EM S I N P H YS I C S .
WH EEL A N D A X LE.
(In these examples the increase in the diameter when the
rope is winding round the axle is neglected.)430 . Describe the wheel and axle, and tell how it differs
from a lever ofthe first class.
431 . What is the rule for finding how one weight willbalance another on a wheel and axle432 . H ow do you find the advantage gained by a wheel
and axle433. Mention two common forms of the wheel and axle.434. What is the mechanic al advantage ofa wheel and
axle in whic h the radius ofthe axle is I 3 inches, and that ofthe wheel I 5 inches.
(Substituting r, the radius of the axle, for ! in the proportion for the lever, and R, radius ofwheel, for L in the same,
P W r : R ’ whence x 1 0 . T he mec hanical1 : x
advantage if435. Ifa weight of 160 pounds be supported on a wheel
whose diameter is 20 inches, the diameter orthe axle being 5inc hes ; what force w ill sustain the weight ?436. What power is required to lift a ton ofore bymeans
ofa wheel and axle of8} feet and 1 0 inc hes diameter teepeetively?
we have,
WHE E L A N D AX LE . 53.
437. An anchor is hoisted by a capstan worked by4men,each pushing at the end ofa handspike ; the diameter ofthec ircle described by the four handspikes is 6 feet 8 inches; thediameter of the barrel of the capstan is 8 inches ; the
anchorweighs 2400 pounds. What is the pressure exerted byeach man
438. A capstan 14inches in diameter isworked by 8 men,and by means of4 levers eac h 7 feet long. A t the end of
each lever a man is pushing with a force of30 pounds ; 2 feetfrom the end anotherman pushes with a force of42 pounds.What is the efl
'
ec t produced ?439. A capstan 14inches in diameter is worked by means
of a horse harnessed to the end ofa lever 7feet long. H ow
long w ill a horse be in pulling a house over a space of5milesifwalking at the rate of2% m iles an hour ?440 . Ifthe radii ofa wheel and axle be as 1 0 is to 4, and
weights of 3 and 8 ounc es hang from them ; which willdesc end ? (M .)441 . A man whose weight is 140 pounds is just able to
support a weight that hangs over an axle of 6 inc hes radiusby hanging to the rope that passes over the correspondingwheel, the diameter ofwhic h is 4feet. Find the weight sup
ported. (M . )442 . Ifthe difl
'
erenc e between the diameter of a wheeland the diameter of the axle be S ix times the radius of theaxle, find the greatest weight that c an be sustained by a forceof60 pounds. (M . )
443. Ifthe radius ofthe wheel be n times as great as thatofthe axle, and t he the maximum tensionofthe string on thewheel, find the greatest weight that c an be raised. (M .)444. If a weight of30 ounc es be supported on a wheel
and axle by a forc e of 2 ounc es, and the radius of the wheelis 6 feet 3 inc hes, find the radius ofthe axle.
54 QUE S T ION S A N D P R OBL EM S I N P H YS IC S .
445. Find the mechanical advantage ofa wheel and axlein which the radius ofthe axle is 4centimeters and the radimofthe wheel meters.
446. Ifa weight of1 0 0 kilograms be supported on a wheelwhose diameter is 0 .5m .
, the diameter of the axle beingm .
,what forc e will sustain the weight447. Find the power required to lift 80 0 k ilograms of ore
by means ofa wheel and axle of 2 and meters diameterrespec tively.
448. T he drum ofa capstan is 18 inc hes in diameter, andthe handspikes are 1 0 feet long. Fourmen are employed to
raise weights from a depth of 50 feet by this machine.
Assuming that when a man exerts a c ontinuous force in pushing or pulling 27 pounds, he c an do the greatest amount ofdaily work—viz . : 1 50 0 0 0 0 units, determine the load thatshould be raised at each lift, and the total load raised daily.
(Passive resistances and weight of rope and box to be
neglected . ) (S . K. )
449. Wherein does the differential wheel and axle difl'
er
from the c ommon wheel and axle ?450 . H ow do you find the advantage gained by means of
the differential wheel and axle451 . Explain why in the diflerential wheel and axle the
r - r’
(In this formula W : the weight or load ; 1 the radius oflarger axle, r’ that of'smaller axle. )
work done by W , in unit oftime, is W(
452 . T women, at Opposite endsofa differential axle, eachpushing with a force of 20 pounds, are turning a c rank of1%feet in length ; the diameters of the axles are 1 0 inches and
8 inc hes respectively. Find the weight that may be raised,two-tenths ofthe effect being lost by friction.
66 QUE S T ION S A N D P R OBL EM S I N P H Y S IC S .
of1 0 leaves. Each pinion is moved by means ofa crank 15feet long, each crank being turned by’
a laborer with a forceof 25 pounds. Find the weight of the stone, three-fifths ofthe power applied being lost by friction.
463. In the previous example, when eac h power passesthrough a space of 1650 feet, what is the work (in horsepowers) done by eac h464. In the same example, if the vel. of the power is 3
feet a second, in what time will the men'
hoist the block 18
feet ?465. T he wheel of the axle ofa second-hand in a clock
has sixty teeth. In order to combine this wheel with a set of
toothed wheels so that the last wheel shall make one revolu
tion in eight days, what proportion in the dimensions of
wheels would you determine
IN OL IN ED P L A N E . 67
INCLIN ED PLANE .
(Advantage gained 2, where l=length,6 base,and a the height ofthe inclined plane.)
467. What weight c an be supported on a plane by a forceof 20 pounds acting parallel to the plane, ifthe ratio oftheheight to the length is one-fourth(Solution T he advantage gained by this inclined plane4. Hence 20 4 80 pounds, answer.)
468. What forc e acting parallel to the plane (or length ofthe inc line) is required to support a weight of140 0 pounds ona plane
“
that rises 2 in 7
469. Find the inclination of a plane, ifa force of 1 0 oz .
ac ting parallel to the plane just moves a weight of35 oz .
470 . A plane rises 1% in What force ac ting parallel to the plane will balance a weight of 1 0 pounds on the
plane?471 . A plane rises 3 in 5. What forc e acting parallel to
the base c an support a weight of133} pounds472 . Find the weight that c an be supported upon an in
c lined plane rising 15 in 25 by a force of 27 pounds parallelto the plane, one-ninth ofthe force being lost by fric tion.
473. T wo planes having the same height are placed backto back, and two weights of 7 and 1 0 ounces connected bya string passing over the summitare balanced. Find the ratioofthe lengths ofthe planes. (M . )
58 QUE S T ION S A N D P R OBL EM S I N PH YS IOS .
474. What weight c an be supported on a plane by a force
ofr0 kilograms acting parallel to the plane, if the plane rises2 meters in 9
475. What force acting parallel to the plane is required tosupport a weight of525 kilograms on a plane rising 1 .5meters
in meters476. Find the weight that c an be supported upon an in.
c lined plane rising meters in meters, by a force of1 2kilograms acting parallel to the incline.
477. A person with a lifting capacity of56 pounds, wishesto raise a barrel offlour 196 pounds) into a wagon 4feethigh. H ow long a plank must he use
TH E SOR EW . 69
T H E S C R EW
(Advantage gained 9. where c the c irc umferenc e ded
scribed by the power applied, and d the pitc h , that is, thedistanc e between two c onsec utive threads480 . A sc rew has seven threads to the inc h . What pres
sure c an be produc ed by a forc e of 1 0 pounds applied at the
c irc umferenc e, the d iameter ofwhic h is 2 inc hesSolution T he c irc umferenc e desc ribed by the power
2 (3 1416) inc hes ; the distanc e between the
threads 5inc h Hence the advantage gained 6 2832
5 Multiplying this by 1 0 , the power applied ,we
have pounds, answer.
481 . Whatforc e must be applied to a c irc umference of 20
inches,ifthe resistance to be overc ome is 1 0 0 pounds, and
the p itch ofthe sc rew inc h .
482 . What pressure is produc ed by a sc rew ,if a power of
1 pound desc ribe a revolution of 2% feet whilst the sc rew
moves through 3, inc h483. What must be the p itc h ofa screw ifa power of 1 0
pounds, acting at the end of a lever 7 inc hes long (rad ius),exerts a pressure of2640 pounds ?
60 QUE ST ION S A N D P R OBL EM S IN P H YS IOS .
484 Any change upon the ratio between power and
weight has what efl'
ec t in the length of the lever to which thepower is applied485. T he pitch ofa screw is m. ; a forc e of5 kilos.
acts at the end of a lever(radius) m. long. What is thepressure exerted486. A screw having a head 1 2 inches in circumference is
so formed that its point advances a quarterofan inch at each
revolution. Find what force must be applied at the circumferenc e ofthe head that the sc rew may produce a pressure of144pounds.
487. An endless sc rew , supposed to move without friction,has a c rank 1% feet long ; its threads work in a wheel of80teeth , whose axle has a circ umference of1 foot ; a rope windsaround the axle, at the end ofwhic h hangs a weight of
7540 pounds. Find the power required to lift the weight488. T he lever of a differential sc rew (or Hunter
’
s) is35inches long, fastened to the ax is at its center, and worked bya power of 1 0 pounds at eac h end; the two pitches are rs
spec tively 111and
767. Find the pressure exerted, the machine
being supposed to run without friction.
TH E P ULLE Y. 61
T H E PULLEY .
(S tiffness ofropes and weight ofpulleys neglected . )
490 . What is a fixed pulley, and what is meant by the
bloc49 1 . What is a movable pulley492 . Describe and illustrate the use ofa fixed pulley.
493. What is the equation ofwork in a S ingle movablepulley ?494. What is the equation ofwork in a system ofpulleys
in which the same string passes round all the pulleys495. What is the equation ofwork in a system ofpulleys
in which each hangs by a separate string496. Find the weight that may be lifted by an arrange
ment of 3movable pulleys, in which the same string passesround each pulley, the power applied being 20 pounds.
Solution Advantage gained by each movable pulley 2 .
Henc e (3 2) 20 1 20 pounds, answer.
497. Find the weight that c an be raised by an arrangement offour fixed and three movable pulleys, in which the
same string passes round all the pulleys, the power appliedbeing 20 pounds. Make a drawing. (Advantage gained498. Find the power which will support a weight of480pounds by an arrangement ofpulleys as in example 496.
499. A man weighing 150 pounds forces up a weight of
63 QUE S T ION S A N D P ROBL EM S I N P H YS IOS .
1 0 0 pounds by means of a fixed pulley over his head . Findhis pressure on the floor.
50 0 . What is the mec hanic al advantage of a system of4movable pulleys
, eac h pulley hanging by a separate string ?E xplain.
50 1 . A weight of80 0 pounds is to be raised by means of
a system of3pulleys hanging by separate strings. Find the
power required .
50 2 . In a system ofone fixed and one movable pulley,what is the force with whic h a man pulls himselfup , ifhe issuspended from the movable pulley, and raises himselfbypulling at the free end ofthe string ?503. E xplain by means of a diagram the action ofthe
differential pulley .
504. Illustrate the general law of mechanical powers bymeans ofthe d ifl
'
erential(orWeston’s) pulley.
505. What is the power required to lift a weight of 1800
pounds by means of a difl'
erential pulley, the circumferencesofthe fixed pulleys being 1 9and 20 inc hes respec tively?506. What is the powerrequired to lower the above weight
by the same differential pulley ?
64 ques t ions sun P aosnmts 11: nam es.
(In this machine the advantage gained by the water
1 00 g 1 25, which multiplied by the power applied, 300pounds, 37500 pounds, answer.)
520 . If the stroke ofthe pump piston in the previous ex
ample is 254inches, how far does the plunger move at everydownward stroke ofthe piston
52 1 . H ow many downward strokes must the piston in ex.
530 make in order that the plungermay advance 2 inches ?522 . A hydrostatic press ' is worked by a power of 30
pounds. T he arm of the lever at which this power sets is
six times as long as the arm at the end ofwhich is the pumppiston. T he cross-area ofthe latter is g‘o that ofthe plunger.R equired the pressure transmitted to the plunger.
523. T he diameter ofthe plunger in a hydrostatic press is1 0 inches ; that of the piston of the pump is 56 inch. T he
piston is fastened 15 feet from the fulcrum ofa lever of thesecond class 6 feet long. T he power applied to the leverbeing 40 pounds, and the friction ofthe machine being equivalent to the low of5‘of the entire efl’ec t, find the
effect ofthe machine.
524. T he sectional area of the plunger in a
press is 0 .5 square meters, and that ofthe pistonofsquare meters. T he
kilograms. Find the entire effect ofthe machipe.
525. T he diameter ofthe plunger inm. , that ofthe pump-piston m.
fastened m. from the fulcrum ofa leverofthe
m. long. T he power applied being 30 kilos.,
theoretical efiec t ofthe machine P526. By means ofa prm ure of 200 pounds on
piston of 54inch diameter. I wish to exert an28800 pounds. What must be the diameter ofthe
m nnosu 'rros. 66
P RESS URE OF LIQUIDS ON THE BASE ANDSI DES OF VESSELS .
(Remember:A cubic foot ofwaterweighsnearly 62 .5pounds.A c ubic inc h ofwater weighs pounds. A cubicc entimeterofwater weighs 1 gram.)
527. State the law regarding the pressure ofliquids on thebase ofvessels.528. A cubical vessel, whose edges are each 1 2 inches
long, is filled with water. Find th e pressure upon the bottomofthe vessel .529. T he same vessel is filled with sulphuric acid, sp. gr.
Required the pressure of the acid upon the bottom of
the vessel.
530 . T he same vessel is filled with waterto the height of6 inc hes. Find the pressure upon the bottom ofthe vessel.531 . A vessel 6 inc hes wide by 1 2 inches long and 24
inches high is filled with water. Required the pressure uponthe base .
(T he press. of liq. upon the base ofvessels depends onthearea ofbase into the vertical height ofthe liquid. N ow
, the
area ofthe base ofthis vessel 72 sq. inches, whichmultipl ied by 24inches 1 728 c ubic inches 1 c ubic foot,the vertical pressure or weight ofwhich is pds. , answer.)532 . T he vessel in ex. 531 containsmercury
,sp. gt . but
standing only 1 2 inches high . Required the pressure uponthe base.
533. A vessel 1 2 inches high,6 inches long and 4inc hes
wide, has a tube 1 2 inches high fitted into its neck. Whenvessel and tube are filled with water, the water in the tube ispressed upon by means ofa p iston with a force of1 0 0 pounds
5
66 questi ons A N D Pnosm s m P H YS IC S .
to the square inch. Required the entire pressure upon the
base ofthe vessel.534. Find the pressure upon the interiorsurface ofa sphere
of4feet diameterfilled with water.
535. Find the weight of the water in the sphere of the
preceding example.
536. A c ylindric al vessel has a diameterof4 inches, andis filled 5 inc hes high with water. Find the pressure uponthe base ofthe vessel .537. T he preceding vessel contains nitric acid, sp . gr.
standing at the same height. Required the pressure upon thebase ofthe vessel.538. A barrel 3feet long stands on one end , which has an
area of 2 16 square inc hes and torms the base of the barrel.A vertical tube 5 ft. high is inserted in the other end ofthe
barrel . Both , barrel and tube, are full ofwater. Required thepressure upon the base of the barrel .
539. I throw a block ofwood into a pail filled with water;will it increase the pressure on the bottom ofthe pail H ow
will it affect the pressure when the pail is not quite full ?
540 . A cubical vessel, eac h edge 1 0 centimeters long, isfilled w ith water. What is the pressure ofthe water upon thebottom of the vessel ?
541 . T he vessel in ex . 540 is filled with sulph . acid, Sp . gr.
Required the pressure upon the bottom of the vessel.
542 . T he vessel in ex . 540 c ontains water to the height ofonly 5 c entimeters ; required the pressure upon the bottom.
543.A vessel 20 c entim . wide .by30 cent. long and 54
meter high is filled with water. Required the pressure uponthe base.
544.Find the pressure exerted upon the base of the
preceding vessel ifthe liquid be mercury, sp. g.
urnsos'ra
'
rws. 67
545. A four-sid ed bottle 25 cent. high, each edge of the
base being 1 0 cent. long, has a tube 50 c entim. high insa ted inits neck . T he whole being filled with water, the water in the
tube is pressed upon by a p iston wi th a force of 1 0 grammesto the square centimeter. Required the pressure upon the
base of the bottle.
546. A cylindrical vessel has a diameter of 1 0 centimeters,and is filled with water to the height of20 centimeters . Findthe pressure upon the bottom ofthe vessel.
547. Find the pressure upon the bottom of the precedingvessel filled to the same height with nitric acid
,sp. gr.
548. S tate the law ofthe pressure of liquids against thesides of vessels.
549 . What is the pressure against each side ofa cubicalvessel, each edge ofwhich is 1 ft. long, if the liquid standsinches high and has a sp. gr. of P
Solufiom—T he pressure of liquids upon the side ofvesselscontaining them depends on the area in contact with the liquidM the vertical height fiom the c enterofarea to the surface ofthe liquid. (This is only approximately correct.) 1 2 ins.
length by 8 ins. height: 96 sq. ins. area; the height ofl iquid4ins. , and 96 . 4 384 c ub. inches 5cub. it. If the
liquid were water, this cub. ft. would exert a pressurepds. ; but the liquid has a 8p. gr. of there
fore pds . answer.
550 . What is the pressure against a side of a cubicalvessel filled with water, whose edges are each 1 foot long i’
551 . Required the pressure against each side of the pre
c eding vessel iffilled with a solution ofpotash, sp . 5.
552 . Required the pressure against each side ofthe va sel
in example 550 containing mercury 1 2 c en. high .
88 common 41m P nosmnts 111 m u ms .
553. Required the pressure against the larger side ofthe
vessel in Ex. 543.
554. A canal-lock is 30 feet wide. Required the pressure
against it, ifthe height ofthe water on one side is 8 feet.
555. T he side ofa tank contains a rec tangular aperture 9
inch . wide and 8 inch . high , which is closed bya vertic al platepressed against the aperture with a force of200 pounds. R e
quired the height above the center of the aperture, to whichthe tank c an be filled with water.
556. What is the pressure upon the four vertical sides ofacube filled with water, whose edges have each a length ofr?557. What is the pressure upon the surfaces of the cube
in ex . 556
v. 558. Required the pressure against one of the four sides
9! the cub. vessel in ex. 540 .
559. Required the pressure against one of the sides of thel ime vessel iffilled with sulph . acid, sp. gr.
560 . Required the pressure against one side of the bottlegiven in ex. 545.
561 . Required the pressure against the side of the vesselin ex . 546.
oou umou ms vnssnns. 69
COMMUNICATING VESSELS .
S tate the laws concerning liquids in communicatingvessels.
571 . One ofthe limbs of a U-shaped glass tube containsmercury (sp. gr. standing m. high ; the otherlimb contains bromine to a height of m . ; both liquidcolumns are in equilibrium. Required the Sp . gr. ofbromine(water x whence x572 . Find the height of a column ofwater in one limb of
a U -shaped tube, if it is in equilibrium with a column ofmercury (sp . gr. m. high in the other limb.
573. One of the limbs of a U -shaped tube contains a
liquid to the height ofll, the other c ontainswaterto a height of171011 ; both columns are in equilibrium. Required the spe
c ific gravity ofthe liquid.
UPWARD PRES SURE FLOTATION.
577. S tate the law of the upward pressure ofliquids on
immersed bodies.578. What is the P rinc iple ofArchimedes
579. S tate what occurs(1 ) When the displaced liquid has the same weight
as the immersed body ;(2) When it has less weight ;(3) When it has more weight.
580 . What is required in order that a floating body he inequilibrium581 . What is meant by the metac enterofa floating body582 . Find the force required to support a cubic decimeter
ofplatinum,sp . gr. 2 1 , in mercury ofsp . gr.
70 ounsrrons A N D P nosnmrs m P H YS IC S .
(T he force will be equal to the weight of the platinumdiminished by the weight ofa like volume ofmercury. T he
weight ofa decimeter ofwater= 1 kil. that ofa decimeterofplatinum= 1 . 2 1= 2 1 kil . ; and the weight ofa decimeter
ofmercury= 1 kil . Hence, 2 1 kil.,answer. )
583. A body weighs in air 90 grams. It is 1 5 c entim.
long, 2 c entim. wide and 3 c entim. high ; required its weightin water.
584. A body weighing 1 0 0 0 pounds has a volume of 1 0
cubic feet, and is held suspended in water. Required(1 ) I ts loss in water;(2 ) T he upward pressure against it ;3) T he forc e requisite to support it in the water.
585. What force is required to lift a man in water whosevolume cubic ft. , and who weighs 150 pds. in the air?
Solution.—H is loss in water is 5 pds hence,
his weight in water=(1 50- 7 5 pounds. This is the forcerequired to lift him in the water.
586. A hall m. diameter weighs in air 20 0 .grs. whatwill it weigh ifsuspended in water?587. Find the weightofa leaden bullet suspended inwater,
whose diam. is 2 c entim. ,1 c ubic c entim. oflead weighing 1 1
grams.
588. Required : the weight of the preceding bullet suspended in an acid ofsp. gr. (A sk yourselffirst, whetherin the acid the bullet will weigh less or more than it weighsin water.)
589. Required : the weight ofthe preceding bullet in alcohol ofsp. gr.
590 . What is the weight ofa floating body whose c apacityis 60 0 cubic centimeters, and which enters in the water two
thirds ofits volume
72 ounsrions A N D P R OBL E M S IN pnrsros.
supported in water by attaching it to a sphere of cork.
What must be the diameterofthe latter, the specific gravity ofcork being and that oflead being 1 i’
(T he volume ofthe lead is 64cubic centimeters its weightin air is, therefore, 64 and its weight in water 64
64 grs.
Ifr be the radius ofthe sphere in centimeters, its volume in4w r
’
cubic c entimeters Will be3
and its weight in grams 15
w r,
oo4
3
0 24N ow,
as the weight of the displaced water is
obviously g 11 r3 in grams, there will be an upward buoyancy41m"41r r
’r’
.
which3 3 3
must be equal to the weight ofthe lead ; that is
represented by
4 ” 13
.
3from whic h r 5 c entim. 925, and the diameter
c entim . ) (A )
SP E C IFIC am vrrx . 73
SPECIFIC GRAVITY .
(For Table ofSpecific Gravilier see Appendix.)
MEANS OF DET E RMIN IN G S PECIFIC GRAVITY .
OF SO L IDS
I . T b: Hydrostatic Balance—T he bodyunderexamination is suspended
below one ofthe pans ofa balance, and its absolute gravity balanced byweights in the other pan. N ext, the body is immersed in water, and equili
brium restored byplac ing weights upon the pan above the body. T hese
additional weights are the weight ofa like volume ofwater.
I I . N it/rolron’r Hydrometer (or A reometer) . —Inorder to sink the appa
"ratus as far as a certainmark on the rod , place the substanc e together withsuffic ient weights in the dish. T he weight of the apparatus the sub
stance the weights the weight ofthe displac ed liquid . N ext, remove
the substance and replace it byweights, so that the apparatus sinks againas far as the mark. T he weights that have replaced the body are its abso
lute gravity or weight. N ow, remove‘
these weights, plac e the body inthe basket and immerse again. T o sink the apparatus as far as the mark,additional weights must be plac ed upon the dish ; these are equal to the
loss ofthe body in water, that is, to the weight ofa like volume ofwater,I I I . T he Pycnometer.
—Fill flask with water oranyother suitable liquid,to the stopper, and weigh (the weight ofthe flask is balanc ed bya coun
terpoise). N ext, plac e the body by the side ofit, and weigh both ; bysubtraction, find the absolute gravity of the body. T hen immerse the
body in the liquid and replace the stopper. Dry carefullyand weigh again.
To restore equilibrium weights must be added ; these weights are the lossofthe body. T his method and the following are spec ially adapted to
bodies in grains orfragments.
74 QUE S T ION S A N D P ROBL EM S IN P H YS I C S .
IV. A T lwumnd -Grain Flack —Fill the flask partly with water and
w eigh (the weight of the flask is balanc ed by a counterpoise) . N ext, immerse the grains or fragments until the liquid rises to the mark. Weigh
again ; by subtrac tion find the absolute gravity of the substance. The
difference between 1000 and the weight of the water employed the
weight ofthe volume ofwater displaced by the substance.
Whenthe bodyunderexaminationhas less spec ific gravity thanwater, thefollowing method may be applied in plac e ofN icholson
’s hydrometer : At
tach the body toa heavymass whose weight, both in airand water, is known.Immerse both in water, and find the loss ofboth bodies. From this loss
subtrac t the loss ofthe heavymass alone ; the remainder w ill be the loss
ofthe body under examination,that is, theweight ofa like volume ofwater.Dividing the weight in air ofthe body by this remainder, the spec ific gravity is obtained .
or L IQU IDS
V. T be Hydrostatic Balance. Find first, ac cording to I , the loss in
water ofe. g. a c ube ofbrass ; next, find the loss ofthe same body in the
liquid under examination.
VI . N ikita/son’
s A reometer or Hydrometer. Immerse the apparatus firstin water, then in the liquid under examination. T he add itional weightsrequired to sink it in water as far as the mark the weight of the appar
atus the weight ofvolume ofwater. T he additional weights required
to sink it in the liquid as far as the mark weight ofappara tus the
weight ofa like volume ofthe liquid .
VI I . A Specific Gravity Flask capable of containing some determinedquantity ofwater, such as 100 grs. or 1000 grs. After balanc ing it on a scale
fill it with the liquid under examination up to the mark ; the weights te
quired to balance the liquid its absolute gravity. N ext divide by 100
or 1000 , ac cording to the capacityofthe flask ; the quotient the spec ificgravity ofthe liquid .
VI I I . Hydrometers. T he volumes displac ed bythe same bodyimmersedin different liquids are inversely as the spec ific gravities of the liquids.Suppose that the number 100 indicates the point to which the hydrometer
sinks in water, and that it sinks in another liquid to 1 25, that is, 25degrees
above 100 , each degree being N ow , these volumes displaced must
S P E C IFIC onavr'rr . 75
have equal weight ; and as, therefore, the volume of the lighter liquidmust be greater than the volume of the heavier, both volumes must be in
versely as the spec ific gravity of the liquids. H enc e : S pec ific gravity ofthe liquid is to 1 (sp. gr. ofwater) as 100 is to 1 25; whnce the sp. gr. of
the liquid is found to be
OF GA S E S .
IX. A Globe qfGlace provided with a stop-cock . S uspend the globe
(filled with air) from one of the scales ofa balanc e ; establish equilibriumby plac ing a weight on the other scale. N ext exhaust the air from the
globe, and weigh again; the weight now found is that of the globe. T he
d ifferenc e between the two weights the weight ofthe contained air.
N ow , let the gas under examination rush into the globe, and weigh again ;
the additional weight obtained the weight of a like volume of the gas.
Divide this by the weight ofthe air ; the quotient the spec ific gravity ofthe gas.
60 0 . Define Specific Gravity .
60 1 . H ow may the specific gravity ofa body be found60 2 . Desc ribe the process ofdetermining the sp . gr. ofa
solid by means ofthe hydrostatic balance .
603. A piec e of platinum weighing 1 kil . loses 46% gramswhen weighed inwater. Required its spec ific gravity(T he weight in air of a substanc e divided by its loss in
water=its sp . gr. N ow H}? 2 1 .5 sp. gr. of the platinum .)604. A piec e of iron weighmg z kil. weighs in water
kil. ; find its specific gravity.
605. A piece of sandstone weighing kil . weighs inwater kil . ; required : its spec ific gravity.
606. A piec e of talc weighs 78 grams ; it weighs in water48 grams. find its specific gravity.
607. Describe the process ofdetermining the sp. gr. of a
solid by means of Nicholson’s hydrometer or areometer.
608. A piec e ofsulphur is plac ed upon the dish ofa N ic holson hydrometer; 20 grams. are required to sink the hydro
76 QUE S T I ON S A N D P nonnmrs m P H YS IC S .
meter down to the mark ; and afterwards 3 grs . to take the
plac e of the sulphur. When it is put in the basket and im
mersed, grams must be on the dish . Required the
specific gravity ofthe sulphur.
609. W ith 31 grs . on the plate, a hydrometer sinks to the
same mark as with 26.5 grs. and a piece ofphosphorus on
the plate. But when the phosphorus is placed in the basket,29 grs. must be laid on the plate to sink the hydrometer to
the same mark. Required the sp. gr. of the phosphorus.61 0 . Desc ribe the process of determining the spedfic
gravity ofa solid by means of the pycnometer.
61 1 . A flask filled with water to the stopperweighed 800grams. When it was weighed with the fragments of the mineral pyrolusite beside it, both weighed 8 1 0 grams. After themineral was put into the flask, a weight of 2 grams was te
quired to restore equilibrium . Find the sp. gr. ofthe mineral.
61 2 . A flask filled with water to the stopper weighed 548grams. When weighed with fragments of a meteorite me
teoric dust beside it, both weighed 560 grams. After themineral was put into the flask
,a weight of grs. had to
be added to restore equilibrium. Required the specific gravityof the substance.
613. A flask filled to the stopperwith oilof specific gravityweighed 760 grams ; together with a quantity of com
mon salt (in grains) both weighed grams ; but when the
salt was immersed in the oil, a weight of grs. had to be
added to restore equilibrium. Required the specific gravityofcommon salt, water being the standard.
614. A flask filled to the stopper with petroleum (spgr weighed 30 0 grs. Grains of blue vitriol weighing6grs . in airwere then immersed both togetherweighedgrs. Required the specific gravity of blue vitriol (water beingthe standard) .
sm ormo ouxvr'
rr. 77
61 5. Describe the proc ess ofdetermining the sp. gr. of
solids by means ofa flask holding a thousand grams or a
thousand grains.
616. A thousand-gram flask c ontaining 90 0 grams of
water, besides fragments of the m ineral Andalusite, was foundto weigh 1 200 grs . Required the sp . gr. ofAndalusite .
(Weight ofmineral=(1 20 0 grs, ; weight of a
like bulk ofwater= ;rooo N ow 138=3. Ans.)
617. When sand was introduc ed into a thousand-gramflask containing 80 0 grs. ofwater, the water rose up to the
mark, and both together were found to weigh 1 2 20 grs. R e
quired the specific gravity of the sand
618. Grains ofP latinum were put into a thousand-gramflask containing 990 grams ofwater, until the water rose to themark ; both together then were found to weigh 1 205 grams.
Find the specific gravity ofthe platinum.
61 9. A thousand-gram flask contained 980 grams of
water. Metallic arsenic (in the form of grains) was then introduc ed ; the water rose to the mark, and both substanc es together were found to weigh 1 092 grs. Required the specificgravity ofmetallic arsenic.
620 . A 1 0 0 0 gr. flask contained 984 grs. of alc ohol (sp.
gr. A piec e ofmaple wood was introduced ; the alcohol rose to the mark ; both together weighed 1 0 0 2
,grams.
Find the specific gravity ofmaple wood. Ans.
62 1 . A hundred -gram flask was filled with 85 grams of
naptha (sp. gr. A piece ofsodium was immersed inthe naphtha, after which the liquid rose to the mark. Bothsubstances together weighed 1 06 grams. Find the specific
gravity ofsodium.
78 QUE S T I ON S A N D P R OBL EM S I N P H Y S I C S .
62 2 . A piece ofwrought iron whose volume is 1 0 8 cubicinches, weighs pounds. What is its specific gravity PSolution—T he weight ofa like bulk ofwater(or the loss in
water) evidently the weight of 1 08 cubic inches ofwater,
15023; of pounds. N ow,
3355
answer.
623. T en c ubic c entimeters of c opper weigh 89 grams.
Find the spec ific gravity ofc opper.
624. A piec e 0 1 marble whose volume 1 5 cubic c enti
meters weighs 42 grs. What is the spec ific gravity ofmarble ?625. A d iamond weighs gram,
and has a volume of
c. c . Find its specific gravity.
626. A piec e of platinum weighing 1 kilo. loses in watergrs. Find its spec ific gravity.
627. A piec e ofgraphite weighing 1 0 grams loses in water4grams ; find its spec ific gravity.
628. A piece ofic e weighs grams ; it weighs grs.
in absolute alc ohol (spec ific gravity temp. of 0° C).Required its Spec ific gravity.
629 . What is the volume ofa piece of z inc whose we ightin air is grs. ,
its spec ific gravity being P
S olution.
3435? 1 20 grs. loss in water, or weight ofa like volume ofwater. N ow , 1 gram ofwater has a volume
1 c . c . henc e the volume of 1 20 grs. 1 20 c. c ., answer.
630 . What is the volume ofa piec e ofglass that weighs inair 60 grams
,and has a spec ific gravity of3P
631 . Find the volume of1 0 0 kilos. ofsilver.
632 . Required the length of the edge of a cube Of iron
(sp gr. 8) weighing 1 kilo.
633. A freight-c ar 22 feet long by 5% feet wide may beloaded 2 feet high with coal of specific gravity Whatweight w ill it c arry P
80 QUES T ION S A N D P ROBLEM S 1N P arsros.
643. A piec e ofsand roc k loses 5 pounds in water ; findits weight in air.
644. A piece ofheavy spar (sp. gr. loses 5 gr. in
water ; find its weight in air.
645. A piece of ivory (sp. gr. loses 5 grams in alcohol gt . find its weight in air.
646: A piece ofic e loses 25 grams in alcohol (sp . gr.
find its weight in air.
647. A piec e offlint glass (sp . gr. weighed in water1 0 2 grams. find its weight in air.
648. A piece ofquartz (sp. gr. weighed in water 17
grs. find its weight in air.
649. A platinum sphere 3 con. in diameter is suspended toto the beam ofa very accurate balance, and is cornpletely
immersed inmercury. I t is exactly couterbalanced by a cop
per cylinder of the same diameter completely immersed inwater. Required the height ofthe cylinder (sp . gr. ofmer
c ury of c opper and ofplatinum (A . )
650 . S tate the process for finding the specific gravity ofbodies floating on water(when Nich. hydrometer is not em
651 . A piece ofcork weighs 8 grams in air ; a piece ofleadto which it is attached weighs 2 2 grams in air
, and the
weight in waterofboth bodies is 4grs. (Sp. gr. ofleadFind the specific gravity ofthe cork.
652. A piece ofwood weighed 1 0 grams in air, and was
then attached to a piece of lead whose loss in watergrams. Both being weighed together in water were found to
lose grs. (that is, to displace a volume ofwater weighing32 .5 grs.) Find the specific gravity ofthe wood.
sp somro GRA VIT Y or S OL IDS . 81
the lead from the loss ofboth, wethe weight of9. vol. Ofwater equal
30 answer.
maple wood weighs 1 8 grs. in air; whenattached to a piece of lead weighing 33 grs. in air, bothwere found to lose 23 grs. in water. Required, the specific
654. A piece ofpoplar wood weighed grs. in air;
it was fastened to a piece Of iron (sp. gr. 8) whose vol.=3 c.c. Both together were found to lose in water31 grs. R e
quired, the specific gravity ofpoplar wood .
655. When a brass ball (sp. gr. weighing 17 grs. was
fastened to a piece ofwax weighing grs ., and both werebined weight in water was grs.
gravity of the wax .
weighing 7 grs. has tied to it a metallicgrs. Both together weigh in water grs.
, the
weighing grs. in water. Required, the spe
of the body.
the weight of1 00 0 c. c. of sandstone?weight of 1 00 0 c. c. ofwater : 1 0 00 grs.
T he specific gravity ofsandstone : hence, the weightof10 00 c. c. ofsandstone : 1 0 00 2400 grs.
What is the weight of 1 cubic meter ofbitum. coal PWhat is the weight Ofa c ubic foot of lead PT he weight ofa cubic decimeter ofa body expressed
in kilograms is also its specific weight. Explain.
1 square c entimeter sectional area,Find its weight.
662 . A substanc e whose volume 1 000 c. c. weighs a
kilogr. Find its specific gravity.
6
82 QUE S T ION S A N D P R OBL EM S I N P H YS IC S .
663. What is the weight Ofa wall ofsandstone tsp. gr.
1 0 meters long, 2 meters high by m . thick (theweightofthe mortar is neglected) P664. Find the weight Ofa bar ofsulphur4c entim . d iam
eter and 1 0 c entim. long.
665. In 60 cubic decimeters ofrock whose average sp. gr.
is 1 .5 there are 45 cubic dec imeters of a substanc e whosesp. gr. Find the sp. gr. of the remainder of the rock.
666. Find the weight ofa sphere oflead of1 meter radius.
c ub. m. An equal vol. ofwater weighs 4189 kils. an equalvol. of lead , therefore, weighs 4189 1 1 =46079 kils.)667. Gold ofsp . gr. has been made into leaves of
ofa millimeter in thic kness; what surfac e c an be cov
ered with 1 0 grams ofgold P (C . M .)
(L et x be the surfac e to be covered, and let it be a rec tan
gular paralle10piped whose height Om. 0 0 0 0 0 0 1 , and whosevolume : x N ow, 1 0 grs. : x 1 9 .
1 0 0 0 0 0 0 0 0 0 0 0
5164755 sq. c entim. 516 sq. m .
, 47 sq. dec im. , 55 sq. c en
tim. )
ALLOYS .
(In these mixtures, or in the combination of alloys, noshrinkage ofvolume is supposed to occ ur.)670 . T he specific gravity Of z inc being 7 and that Of cop
per 9, what weight oi each metal must be taken to torm 50
grams ofan alloy having the Spec ific gravity of it beingassumed that the volume ofthe alloy is exactly the sum of
the alloyed metals P (A .)
S P E C IFI C GR AvrTr OF AL LOYS . 83
S olution—L et x the weight ofthe z inc,and y that of
the copper. Then x+y 50 , and as the loss of the z inc together w ith the loss ofthe c opper constitute the loss ofthe
whole, we have 5 From both equations we obtain11 : and y671 . Find the specific gravity ofan alloy composed of5
pounds of tin and 8 pounds of C opper.
Solutz'
on.—L et x the Specific gravity ofthe alloy. N ow
,
793 the loss oftin in water, and 593 that ofcopper. Hencethe equation 793+393 J} ,
whenc e x sp. gr. Ofalloy.
672 . A certain kind ofbrass contains 75 per c ent. Ofc opper and 25 per cent . of z inc (sp . gr. as in Find its spec ific gravity.
673. An alloy is composed of6 parts ofweight ofc opper,3parts ofz inc, parts of lead and part Oftin. Findits specific gravity . (Sp . gr. ofmetals 9, 7, 1 1 , 7, respectively.)674. H ow much copper(sp . gr.8.8) must be combined with
6pds. oftin (Sp . gr. if the alloy is to have a sp. gr. of8 P675. H ow much gold must be added to3pounds ofS ilver
to make an alloy ofspecific gravity 1 5P676. I wish to Obtain brass Of8.5 specific gravity. Find
the percentage ofcopperand z inc required (sp . gr. as in table)677. A nugget of gold quartz weighed 3 oz . in air
, and
lost 0 2. when weighed suspended in water. Required theweight of gold in the nugget.(L et x the weight Ofgold and 3—x the weight Ofquartz .)678. What is the spec ific gravity of sulphuric acid that
has been Obtained by mixing 7 pounds ofsulph. ac id ofSpe
c ific gravity Of with 3pounds ofSpec ific gravity 1 .5?
679. H ow muc h antimony must be added to 1 0 poundsof lead in order that the alloy may have a sp . gr. of1 0 .5P
682 . A 1 000-grain flask holds 2966 grains of bromine,1848 grains sulphuric ac id, 13590 grains of mercury, 718grains ofether. Required, the Sp . gr. ofthese683. A platinum c ube, suspended 1n water, 1
ifsuspended inmercury, it loses grains.
c ific gravity ofmerc ury.
684. A flask weighing 20 grams weighs, whenwater, 60 grams ; when filled with sulphuric acid
,
Required, the Specific gravity ofthe acid.
685. A flask weighing 30 grams weighs, whenwater, 71 grams ; whenfilled w ith another liquid, 55Required, the Sp . gr. of the liquid.
686. A glass ball loses in water grams ;grams. What is the specific gravity ofthe oil P687. A heavy body loses in water 1 1 grs. ; in
17grs. Find the specific gravity ofthe acid.
688. What will the body in the previousmuriatic acid, sp. gr. P689 . A man weighs 150 pounds, and has a sp.
Required, his weight in ocean water(Sp. gr.
690 . A body loses 25grs. in water, 1 8 grs. in
grs. in alcohol. Required, the Sp . gr. ofthe Oil69 1 . A body weighs 230 0 grains in air, 1 1 0 0
ter, and 130 0 grains in Spirit. What is the Specificthe spirit P
S P BOI I'Io GR A VIT Y OF L IQUIDS . 85
692 . T he specific densities of the upperand lower oftwofluids that do not mix are and the upper fluid is4inch. deep a cube with an edge Of 1 ft. and sp. gr. floatsin the liquids ; how much Of it is immersed P (S . K. )693. A wooden block floating on water has one-halfOf
its volume immersed ; when floating on alcohol it displacesfive-eighths ofits volume. What is the sp . gr. Ofthe alcohol P
(S inc e a floating body displaces its ownweight Ofthe liquidin whic h it floats, the weight of54 vol. ofwater the weightof vol. ofalcohol . N ow the densities or Specific gravitiesoftwo liquids are to each other inversely as their volumes ofequal weight ; therefore the spec ific gravityofwater, 1 , is tox, thespec ific gravity ofalc ohol , as 54; is to whence x694. A weighted test-tube floats vertic ally in water. De
grees Ofequal parts are ind ic ated upon it, ofwhich it displaces30% inwater, and 30 in milk . Required the sp. gr ofthe milk.695. A hydrometer displaces parts ofwater
,and 20
equal parts ofether. What is the sp . gr. of the latter?696. A hydrometer displac es 28 parts in glyc erine, and 35
equal parts in water. Required, the sp . gr. Of the glyc erine.
697. A hydrometer displaces in water a volume v ; in
sulphuric acid, a volume d, 71 . Required , the spec ific gravity ofthe acid .
698. A hydrometer displaces in water a volumeOil
,a volume 1
3° 11. Required, the sp . gr. of the oil.
699. A hydrometer displaces in four different liquids, re
Spec tively, a volume 1 , I .3. T he liquid th irdin order being water(s. find sp. gr. ofthe other liquids.
70 0 . What volume is occupied by pounds Of’ sulphuric acid (sp. gr. P70 1 . What is the volume occupied by 1 kilogram ofmer
cury P
QUE S T ION S A N D P R OBL EM S I N P H Y S IC S .
70 2 . A bottle holds two pounds of water ; how much
ether, Sp . gr. will it hold ?703. A flask holds 50 0 grams ofnitric ac id (sp . gr.
how many grams ofmuriatic acid (sp . gr. w ill it hold ?704. A graduated test-glass that contained 30 c . c. ofS111
phuric acid is to be filled with a like weight ofwater ; howmany 0 . c. ofwater must be put in P705. H OW
‘
would you graduate a hydrometer for ascer
taining the strength ofalcohol P706. H ow would you graduate a hydrometer for asoer
taining the specific gravity of liquids heavier than water?
SPECIFIC GRAVITY OF GASES .
(In each example the weighings are supposed to have beentakenat the same temperature and barometric pressure. The
weight Of 1 liter 1 c ubic decimeter) ofdry air at a temp.
of0 °C ,and underan atm . pressure of760 mm . for latitude45
°
at the level of the ocean 54grams. )
71 0 . A glass globe, when filled with atmospheric air,
weighed grams ; when deprived ofair it weighedgrams when filled with illuminating gas it weighed grs.
Find the specific gravity of the gas.
71 1 . T he same globe, when filled w ith oxygen, weighedgrs. What is the Specific gravity ofoxygen P
71 2 . T he same globe, when filled with hydrogen, weighedgrs. Find the Spec ific gravity ofhydrogen P
713. T he same globe, when filled with carbonic ac id gas,was found to weigh grs . Find the sp . gr. of the gas .
714. A globe deprived ofair weighed 36 16 grams ; whenfilled with dry air at a temp. Of 0
°C ,
and w ith the barometer
88 QUE S T I ON S A N D P R OBL E M S I N P H YS I C S .
725. T he aperture at the bottom ofa tank is 9 ft. beneaththe surface of the water in the tank. Find vel. ofthe stream.
726. Find the velocity Ofa stream issuing from the baseofa vessel filled with water 5meters high .
727. A reservoir 7 meters wide and 3 meters deep is always kept full, and contains kils. Find the velocityofa stream issuing from the base ofthe reservoir. m.)728. T he water in a vessel stands 18 feet high . What is
the velocity ofa stream issuing from a narrow aperture 9 feetabove the base ; and how far from the base of the vessel,horizontally, will it strike the ground P729 . A stream issuing from an orifice at the base ofa ves
sel is to have a veloc ity of36 feet. H ow high above the orific e must be the surface of the liquid P730 . A stream of liquid flows from the base of a vessel,
and is to have a vel. of5meters. H ow high above the orificemust the surfac e Ofthe liquid be kept P731 . Compare with eac h other the velocities of water
issuing from two orific es in a c onstantly replenished vessel,one orific e being at the base, the other 1 6 feet above it and 9feet below the surfac e of the water.
732 . Compare the velocities ofwater flowing from threeorific es in a replenished vessel ; the first orific e is at the baseof the vessel ; the second is 2 meters above the first ; thethird 3meters above the second and 5meters below the sur~
fac e of the water.
733. H ow muc h water flows in a second from an orifice
one inc h wide at the bottom of a vessel, the water in the
vessel always standing 9 feet high P
H YDR A UL I C S . 89
(Area of orifice time velocity volume discharged.
N ow,1 sq. inch sq. foot ; therefore, Th 1 sec .
volume, Th—76
v,whence v 5c. ft.
,ans.)
734. What quantity Ofpotash (sp. gr. will flow fiomthe preceding vessel, the other c onditions being as in the preceding example P735. Find the quantity ofwater per hour that flows from
an orifice Ofan inch diam. in the S ide ofa vessel, the surface Ofwater being feet above the c enter ofthe aperture.
736. An aperture in the base ofa vessel is I c entim.
square ; the water in the vessel stands 1 meter high . Findthe quantity ofwater discharged through the aperture in halfan hour.
737. Find the weight ofbrine, Sp. gr. disc harged inhalfan hour; other c onditions the same as in example 736.
738 . T he aperture in the side Ofa vessel has an area of
inch ; the quantity ofwater to be disc harged per hour is6250 pounds. Find the height at whic h the water mustremain above the aperture during that time.
739. What is the pressure that must be exerted upon a
c olumn ofwater 2 meters high,in order that a vel. of 1 0 m.
may be produc ed at its base (g 1 0 m . )
Solution— 1 0 :I/z gh i henc e, I o
22gh, and
1 03
h : 528
m . 50 0 c en. But as the actual height is only 20 0 c en. the
additional pressure must be as great as a column of30 0 c en.
is heavy, or 30 0 grams for every E! c en.
740 . What pressure must be added to a column ofwater1 meter high in order that a velocity of 1 0 meters may beproduc ed at the base P741 . Find the quantity ofwater flowing per minute from
a vessel in whic h the surface of liquid is c onstantly 1 meter
above an orifice whose area meter.
QUES T IO N S A N D P ROBL EM S I N P E T ERS .
742 . H ow far below the surfac e ofwater 1mm an a ifioe I
c entimeter s quare be plac ed in order that 300 lite s shallbe
disc harged perminute ?
743. In what time will 72 gallons ofwater flow duongh
an orifice, 1 inch in area, at the base ofa vers e! in which the
liquid always stands 9 feet high P
744. In what time will 1 00 0 liters ofwater flow through
an orific e whose area 2 square c entim. , which is at
the harmofa column ofwater 5meters high P
745. Inwhat time will a vessel filled with water be emptiedbymeans Ofan aperture at the base, having an area of 1 sq.
c ontim. , ifthe vessel is 80 c en. high , and if the area ofits
base 20 0 sq. c ontim. (C oefi'
. ofemu’
x P
(160 0 0 e . c . x I l/In; 160 0 0 c . c.
t/3(looo) 80 ; whence x 133sec . answer. )
740. lfa filled water tank is emptied in }4hour by meansOfan aperture at the base, in what time will it be emptiedwhen llw m ilive has twic e the area ?
747. l"ind the time required to empty a cylindric al vesselfilled Wllll water, having a diameter of feet, a height of
5 leet, and an orific e at the base of square inch area.
(Goelli. ofc lllux
748. In what time will a filled Mariotte’s flask be emptiedifits d iame ter : 4inc h . its height 8 inch. , and the area of
the Orific e at the base square inch ?
749. What is the shortest time in which a pond of5 m.
depth , 15m . length and 1 0 m . breadth is emptied by meansofa gate I m. high and 2 m . broad (C oefl
'
. ofc ontractionc oefi
'
. ofefllux
92 QUE S T I ON S A N D P R OBL E M S I N P H Y S I C S .
765. Find the side ofa square subjected to the same
amount ofpressure as the piston in the preceding example.
766. A boiler4meters long and 1 m. in diameter, is sub
jec ted to a pressure of 1 0 atmospheres to the square cent“ .
Find the amount ofpressure upon its inner surface (thicknessof the sides disregarded) .767. A boiler has a c ircular aperture of m. diameter
which is covered by a plate. Whenever the pressure ofthesteam in the boiler exceeds 2 atmospheres it raises the plate.
Find the weight ofthe plate.
768. Ofthree columns ofwater, one is 357feet high, thesecond 306 feet, and the third one 30 feet. Find the pressure ofeach expressed in atmospheres.
769. Find the pressure (in atmospheres) exerted by a c ol
umn ofwater 76 meters high .
770 . If the atmospheric pressure in a certain loc ality supports a column ofwater 30 feet high, what will be the heightofa column ofmercury supported by atmospheric pressure inthe same locality and at the same time P771 . A pressure gauge was applied to the airvessel ofa fire
engine. When the men were doing their best it was Observedthat the index showed 45 pounds per square inc h as themaximum. What height would the water have in a vertic al column with such a pressure P and why does the jet from the fire
engine fail to reach that height when worked at the 45 poundpressure P772 . Find the height ofmercury
,as in example 770 , when
the column ofwater is meter high.
773. With conditions the same as in 770 , what would bethe height ofa column ofsulphuric ac id (sp. gr. P774. With conditions the same as in ex . 772 , what would
be the height ofa column ofbromine (sp . gr. 3) P
BA R OM ET ER . 93
775. With conditions the same as in ex . 770 , find the
h eight of a column of alc ohol , sp . gr.
776.Find the specific gravity ofa solution standing 36
feet high where the merc urial c olumn supported by the atmos
p here inches.
777. T he specific gravity ofair being what is the
theoretical height ora columnofair that supports a c olumn of
mercury 760 millimeters high ?
778. What are the pressuresofairon a square centimeterofsurface, where the mercury stands respectively 70 0 , 600 , 50 0 »
50 and 1 m. m. high P
B A R O M E T E R .
780 . What is a barometer P781 . Desc ribe the c istern-barometer.782 . Describe the syphon-barometer and explain its ad
vantage over the cistern-barometer.
783. Describe the aneroid barometer.
784. S tate the three most important barometric correetions785. T he readings of a barometer suspended within a
room are the same as when it is suspended out ofdoors.
Explain786. What are the relations between the barometer and
the weather787. T he mercurial column in a barometer has a diameter
of m. the mercury in the c istern one of m. Whenthe mercury in the tube rises 3m. m. , how much will the sur
face of the mercury in the cistern sink P
94 QUE S T I ON S A N D P R OBL EM S I N P H YS IC S .
788. Supposing the density of the atmosphere to be uniform
,and the barometer to stand 30 inc h . at the level ofthe
sea, what would be the height of the atmosphere (sp. gr. Of
air7376) I
’
789 . A barometer was filled with impure mercury ofspec ific gravity 13. Find its height at the sea level, expressedin m. m .
790 Merc ury was poured into a barometer tube until thetube still contained 1 5 c . c. ofair Of the ordinary atmosphericpressure. T he tube was then inverted in amerc ury bath ; the airnow Oc c upied a spac e Of25 c . c .
,and the c olumn ofmercury
stood 30 2 mm . high . What was the pressure ofthe atmosphere P (A .)(L et x : the amount Of this pressure. T he pressure ofthe
air in the upper part of the tube : g x, whic h , added to
30 2 mm . ,will be the pressure exerted within the tube upon the
surfac e Ofthemercury in the bath , and is equal to the pressureOf the atmosphere. That is : i t; x 30 2= x
, whence x
755mm .
, answer. )
79 1 . A barometer tube was filled with mercury and in
verted in a cistern filled with mercury. Then 1 0 c . c. ofatmospheric air were admitted into the tube, and there oc cu
pied a spac e of30 c . c .
, the merc ury standing 50 0 mm. highFind the pressure ofthe atmosphere.
M AR IOTTE’S LAW.
(V :V'
P’ P ,
whence formula P ' iv
, in which V s :
the volume ofgas, and P its pressure ; V'the volume ofthe
same quantity Ofgas subjected to pressure
96 oussrroN s A N D P ROBL EMS LN P H YS IC S .
804. T he density ofa c ub. ft. ofa certain gas 1 ,with
the barometer at 28 in. What will be the respec tive densitiesofa c ub. ft. ofthe same gas, when the bm meter stands at
and inch P (Express answersin decimals.)80 5. T he volume ofa certain gas : I , with the barometer
at 20 inch. , and diminishes under different pressures, becoming successively and Find the c om pondingtensions of the gas, expressed in mercurial columns.
806. Find the corresponding tensions of the gas in the
preceding example, with the barometer at 40 0 mm . when the
volume 1 .
807. A body ofair fills the space of 1 c ub. ft. , barom. at
30 inch. Find the space it occupies with the bar. at 27 inch.
808 . The volume Ofa body Ofair 1 c ub. m . ,barom. 600
mm. Find the volume with barometer at 700 mm .
809 A balloon, diam. 1 0 ft. , was filled to its utmost cape»
city Wltll air when the barometerstood 29 inc h . What volumeofair will pass out when the bar. sinks to 28 in. P81 0 . What is the difference between the weight of a cubic
meter ofair at 760 mm. and one at 700 mm. P (Take weightofa liter ofair at 760 mm. grams.)81 1 . A receiver Of5 liters capac ity was mad e to contain
the following gases : 2 liters of hydrogen at a pressure of3atmospheres 5 liters ofcarbonic acid at a pressure Of2 atmos
pheres and 3 liters ofoxygen at a pressure of 1 atmosphereRequired the pressure of the mixture, the temperature dunngthe experiment being supposed to remain constant. (C . M.)81 2 . T he receiver ofan air-pump contains 5 liters of air.
I ts upper portion communicates with a barometer, the merc ury ofwhich stands at 0 as long as the receiver containsair Ofordinary atmospheric pressure. After a few strokes of
A IB P UM P . 97
the piston the mercury rises to 650 mm. T he pressure Ofthe
atmosphere during the experiment 760 mm., the temp .
0°C . Find the weight Ofthe airwithdrawn from the receiver.
AIR-PUM P .
(After the first stroke ofthe piston, the pressure, or tension,P V
V+v
(V v) ; where v c apac ity of cylinder,V capacity of
rec eiver (and communicating tube) , P the original pressure
of air in receiver, x , or by proportion, x P V
ofthe air. And the pressure after2: strokes: P (V
V
81 5. Describe the princ ipal parts ofthe common air-pump.
816. Why c an no perfec t vacuum be Obtained by meansofthis air-pump P817. Give position Of valves during upward and down
ward strokes Ofthe piston.
818. What causes each valve to close P Why should thevalves weigh but little P819. Why is the tension of the air in the rec eiver reduced
after every stroke ofthe piston P Give formula for finding theamount ofthis reduction.
820 . I place a receiver upon the plate ofan air-pump, and
then greatly rarify the air outside Ofthe pump. H ow will thisaffect my subsequent exhaustion ofthe receiver by the pump P(In the following examples disregard the capac ity ofthe tube. )82 1 . T he capacity of the receiver of an air pump 240
cub. inch. ; that ofthe cylinder 48 c ub. in. Find the ten
sion of the air remaining in the rec eiver after the fifth strokeofthe piston. (Solution on next page. )
7
98 commons A N D P ROBLm L! m rsrc s .
(C apac ityofthe cylinder capad ty ofrec eiver ; henc e,
the pressure or tension ofair in rec eiver after the i r: stroke
5 15 . t pds. ; and after the fifth stroke :
g s 6+ pds. persquare inch ofsurfac e. )822. i’ind the tension ofthe air in the rec eiver of an air
pump after the first stroke of the piston, the cylinder having
the same c apacity as the rec eiver.
823. in the preceding example find the tension ofair after
the second stroke after the tenth ; after the 1 th.
314. Find the tension ofthe air in the rec eiver ofan z ir
pmnp after the first stroke of the piston, the c apac ity of the
recmvet being twice that of the cylinder.
this. As in preceding example, find the tension ofairafierthe lnnt stroke ofthe piston, the capacity Of the receiver being three times that of the cylinder.
m . Final tension ofair after the first stroke of the pistonwhen cupuc ityofrec eiver is ten times, and when n times, thatofcylinder.
8117. in example 82 1 find the we1ght of the air leftin the rec eiverafter the fifth stroke, if before exhaustion theweight m 40 grains (temperature disregarded) Pans. in example 82 1 find the height ofmercury indicating
the tension ofair in the receiver after the fifth stroke.
829. ifind the tension Of the air in the receiverofan air
pump after the second stroke of the piston, the c ap. of,
rec eiverand cylinderbeing respectively 5 lit. and I lit.8311. Required the weight of the air remaining after the
fourth stroke in the preceding example .
831 . T he exhaustion ofa pair OfMagdeburg hemispheres,10 cent. d iam , was discontinued when the mercurial columnconnec ted with them stood 3mm. high. Find the force re
,
quired to pull them asunder(barometer 750 mm. thic knessof
hemispheres neglected) .
100 QUE S T ION S A N D P R OBL EM S IN P R YBIOS .
841 . Find the tension Of the air in the cylinder ofa con
denser whose capacity is the same as that Of the receiver,after the first (downward) stroke of the piston after the sec
ond and after the third .
(L et v c apacity of cylinder ; after the first stroke the
receiver will contain the original volume Of air plus anotherv, in all, 2 v, and the tension 2 atmosph . after the secondstroke it will contain 3v, and the tension then 3atmosph. ;
after the third stroke the tension 4atmospheres.)842 . In the preceding example what will be the tension
respectively after the tenth, thirtieth, and nth stroke P843. What will be the tension of air in the receiver after
the first stroke ofthe piston, the capacity ofthe cylinder being)6 that ofthe rec eiver P844. What will be the tension after the first stroke, if c ap.
ofc ylinder i t hat ofreceiver P Ifi P 715 P"1 P
845. T he capacity of the receiver of a condenser 200
cubic inches, that of cylinder 25 cubic inches. Find the
pressure of air in receiver after the first stroke ofthe piston.
Find the pressure after the fifth stroke, and after the tenth .
846. Supposing the air in the receiver of preceding ex
ample, before condensation, to weigh 33 grains, what will beits weight respectively after the first, fifth and tenth strokes P847. In preceding example find height ofmercury indi
eating the tension ofthe air in the receiver after the first, fifthand tenth strokes, barometer at 28 inch. before condensation.
848. T he c ap. of the receiver of a condenser 4liters ;find the tension (per square centimeter) ofair in receiver afterthe first, fourth and tenth strokes Of the piston ; capac ity ofcylinder 1 liter.
849. What weight Of air will be in the rec eiver Ofthe
preceding example after the tenth strokeP
SYP H ON . 101
850 . Find height of mercury columns corresponding to
tensions found in example 848,with the barometer at 750 mm.
851 . T he capacity Of cylinder and rec eiver being as 1 to
154, after how many downward strokes of the piston will theair in the receiver have four times its original tension P852 . Capacity of receiver a c ap. ofcylinder 6
find amount of compression after a downward strokes Ofthepiston.
SYPHON .
855. What is a syphon?856. On what conditions will the syphon flow P857. Explain the action Ofthe syphon.
858. Underwhat circ umstanc es will the liquid in a syphonremain stationary ? Under what circumstances will it flowback into the vessel P859 . Is it true, as is commonly believed, that the two limbs
ofa syphon must be ofunequal length P Explain youranswer.
860 . Why is the height limited to which a liquid can be
raised in a syphon P On what does that height depend ?861 . T he tube ofa syphon has a cross-area of2 sq. inch,
and its Open end is 16 inches vertically below the surface of
the liquid in the vessel . What is the effect of atmosphericpressure P(I 1 6 1 2 cubic m. , and 1 2
pounds ofwater. Subtracting this from 15 pounds, we have14.56572 24pounds, answer. )
862 . Find the vel. ofthe stream in the preceding example(the vessel not being replenished) .
102 QUE S T ION S A N D P ROBL EM S I N P H YS IC S .
863. Find the volume ofwater issuing fi'
om the syphonofthe preceding example in an hour, the vessel being constantlyreplenished .
864. Ifa syphon be made to float on water, does thataffect the velocity ofthe stream issuing from i t P865. T he tube ofa syphon has a cross-area of 1 sq. cent ,
and its open end is meter vertically below the surfac e Ofthe
water in the vessel. Required the effect of atmospheric pressure.
866. In the preceding ex. what is the vel. of the stream?867. H ow many liters ofwater will issue In an hour from
the syphon ofex . 865, the vessel being constantly replenished?868. H ow far vertically below the surface Of the water in
the vessel must the Open end Ofa syphon be whose sectionalarea 2 square c entimetres, so as to yield 24liters ofwaterperminute P (g 1 0 m .)869. A quantity ofalcohol, sp. gr. is to be transferred
by means of a syphon where the barometer stands inch .
Find the maximum vertic al height to which the alc ohol may
be raised in the immersed branc h ofthe syphon.
870 . Find the maximum vertical height towhic h sulphuricacid, sp. gt . may be raised in the immersed branc h of a
syphon, with the barometer at 29 inc h .
871 . With the barometer at 756 mm. find the height ofalcohol in example 869.
PUM P S AND AIR- CHAMBERS.
(Force necessary to lift the piston in a suction-pumps, where h = height (above the piston) ofa column
ofwater whose base is area 5 ofpiston, and h’= height ofcolumn Ofwater below the piston.)
l04 QUE S T ION S A N D P R OBLEM S I N P H YS IC S .
888. T he suction-pipe ofa lifting-pump has a length of
3m., the barrel a length of 2 m. from the pipe to the spout ;cross-area ofpiston m . ; at every upward stroke the pistonpasses over m. how many such strokes are required toyield 50 liters ofwater P889. Explain the essential points ofdifi
'
erenc e between a
suction-pump and a force-pump.
892 . Ifthe air in an air-chamber or a Hero’s fountain becompressed into halfits former space, what will be the heightofa vertically rising jet supposed to move without resistance ?(Barometer 29 inches. )893. What would be the height of the jet with the baro
meter at 750 mm . P894. H ow long would the jet in examples 892 and 893
remain at that height P895. T he airenc losed in a Hero’sfountain occupies a spac e
of1 liter. I then blow 20 0 c . c . Ofair into it by means ofa
tube. What will be the height of the jet (bar. 756
BALLOONS .
(T he ascensional power Of a balloon, that is, the amount
which a balloon will carry up,= the difference betweenweightofvolume ofair displaced and weight ofballoon weight ofcontained gas ; or=W where W is the weight ofair displac ed, W'
the weight of the gas and w the weight ofthe balloon. Take the ascensional pOWer ofhydrogen
grams for every liter ofhydrogen.)
BA L LOON S . 106
90 0 . A body occupies a space Of4cubic feet ; find itsweight in vacuo, ifits weight in air(3. g. 68775.
90 1 . A body occupies a Space of cubic meters ; find
its weight in vacuo, ifits weight in air 3542 kils.90 2 . A body weighs 1 0 0 0 pounds in vacuo, and occupies
a Space of5 cubic feet ; find its weight in air.
903. A body weighing 40 0 kilos in vacuo occupies a spaceof cubic meters ; find its weight in air.
904. A leaden bullet, diam. m., suspended from one
end ofthe beam ofa balance is balanced by a glass ballm. in diameter suspended from the other end ofthe balanc e ;but ifthe whole be placed under a receiver trom whic h the air
is entirely removed, one ofthe balls will sink. Question : In
vacuo which ball will sink, and what is then the differenc e inweightP (B. )
905. A balloon of1 0 0 0 cubic feet capac ity is filled with a
gas ofwhic h a c ubic foot weighs gounces. T he balloon itselfweighs 1 5 pounds. Required its ascensional power (sp . gr.
ofair
I OOO
77081 . 15pds.
Weight ofballoon+gas 65 pds.; 65
pds. ,answer. )
906. A balloon filled with hydrogen gas occupies a spac e
of20 0 c ubic meters. T he weight ofthe balloon, cordage, basket, etc . 60 kilos. T he weight of a liter of atmosphericair grams the sp. gr. ofhydrogen (air I ).Find the ascensional power of the balloon, that is, the
weight which the balloon c an lift at the instant ofits rise.
907. A balloon whose capac ity is 1 0 0 c ub. meters is filledwith gas, a literOfwhich weighs grams. T he balloon itselfweighs 20 kilos. Required its asc ensional power.
(Weight of 1 0 00 cubic feet of air
106 QUE S T ION S A N D P ROBL EM S I N P H YS IC S .
908. A spherical balloon of40 m. diameter is filled withilluminating gas ofsp. gr. One square meter Ofthe tis
sue weighs 200 grams the basket, ropes, etc ., weigh together
kilos. Required the ascensional power of the balloon.
909. A balloon made of tissue paper has a diameter of5feet ; it is filled with air, which, having been heated, has ex
panded l, ofits former bulk. T he balloon itselfweighs 3ozsRequired the ascensional power ofthe balloon.
AERODYNAMICS .
(Vel. ofefl ux ofgases into a vacuum \/2g2, where h ..
height ofcolumnofatmosphere indicated by height ofcolumnOfmercury or water ; d= density (either n ic e or
7310) of
atmospheric air, (mercury or water being I ).Vel. ofefllux of air into a spac e filled with air, or any other
gas, of less tension V2g where h' is the ideal height
ofcolumn ofair, or gas, ofless tension.
9 13. Explain the formula for velocity ofgases flowing intoa vacuum.
9 14. Give the formula for the velocity of gases issuinginto a spac e containing air or a gas of less pressure.
9 1 5. Prove that the lightera gas, the greater its velocity ofefi ux, and state the precise law.
9 16. What is the veloc ity ofair flowing into a vacuumwhen the barometer is at 28 inc hes P
(v \/2g 1
: 313
n ew 3°
1 252 ft.
108 QUEST ION S A N D P ROBLEM S
P R OPERTIE S OF
928. Define the term P hysics or Natural P hilosophy.
’
929. What is aphenomenon? Illustrate your answer.
930 . What is a physical law P
931 . What is a physic al theory P A physical hypothesis?932 . S tate the methods by which physical sc 1enc e has been
studied, and explain each.
933. Mention an instance of a physical change as dis
tinguished from a chemical change.
934. What is understood by the term physical sc iences?935. H ow Old is the sc ienc e ofphysic s proper P
936. What is the purpose ofphysics?
937. I ask you to represent grapfiz’
cally the variations ofthe barometer during a day. Show by a sketch how you willdo it.
938. Represent graphically any series of variations ofa
thermometer.
939. Ifall time-piec es on the globe were lost, how couldwe tell the time P
940 . What connection has a second of time with the rev
olution ofthe earth round the sunP
941 . What are the universal properties ofmatter P
942 . Mention two properties ofmatter without which theexistence Ofbodies c annot be conc eived .
PR OP ER T IE S OE M A TT “ . 109
943.What are accessory properties ofM P Mention
and illustrate five .
944. S tate the properties ofmatterexhibited in a rain drop.
945.What properties ofmatter does compressed air illus~
trate I
946. What are the three states Ofmatter?
947. S tate two ways in which the volume ofbodies c an bechanged.
948. What properties ofmatter are illustrated when in a
pint ofwater I dissolve, first, sugar, until the solution is saturated next, a small quantity ofsalt P
949. What do you understand by a molecule ofcommonsalt P950 . What is meant by an atom ofchlorine gas P Ofgold P
951 . H ow would you prove the impenetrability ofbodies P
952 . Find the length ofa k ilogram of c Opper drawn intowire of cent. diam . (sp . gr. ofcopper (A .)
953. A silver wire 6 mm. in diameter and m. in lengthwas drawn out into wire of 225 kilometers length ; find itsdiameter.
954. A leaden bullet 5“ inch in d iameter is hammeredinto a sheet of sq. ft. surface. Find thickness ofsheet.955. A cylindrical silverwire m . in diameterweighs
grams it is to be covered with a layer of goldm. in thic kness. Required the weight of the gold (sp. gr. of
silver ofgold (A .)S ch em a
— Ifr is the radius of the silverwire, and R its
radius when covered with gold, then r cm. and Rcm . T he volume of the silverw ire will be 11 r
'l, and
its weight rr r’l from which 1 cm .
T he volume ofthe layer ofgold is tr(R ’
768, and its
weight : 11 (0 .O95‘—0 . 3.657 nearly.
110 common A N D P R OBL E M S I N P H YS I C S .
956. Distinguish between adhesion and cohesion.
957. Give instances ofcapillary attraction,capillary repul
sion, and capillary depression.
958. S tate the law concerning the heights to which a
liquid may rise in tubes ofdifi'
erent bores.
959 . Explain endosmose and exosmose.
960 . S tate six properties ofmatter, and mention their ap
plication, or use, in daily life.
961 . Define elasticity.
962 . Define malleability, ductility and brittleness.
963. Define hardness. H ow would you ascertain the
relative hardness ofquartz and limestone P964. What is meant by the limit of elasticity P
965. Compare gases, solids and liquids with each otherasregards their elastic ity.
966. Define tenacity or absolute resistance.
967. Compare the characteristic properties of a c Opper
wire, a steel spring and a glass rod with each other.
968. H ow c an you render a steel spring inelastic, and aglass rod elastic P969. What is meant by elasticity of torsion P offiexure?
ofcompression P of elongation P970 . Define the term perfect elasticity.
971 . What is meant by the modulus ofelasticity P
112 QUES T ION S A N D P ROBLEM S Pa rsros.
S O U ND .
5}
C—zC—
'C D E F G A B C
1
R eL numb. g Q ? 3 3 155 2
N ew scale ofdouble vibr. 33 66 132 1485 165 176 198 220 264Length ofwave (in meters) 2 .585
Length ofsound-wave , air 1 . Vel ofsound ,air 838m.
c arb .ao. c arb . I la 888m.
ill. gas ll!. 338 . 533111.hydros . hydrog . —nmm.
1 0 1 2 . Define Sound.
1 0 13. Describe a wave ofsound. What is meant by thelength ofa wave ofsound .
1 0 14. Describe the manner in which sound is propagatedthrough air, water or wood.
1 0 15. Describe an experiment to prove that sound cannotpass through a vacuum. (S . K.)
1 0 16. H ow are echoes produced P S tate all you know te
garding the law whic h regulates the production ofechoes.10 17. S tate what is meant by the velocity of sound
, the
intensz'
b' ofsound, and by the pitch ofa musical sound.
1 0 18. H ow has the velocity of sound been determined?1 0 19 . You fire a shot before a cliff, and hear the echo five
seconds afterward. What is the clift’s distance from the c entreofexplosion P
50mm . 113
10 20 . One day when the temperature ofthe airwas 32°F. ,
I saw the flash of a gun, and heard the report halfa minuteafterwards. What was the distance ofthe gun, and why do Imention a particular temperature P (T .)
1 0 2 1 . H ow is the vel. of sound affected by temperature ?1 0 2 2 H ow is the velocity ofsound afi
'
ec ted by the rarityor densi ty ofthe atmosphere ?
1 0 23. Supposing the velocity of sound to augment 2 feet
per second for every degree C. of temperature above the
freezing point, what will be the temperature ofair in whichthe veloc ity ofsound is 1500 feet a second P
1 0 24. T he velocity ofsound in water is muc h greater thanits velocity in air. Why is this the c ase ?
1 0 25. A steam whistle is to be heard with equal loudnessby three persons occupying the c orners ofa triangle. Wheremust it be placed to be heard equally well by each person P
1 0 26. A cannon was fired on board a vessel in distress.An observer on shore c ounted 46 beats ofhis pulse from the
time he saw the flash until he heard the report, H is pulsewas beating 69 times a minute ; the temperature ofthe air
was 16°C . Find distanc e ofthe vessel from the observer.
1 0 27. T he vel. ofsound in air at a temperature of0°C is1 090 feet a second ; the length ofeach sound wave ofa seriesin such air is four feet. Determine the number ofvibrationsexecuted by the body which produces the sound P (T .)
1 0 28. T he wave-length ofa sound 6 ft. ; find the num
ber ofvibrations ofthe sound.
1 0 29. T he numbers of vibration of two sounds are as 5 to
find the ratios oftheir wave-lengths.
1 030 . H ow many vibrations per second are necessary forthe formation ofsound-waves 3feet in length P
Give the law 0 1 intensity of sound, and illustrate it.
VIBRAT ION S .
1037. T he circumference ofa wheel has 1 00 teeth whichstrike against an elastic strip. Find the number ofvibrationsof the sound produced per second, when the wheel rotates 3times per second .
1 038. Find the number of vibrations per second ofG..
1 039 . Give number ofvibrations per second for the tonesofthe scale from C 2 to C 3
.
1 040 . Find the numberofvibrations ofE 2 ofA 4 ofA , .
1 041 . T he tones within the compass of the human ear
range between 16vibrations and 380 0 0 vibrations. H ow manyoctaves is this P
1 042 . Find the number of vibrations of a tuning forksounding D
3. A lso
‘
the wave-length ofD3.
1 043. What is the c ause of consonance and dissonance inmusic P
1 044. Explain beats in music P1 045. H ow are music al sounds produced P On what do
pit”: and intensigy ofmusical sounds depend P1 046. H ow may the
“singing ” of telegraph wires be pre
vented P1 047. What is the part played by the wooden portion ofa
violin in the production ofsound P1 048. T wo music al sounds, the one produced by 40 0 , the
other by41 0 vibrations per second, pass through the same air;state and explain what is heard P (T .)
116 QUE S T ION S A N D P ROBL EM S nr en ema
1 060 . Wherein does the transmission of sound through a
smooth tube difi'
erfrom its transmissmn through the Openair?1 061 . Describe the manner in which the air vibrates
within an organ pipe when it sounds its fundamental note,its first harmonic and its second harmonic. (T .)
1 062 . A ir and hydrogen gas are urged in suc cessionthrough the same organ pipe. Describe the efi
'
ec ts and ex
p lain them.
1 063. A jar containing air and another containing hydrogen resound to the same tuning fork. A re the jars alike P Ifnot, state and explain the difference between them. (T .)
1 064. T wo 0pen organ pipes are in perfect unison beingof the same length . I shorten one of them slightly. Whatwill be the effect upon the ear when both of them are now
sounded together P (T1 065. What is the length ofan0penorgan pipe which pro
duc es sound-waves four feet long P What is the length ofas topped pipe producing waves of this length P
1 066. What is the fundamental toneofanOpenorgan pipemeters long ?
1 067. What is the fundamental tone ofthe preceding pipewhen covered ?
1 068. A tuning fork vibrates 51 2 times a second. Whatis the length of the sonorous wave which it would produc e inan atmosphere of hydrogen, supposing the velocity of soundin hydrogen to be 420 0 feet a second. (T .)
1 069 . Describe the manner in which a bell divides itselfwhen it sounds its fundamental note. What other notes andmodes ofdivisionare possible to the bell P (T .)
1 070 . What is the cause ofvariationsofpitch produced bythe fingering of a common flute P In other words, explainthe action ofthe flute as a musical instrument. (T .)
vmnarrons. 117
1 071 . H ow are the musical sounds of an accordeon or
mouth harmonica produced P S tate the similarity betweenthe production of these sounds and that ofthe human voice.
1 072 . H ow do you suppose the human voice to be produc ed P
1 073. What occurs in the case ofyour voice when yousing high notes and low notes P I mean, what is the con
d ition of the vocal organ when the two kinds of notes are
sounded P (T .)
H T .
SOURCES—MECHANICAL EQUIVALEN T .
(A heat-unit 772 ftpds. for 1°F ; or425meterkilograms for 1°C . )
1 081 . Give the sources ofheat and state which is the mosth portant.
1 082. What is the probable cause of the heat of the 81111 ?1 083. H ow is the heat ofa fire produced P Ofcoke P 0 1
the human body P1084. Why do ungreased wagon wheels become easily
heated P H ow do you account for the sparks emitted fromdry , rotating grindstones when steel utensils are beingsharpened P
118 QUES T ION S A N D P ROBL EM S 111 P arsros.
1085. State what you know regarding the difi'
erent kindsofrays emitted by the sun.
1086. Describe some one means of determining the
mechanical equivalent ofheat P1087. What is a heat-unit P1088. Give a c lear statement ofthe mechanical theory of
heat, and explain how it differs from the material theoryofheat P
1 089 . Explain what is meant by the conservation of
energy.
1 090 . A weight of a ton is lifted to a height of386 feet ;into what amount ofheat may this motion be converted P
1 09 1 . What is the mechanical equivalent of the heat tequired to convert one pound of ic e into water at 0
°C ?
One pound ofwater at 1 0 0 °C into steam at 1 0 0°C P
1 09 2. H ow many meter-kilograms ofwork are equivalentto the heat required to raise the temperature of 5 kilos ofwater 2
°C P1 093. H ow many units ofwork are involved in raising the
temperature of3 pounds ofwater40 °F P1 094. H ow many units of work are involved in raising
the temperature of3kilos ofwater40°C P1 095. From what height must a block of ic e at 0
°C fall,
that the heat generated by its c ollision with the earth shall bejust competent to melt it P (D .
1 096. From what height niust a bloc k of10s at 0°fall that
the heat generated maybe suffic ient to convert it into steam?
1 0 97. A twelve-pound cannon ball with a velocity of
feet a second strikes against a wall. Supposing all theheat generated by the collision to be communic ated to 1 2
pounds ofwater at 160 ° F ; to how many degrees would thetemperature ofthe water be raised P (g 16 ft.)
120 QUE S T ION S A N D P R OBLE M S I N P a rsros.
1 1 1 2 . H ow may a large mass ofwater, such as that in a
steam boiler, be readily heated P1 1 13. Give fourmetals in the order of their conduc tivity.1 1 14. A re gases good or bad conductors ofheat P1 1 1 5. Give a clear statement ofwhat you understand by
the radiation ofheat, and state the laws ofthe same.
1 1 16. S tate what you know regarding the radiation of
heat from the earth , and the eflec ts produced by this radiation. (T .)
1 1 17. H ow is the earth heated by the sun P H ow is our
atmosphere heated P
ABSORPTION AND REFLECTION .
1 1 20 . S tate and illustrate what is meant by Athermancyand Diathermanc y.
1 1 2 1 . Benjam in Franklin once exposed to sunl igh t onsnow bits ofcloth of different colors, and found that thedarker the cloth the deeper i t sunk in the snow. Givethe explanation of this experiment.Is it a fact that dark bodies are always more highly heated
by the sun than light ones P Ifnot, state and explain an ex
c eption. (T . )1 1 2 2 . What is the effect ofa transparent glass screen on
the heat ofa common fire P1 1 23. T he air ofa glass house into whic h the solar rays
enter, may be warmed by those rays to a muc h greater degreethan the air outside the house. What do you suppose to be
the cause of this P (T . )
A BS OR P T ION A N D R EFL EC T ION . 121
1 1 24. A black hat is more heated by the solar rays than a
white one. What is the reason P Dark iodine is, however,less heated by the same rays than white sugar. What is thereason? (T .)
1 1 25. Explain the influence of the earth’s atmosphereupon the temperature ofthe earth P (T . )
1 1 26. DO you consider it possible by means ofan atmos
phere to raise the temperature ofa planet more distant thanthe earth from the sun to the earth’s temperature P If so, ex
plain how it might be done. (T .)1 1 27. You are provided with plates ofcopper, silver, gold
and platinum, and are required to devise a means of determining their radiative powers ; how will you proceed P (T .)
1 1 28. A thermometer placed in an Open blac k box and
exposed to the sun,rises to 80 ° F. A glass cover is placed on
the box,and the temperature rises to Explain this,
and apply your explanation to the possible influence ofa
planet’s atmosphere in augmenting its temperature. (T1 1 29 . A plate ofroc k salt ifplac ed in front ofa hot fire will
not be heated, while a plate of glass will be heated. A hotplate ofroc k salt held at a short distance from the face hardlywarms the face, while a hot plate ofglass does warm it. Explain these eflec ts. (T .)
1 130 . S tate what you know regarding the absorption of
radiant heat by solids, liquids and gases. Explain in ac cordanc e w ith the mechanic al theory ofheat, what is meant by radiation and absorption. (T . )
1 131 . S how that a good radiator is also a good absorbent,and that bad radiators are bad absorbents.
1 132 . A thin plate ofrock salt is heated to I ts heatis allowed to pass through a thin plate ofcold roc k salt, andthen to fall on a thermometer. T he thermometer will showthat the c old plate has stopped nearly three-fourths of the
heat that it received from the hot plate Explain.
m oons'rrON s
T EMPERATUR E .
(See A ppendix. )
1 134 Define the temperature ofa body P1 135. Explain what is meant by the statement
bodies are ofthe same tempera1 136. Explain the construction of the common mercurial
thermometer. H ow are the Fahrenheit,Reaumur and Cen
tigrade thermometers graduated P1 137. H ow many degrees C 540 R ? H ow many de
grees F 40° C and how many degrees R 1 0 0 F P
1 138. ! inc boils at 1 204° F, mercury at 608° F. Changethese readings to degrees C.
1 139 . Change the following readings into degrees CPolished steel is ofa deep blue c olor at 580
° F ; it is ofa palestraw c olor at 460 ° F.
1 140 . Express in the Centigrade scale the following temperatures ofFahrenheit : and
1 141 . What is the advantage ofan alcohol thermometer
over a merc urial thermometer P1 142 . Desc ribe Breguet
’
s metallic thermometer, and stateits advantages.
1 143. A c ertain definite amount ofheat is communicatedto a solid body without c hanging its state of aggregation.
H ow is that heat disposed ofwithin the body P1 144. Define absolute temperature and absolute z ero.
124 QUE S T ION S A N D P EODm S I N P H YS I C S .
1 159. What is the coefi cient ofexpansion ofatmospheric
airP Why is it that the coefficient ofgases exhibits a much
c loser agreement than those ofliquids and solids P1 160 . Certain gases deviate from the normal standard in
their expansion by heat. S tate what you know regarding thec ause of this deviation
,and the circumstances under which it
is observed to occur.1 161 . Why is it possible to fuse platinum wire into glass
without frac ture on cooling P1 162 . If 20 0 cubic centimeters ofa liquid at 0°C become
2 1 0 cubic centimeters at what is the average c oefl'
rcient
of expansion of the l iquid ?(20 0 c ub. c. expand 1 0 c ub. cent. for 5O°C , hence 200 cub.
0 . expand c ub. c. for 1°C ; and 1 vol. expands
for 1°C that is, the c oefl
‘
. ofexpansion ofthe
1 163. If20 0 c ubic inc hes ofalc ohol at 0"bec ome 250 cub.
inches at what is its average c oeflic ient of expansion?1 164. Suppose that a person bought a liter of Spirits of
wine at a temperature of 1 O°C . What Space would this
occ upy at+32° C P (T he c oeffic ient of expansion is1 165. What is the average specific gravity of water at
80 °C ,water at 4
°C being taken as the standard P T he coeffi
cient ofexpansion is
(In rising from 4° to 80
°water will expand 76 times
1of118 volume. Hence its Sp. gr.=m )
1
1 166. T he specific gravity of a piece of lead at 0° was
Find its spec ific gravity at I OO°C .
1 1 67. T he specific gravity ofmercury at 0° is what
is it at 30°C P
Ex p A N S ION . 126
1 168. If273 c ub. cent. ofs ir at 0° are heated 1°C , what
will be their volume P
(S ince the coed'
. ofexpansion for gases oftheir bulkat we have 273+(2ir of273) 274c. c .; or, by proportion, 273
°273 c. c. x, whence x 274c. c.
1 1 69. If1 00 c. c. ofair at 0° are heated 1 O°C , what will
be their volume P1 170 . What volume will 546 liters of hydrogen at 0° C
oc c upy when heated to 2 1°C ?
1 171 . If 588 liters of hydrogen at 2 1°C are reduced in
ternperature to 0°C ,
what space will they occupy P(588 x, whence x 546 lit.)1 1 72 . What space will 20 cubic feet ofair at—I OO
°C 0 c
c upy when heated to I OO°C P
1 173. What space will soo c . c. of air at 15°C occupy
when cooled to 0°C P1 174. T o what temperature must 273 volumes ofa gas at
0°C be raised to expand to 295 volumes ?1 175. What space will 1 00 0 c. c . ofhydrogen at 0°C take
up when raised in temperature to 20°C ,
and what will be theweight of1 00 0 c. c. ofhydrogen at 2O
°G P
1 176. I fa liter ofair at 0°C weighs grams, what willa liter ofair at 40 °C weigh ?
1 177. If the liter ofair at 0°C in the prec eding ex. was
measured at a barometric pressure of750 mm. , what volumedid it occupy at 40 °C with a merc urial pressure of740 mm. P
1 178. Find the volume of 1 00 cubic meters ofair at 0°Cand a memorial pressure of760 mm .,
ifthe temperature beraised to 100°C and the pressure lowered to 740 mm!
120 QUE S T ION S A N D P sosnnx s IN P HYS I C S .
C HA N GE OF ST ATE.
1 180 . Distinguish between solids and liquids ; betweenliquids and gases.
1 181 . When does a liquid boil ?1 182 . What is meant by the boiling point of a liquid?
What is the boiling point ofwater, and how c an water beheated above its ordinary boiling point?
1 183. H ow is the boiling point affected when we ascend amountain P A nd why P
1 184. Give two illustrations ofquestion 1 1 83.
1 185. What is the chemical and physic al constitution of
aq. vapor, and how is it distributed in the atmosphere P (T .)I 186. H ow are clouds and rain formed P1 187. What is the meaning of the term saturated
, as ap
plied to air charged with vaporP
1 188. Explain the formation ofdew and hoar frost.1 189 . Desc ribe the influenc e of clouds and winds upon
the formation ofdew.
1 1 90 . If two bodies, one ofwhich is a good radiator, theother a bad one, be put out of doors on a clear night, onwhich will most dew be deposited, and why P
1 19 1 . Explain regelation.
1 192 . I c e may be formed on a clear night in India whenthe temperature of the air is 1 5 or 16° F above the freez ingpoint. H ow is this possible P (T .)
I 193. What is distillation P Onwhat does it depend ?1 1 94. Distinguish between condensation and distillation.
I 1 95. Explain and illustrate sublimation.
128 QUE S T ION S A N D P R OBL E M S IN P H Y S I C S .
1 207. What essential difi'erenc e is there between the temperature ofa body and the quantity ofheat it contains P
1 208. I c e at a temperature of 20°F,
w ith a thermometerimbedded in it
, is placed in a saucepan, and the saucepan isplaced on a fire. T he ic e melts, the water is warmed, andfinally boils. You observe the thermometer from first to last,what are its indications I
1 209. What is the latent heat ofwater P Ofsteam P1 2 1 0 . Distinguish between sensible and latent heat.1 2 1 1 . Underwhat circumstances does heat bec ome latent?1 2 1 2 . Explain latent heat in termsofthe dynamical theory
ofheat. (T .)1 2 13. H ow may the quantity of heat in a body be
measured P1 2 14. M ention two uses made oflatent heat.1 2 15. A pound ofwater at 0°C is placed togetherwith a
pound ofwater at 80 °C . What will be the temperature ofthetwo pounds ofwater P
1 2 16. A pound ofic e at 0°C and a pound ofwater at 80°Care mixed together. Find the temperature of the mixture,and explain your answer.
1 2 17. A kilo. ofsteam at 1 0 0° is mixed with 1 2 pounds
ofwater at 0°C . Find the resultant temperature.
(In latent heat, the number ofheat-units received the
number ofheat-units given out. L et x the resulting temp.
Then the loss ofthe steam is (1 0 0°
and the
gain ofthe water 1 2x . And 5 x) 1 2x , whence11 answer. )
1 2 18. A pound ofsteam is conducted into4pounds of
c rushed ic e at Find temperature ofmixture.
1 2 19. Find the number of heat units required to convert1 8 kilos. ofic e at 0°C into steam at 1 0 0 °C .
L A T E N T H E A T . 129
1 220 . Find the temperature ofthe water which is obtainedwhen 4pounds ofboil ing water are poured on 3pounds ofic eat 0
° C .
(L et x temperature. I t is clear that the heat lost by theboiling water the heat gained by the ice. N ow the loss ofthe water= 4(1 00—x) ; and the gain ofthe ic e 3
Sinc e 4(1 0 0 x) 3 we have x 223°C , temp.
ofthe mixture.)1 2 2 1 . H ow many pounds ofsnowat0"C must bemixedwith
6 pounds ofwater at 1 0 0 °C in order to obtain water of1 0 °C P1 2 2 2 . H ow much ic e w ill be converted into water at 5
°C
by 1 0 pounds ofwater at 90°
C ?
1 2 23. H ow many pounds ofwe at 0° will be melted and
raised in temperature to 1 0°C by 90 pounds ofwater at 19
°C ,
falling in temperature to 9°C P1 2 24. T wo masses, m and m
’
, of the same liquid, havingthe temperatures t
1and ta respectively, are mixed together.
T he ternperature of the mixture t°
. Find the equationexpressing all this.
1 2 25. T en pounds of steam at 1 00"are passed into 1 200
pounds ofwater at4°C , and 20 pounds of floating ic e atWhat will be the temperature ofthe m ixture P
1 2 26. Find the smallest weight ofwater at 32°F sufficient
to condense a pound of steam at the ordinary atmosphericm eme into boiling water.
1 227. H ow much water at 8°C must be added to 80 kils.
ofwater at 50°C to produce a temperature of20 °C P
1 2 28. An ounce of steam at 2 1 2°F is added to a pound
ofwater at 50°F. Find the temperature ofthe mixture.
1 229. Describe an apparatus for the artific ial productionofic e .
130 QUE S T ION S A N D P R OBL EM S IN P H YS I C S .
S PECIFIC HEAT.
(See T able in Appendix . )
1 232 . Define specific heat.1 233. I heat a ball oflead and one of iron to the temper
ature ofboiling water. I then place both balls on wax or
snow . Will they sink to the same depth P S tate what youknow regarding the subject touc hed upon in this question.
~ (T .)1 234. H ow much ic e may be melted by means of54pds.
ofiron having 50 0 °C oftemperature ? (Take specific heat ofiron iv)
(54 50 0 g, 80 x, whence x pounds.)1 235. A pound of iron at a temperature of 160°C is im
mersed in a pound ofwater at a temperature of50°C . H ow
many degrees will the temperature of the water be exalted ?
(Spec ific heat ofiron 0
1 236. A pound ofcold iron is plac ed in a pound ofwaterof a higher temperature. T he water loses 5° of temperature. H ow muc h has the iron gained in temperature ?
1 237. A pound of lead at 50°C is immersed in a pound
ofwater of 0°C . What will be the resulting temperature of
both , the Spec ific heat oflead being P1 238. Y ou are furnished with an ounc e ofeach ofthe fol
lowing metals, and are required to determine their spec ificheats : Gold, silver, copper, iron, lead, bismuth . H ow willyou proc eed, and what results would be obtained P (T . )
1 239. One pound ofmercury at 96°C is thrown into one
pound ofwater at 5°C . Find the temperature ofthe mixture.
1 240 . One kilogram ofiron at its welding point, 833°C ,is
thrown into 50 kils. ofwater at Find the temperature of
the mixture.
182 0111 51 10113 u rn 1 110a 111 P H YS IC S .
into a mass ofwater whose weight was one kilogram and
temperature 9°C ; and, when the temperatures had becomeequalized , the resultant temperature was found to be 13
°C .
What was the temperature ofthe furnac e P (D.)1 251 . An iron ball weighing 83 grams, and heated up to
340°C , was plunged into 50 grams ofwater at 1 0
°C whenthe ball had thoroughly cooled, what was the temperature of
the water P (D.)1 252 . A platinum ball weighing 200 grams was heated in
a furnace, and then plunged into 1 00 0 grams ofwater. In
consequence of this the temperature of the water rose from
13°to 20
°C . What was the temperature ofthe furnac e P (D.)1 253. A cubic foot ofwater at 70
°F is placed in contact
with 1 00 cubic feet ofairat the water sinks to sup
posing all the heat that the water has lost to be communicatedto the air, what would be the exaltation ofthe temperature ofthe air P (Take the weight ofa c ub. foot ofwater at 70 °
62 pounds.)1 254. Find the number of heat-units required to convert
eighteen pounds ofic e at 1 0°C into steam at 10 0
°C
n eonL L Annous. 188
MISCELLANEOUS .
Explain whys—water6—waterboils sooner in vessels with dull outside surface than
c—metallic objects should in severe cold not be touched withmoist hands
—aburning taperis readilyextinguished ona cold met. surface ;p—d ouble sets ofwindows protec t against cold better than
panes ofdouble thickness ;l—more time is required to heat water when the fire is by the
side ofit than when the fire is below the water.
Explain whya—a thermometer whose bulb is blackened with soot, when
exposed to the sun’s rays, rises more rapidly than one
not blackenedM ac w, ifcovered with a film of sand or soot, melts more
rapidly in the light ofthe sun ;c—fruit growing against a wall ripens a little sooner ;d- no dew is formed in c loudy weather ;e—when the hand is held a heated objec t, the side of
the hand turned tow the objec t feels warmer than theother side ;
f—steam radiators should have a rough. dull surfac e, whileboiler-steam tubes should be brightly polished.
Explain whya—tires are heated before being
plac ed on wheels ;
6—oil barrels iffilled in winter 5 ould not be made quite fullo—glass and some other bodies crack ifnot heated or cooled
uniform!
d —glass vessels, suc h as retorts, that are to resist intense heatshould be made thin
c—before filling a flask with hot liquid it should firstwarmed ;
j—the rails ofa railway track, if laid in cold weather, shouldnot be laid so as to touch one another ;
g—ih accurate measurements the temperature of the meas
uring instrument must be considered ;sudden chan oftemperature changes the tone ofapiano.
S tate how t e tone is altered when the change is frmcold to warm.
184 QUE S T I ON S A N D PnoBLmrs 111 1411 8108.
1 263. Explainwhyc layorwood contracts on being heated ;
6—the cover ofa book lyin in the sun warps ;c—water pails are moist in summer, but left dryin
Winter ;0' itchers crack ifcontainingwater in the state offleec ing ;42‘
s ofwaterform on the inner side ofthe coverofa vessel
ed with warm water;
f—a c old tumbler on being held over steam becomes coated
with moisture ;
g—the outside ofa vessel filled with cold water and brought
into a warm room becomes coated with moisture.64. Explain why
a—the boiling point ofwater is lower as the atmospheric
pressure decreases ;6—on high mountains meat to be done well must be boiled in
closed vessels ;c—the alcohol in a thermometer may indicate 100
°C , or be
yond , although alcohol boils at 78°C ;d—why c lothes drymore rapidlyonwindydays than in moist
weather ;e—the sensation of cold aftermoistening on'
e'
s forehead withether
f—to detec t the existence ofwind, mariners sometimesmoistena finger and hold it up in the air ;
g—in summer rooms are kept 0001 by sprinkling ;b—we cool ourselves byfanning ;i—moist garments are 1n
°
urious to health ;
j—water or ether lac e on the bulb ofa thermometer causesthe liquid wit in to sink ;
é—fluids in vessels may be kept cool in summer by beingtightly covered with wet flannel;
I—ice forms readily in a vac uum ;m—whenfroz en potatoes are placed in cold water, the water
willfreez e around the potatoes ;n- salt is plac ed on rails covered with snow orme.
1 265. What are the effects ofheat P Illustrate each by a
familiar instance.
136 QUE S T ION S A N D P R OBL E M S I N P R rsros.
1 281 . Describe the construc tion of a piston, and explainhow the piston and piston rod are kept steam-tight .
1 282 . Explain the purpose ofthe fly wheel .1 283. Describe with a sketch the locomotive boiler. Why
is it essential to discharge the waste steam up the chimney ?1 284. Describe the safety-valve ofa locomotive boiler.1 285. Sketch and explain the arrangement of the feed
pump, and valves connected with it, as fitted to a locomotiveboiler.
1 286. What are the main difficulties which were overcomeby S tevenson’
s inventionofthe locomotive engine and boiler?1 287. Point out the advantages resulting from the expan
sive working ofsteam .
1 288. Desc ribe generally the improvements introduced byWatt into the steam engine.
1 289. Explain whyWatt’s single-ac ting pump ing engine
is so much more economic al in steam than N ewc omen’
s.
1 290 . Desc ribe the arrangement ofthe condenser and air
pump ofa condensing engine and the valves c onnected therewith .
1 29 1 . T he length ofthe stroke ofan engine is 8 feet ; thepressure ofthe steam on entering the cylinder is 30 pounds tothe inc h ; at what point should the steam be c ut ofl so thatthe pressure at the end ofthe stroke may be 5 pds. per inc h l
’
1 292 . T he stroke of the piston ofan engine is 24 inches,and the diameter ofthe driving wheel is 8 feet. What is thenumber ofstrokes per minute ofthe pistonwhen the engine isrunning at 40 m iles an hour P
1 293. Desc ribe the indic ator.1 294. What is meant by the terms cur/tim ing and clear
ance t
1 295. Describe the screw propeller. H ow is the thrust ofthe propeller received upon the vessel P
L tsnr. 187
L I G H T .
130 1 . What is meant by the corpuscular theory of light,and how do you explain the undulatory theory P
130 2 . Which ofthese theories seems to you the true one ?
S tate at least two reasons for your assertion.
1303. Explain the necessity of assuming the existence ofan fi lter, and state what its vibrations give rise to.
1304. What are the sources oflight, and which is themostimportant one P
1305. Give some proofthat light itselfis invisible. (T .)1306. Define a ray and a penc il oflight.1307. What is meant by the scattering of light, and what
by its regular reflection P (T .)1308. Distinguish between a luminous body and an illumi
nated one.
1309 . Distinguish between transparent and opaque bodies.1310 . When are shadows formed P When penumbras P131 1 . An opaque square plate, each side z jé inches long, is
held in front of the eye and 8 inches from the eye ; find the
area which at a distance of40 0 feet is concealed by this plate.131 2 . A disk of m. diameter is illuminated by lamin
ous rays proceeding from a point m. distant from the
centre of the disk ; at what distancewill the shadow have a
diameter of m. P (B. )1313. A square plate, each side m. long, is held
in front ofthe eye, 50 centimeters from the eye ; find the
area which , at a distanc e of 200 meters, is concealed by thisplate.
138 0111132 10 115 A N D P R OBL EM S I N P H YS I C S .
1314. Light issues from a luminous globe 1 2 inchesind iameter, and falls upon a second, opaque, globe 6 inches ind iameter; show by a diagram the kind ofshadow cast by thelatter. (T .)
1315. A c loud is composed oftransparent water particles;but if transparent, why are clouds able to interc ept somuchofthe sun
’s light (T .)
1316 Define the difl'
erenc e between the forms ofa treewhen the tree stands in the sunshine and throws its formupon the ground ; when the tree stands near still waterand its form is seen in the water.
1317. What is the velocity of light, and how has it beenascertained (T .)
1318. Describe and explain Bunsen’s photometer.
1319 . I wish to c ompare the light of a candle flame withthat ofa gas flame of the same siz e. H ow would you determine and express numerically the relative intensities ofthetwo lights P (T . )
1320 . S tate what you know regarding the intensity of
light.132 1 . By what means do we ascertain that one light has 8
-or 1 0 , or any other number of, times the intensity ofanother?1322 . Inwhat ratio is a book illuminated if, first, it is
m. distant from the sourc e of light, and next m. d istant ?1323. In order to compare the light ofa petroleum lamp
with that ofa tallow candle, both were so placed as to throwshadows of equal intensities on a wall the distanc e betweenthe lamp and the wall was 5 feet, that of the candle and the
wall 1 foot. Give the ratio oftheir intensities.
1324. Work the preceding example, the lamp being 2 m.
and the candle m. from the same wall.
140 QUE S T ION S A N D P R OBL EM S I N P H YS I C S .
1340 . A large concave mirror is plac ed before you ; yousee your image first mverted 1n the air you c hange yourdistance from the mirror, and find that in a certain position yourimage vanishes ; again
, you change your position and find
your image erect. Under what circumstances are these effectsobserved P S tate whether the images observed are ofgreateror less siz e than yourself, and give the reason ofthe increaseor diminution. (T .)
1341 . When an image is formed by a concave mirror, incertain positions you see the 1mage in the air
, while 1n certainother positions you do not see it. If, however, a sheet oftracing paper rec eive the image, it is seen from positions, before and behind, in which the a ria! image was invisible. Ex
plain all this. (T .)
1342 . I plac e a c andle in front ofa c onvex m irror. Con
struct the image, and explain the c onditions ofthe image.
1343. Desc ribe and show by a diagram the charac terofthe image formed by a c onvex m irror. (T .)
1344. Describe and explain the character of the imagesformed by a conc ave mirror. Why do I employ the termimage in the previous question, and the term images in thisone P (T .)
1345. What is meant by total reflec tion P1346. Desc ribe the circumstanc es under which total te
flec tion takes place.
1347. A white towel spread on a table has water sprinkledupon it ; the parts on which there is water look darker; butif you look at a light through the towel the wet parts seem
brightest. Explain this.
1348. Why are the colors of a diamond more brilliantthan those Ofa piece ofglass c ut after the same pattern?
am m on. 141
R EFRACTION—THE EYE—VIS ION.
1354. Define refraction,and illustrate by an example.
1355. S tate the laws ofrefraction.
1356. What is meant by the index ofrefraction P1357. Why should a lake, the bottom of which you c an
see, appear shallower than it really is P1358. I fill two cups ofthe same depth with two difl'erent
hquids, and notice two things : firstly, both cups appear shallower than when they were empty and secondly, one ofthemappears shallower than the other. Explain. (T .)
1359 . Show by a diagram the manner in which a stickappears bent when it is thrust obliquely into water. Explainthe appearance. (T . )
1360 . When a ray oflight is refracted through a windowpane, the exit ray is parallel to the incident ray. Why P
1361 . S tate the likeness that exists between light andradiant heat as regards reflection, refraction and transmission.
1362 . What effect has the greater or less thickness ofaglm plate upon the displac ement ofobjects seen through it P
1363. Show by a diagram the course ofa rayoflight passing through a sphere ofsolid glass without striking the centreofthe sphere.
1364. Describe a prism, and show by a diagram how itac ts upon light. (T
1365. Draw a section ofa prism ; draw also the sectionofa beam of sunlight passing through the prism,
‘
and show byyour sketch how this light is acted upon by the prism. (T .)
1366. Describe some experimental mode of determiningthe index ofrefraction ofa transparent liquid . (T .)
1367. What are lenses P What is their purpose P
QUES T I ON S m Pnonmnrs m Puxsros.
1368. Into how many k inds do lenses divide themselves P1369. What is meant by the princ ipal focus, and the main
axis ofa lens P1370 . S tate four cases ofrefraction through a c onvex lens.1371 . Describe the manner in which imagm are formed
by a convex lens. (T1372 . Desc ribe and explain the camera obsc ura.
1373. Show by a diagram the course ofa ray oflight falling (parallel to the main axis) upon a double convex lens.
1374. Show by a diagram the course of a ray of lightstriking (parallel ‘to the main axis) a plano-convex lens.
1375. Show by a diagram the c ourse ofa rayoflight striking(parallel to the main axis) the convex side ofa c oncavo—oonvex lens.
1376. Show by a diagram the c ourse ofa ray oflight falling upon a double c onvex lens ofequal radii and small thickness, and starting
a . From beyond the principal focus.
5. From the principal focus.
c . From between the principal foc us and the lens.1377. Show by a diagram the condition and position01
images formed by an object situated respectively at a , b and cin the prec eding example.
1378. Show the likeness that exists between sound and
light as regards reflec tion and refrac tion. (T .)1379. H ow is the linear magnifying power ofa single bi
c onvex lens found P1380 . What is the magnifying powerofa bi-c onvex lensof
96 inc h foc al distance, the mean distanc e of d istinct visionbeing 1 0 inc hes?
1381 . Ofwhat ratio are the magnifying powers ofthe bic onvex lens in the preceding example, for a near-sighted per
through a film of water, one of alcohol, one Of bisulphidt of
w homand lastly through air again. T rac e its path throngh‘
out these media.
1394. Show by a diagram the spherical aberrationof8
1395. S tate what you know regard ing the structure ofthehuman eye. (T .)
1396. What is meant by the distance Ofdistinct vision?1397. Dm ribe the human eye, and state the conditions
which must be fulfilled to render vision distinct.1398. What is meant by the adjustment ofthe eye fordis
tinct vision at different distances, and how is the adjustmmt
ac complished P1399 . What is meant by the visual angle P140 0 . Define irradiation.
140 1 . What form Oflenses do you consider most usefulfor a diver? S tate the reason.
140 2 . Why is the human eye not adapted for visionunderwaterP
COLORS , E T C .
1407. What is meant by the dispersion oflight ?1408. What is the difference between the scattering” of
light and the dispersion Of light ?1409 c ribe the solar Spec trum. H ow may it be pro
duc ed ?
141 0 . Describe clearly an experiment by which whitelight c an be resolved into the difi
'
erently colored lights whichcompose the white. Desc ribe also an experiment by which
(T .)
OOLons, m o. 146
141 1 . What are the colors ofthe spectrum P141 2 . What are the properties ofthe spectrum P1413. Show that colormaybe compared topittainsound.
1414. Define color.1415. When is a body black ; when white P1416. Looking through a red
.
glass at the white body Of
the sun you see it red ; in what way does the red glass ac tupon the light so as to produce this impression? (T . )
1417. Why is a rose red , and grass, green (T .)1418. H ow are the colors offlowers produced P (T .)141 9 . Y ou enter a room by daylight and find the walls
covered with vividly colored paper ; you close the windowsso as to reduce the room to total darkness ; are the colorsstill there? Give a full reason for your answer. (T .)
1420 . T he length of a wave of yellow light is 528
ofa line ; find the number ofsuch waves striking the retinaper second . (A line is the twelfth part ofan inch .)
142 1 . T he average length of a wave of white light isofa line ; find the number ofwaves per second.
1422 . Sunlightfallsona surfacepainted red ; a portionofthelight is reflec ted from the surface ; what is the color ofthisportion P A portion enters the paint ; what becomes ofit?(T .)
1423. S tate what occ urs within a black body which ren
ders it black ; and state what occurs within a white bodywhich renders it white. (T
1424. A spectrum cast upon a white screen is looked at
through a purple glass ; what appearance does it present, andwhat is the cause ofthis appearanc e? (T . )
1425. I place a red ribbon suc c essivelv in the green andthe red ofthe spec trum ; how is its temperature afl
'
ec ted P Ido the same with a green ribbon; how is its temperatureafl
'
ec ted ? (T . )
146 QUE S T ION S A N D P R OBLmrs m a eros.
1426. What are complementary colors P Give a list ofthem.
1427. What is an achromatic lens P1428. What is meant by the dispersion of light ? State
what you know regarding ac hromatism.
1429. T he rays ofthe sun are received upon a large con
verging lens ; a screen placed within the focus shows a whitecircle surrounded by a red fringe ; ifplac ed beyond the focusit shows a white circle surrounded by a blue fringe. Explainthese appearances. (T .)
1430 . S tate what you know regarding the lines ofFraunhofer. (T .)
1431 . Describe and explain the lines OfFraunhofer, anddeduc e from them a theory of the c omposition and temperature ofthe sun. (T .)
1432 . Describe an experiment which shall illustrate thechromatic aberration ofa lens. (T .)
1433. Define spectrum analysis.
1434. H ow is the primary rainbow produced ?1435. H ow is the secondary rainbow produced P1436. What is meant by diffraction P1437. Explain double refraction.
1438. Define polariz ation oflight.1439. Describe the polarization of light by reflection, by
refi'
ac tion, and by double refrac tion; and assign the conditionsnec essary to render the polariz ation complete.
1440 . Define the terms Calorescm e, fl uorescence, Inter
148 commons A N D 9 itoa 111 a os.
1459. Explain the termspamm gnd ir and M agnets} .
1460 . Five balls ofiron hang in a series from the north endofa magnet, but you cannot get a sixth ball to hang ; whyT he north end ofa second magnet is brought over that ofthefirst ; seven balls of iron now cling together ; why? You
plac e the second north pole below the series of ballsseveral of them fall away. Explain this.
1461 . Distinguish betweenpm m t and W W magnets.
1462 . What is the keeper or armature ofa magnet P1463. What efl'
ec t has heat upon magnets P1464. You are required to magnetiz e a sewing needle so
as to make the eye ofthe needle a north pole ; how will youdo it P T he point ofthe needle is then presented to the
north end Ofa mariner’s c ompass needle ; what w ill occur?1465. What is the difl'
erenc e between iron and steel as re
gards their acceptance and their retention of the magneticc ondition P (T . )
1466. Mention three modes ofmagnetiz ing steel bars.
1467. T he pole ofa magnet is drawn over an unmagnet
ised bar ofsteel ; state in the language ofthe theory ofmagnetic fluids what occurs.
1468. What is meant by the coercive force ofmagnets P1469 . H ow would you demonstrate magnetic induction?1470 . What dm terrestrial magnetism imply P1471 . S tate any one theory ofmagnetism.
1472 . A bar of iron is held vertical, and a magneticneedle is passed slowly from its bottom to its top ; describethe action Of the iron upon the needle. What is the effect ofreversing the bar P (T .)
1473. What is meant by magnetic declination P1474. S tate what you know regarding the action of the
1140 11111 1511. 149
earth upon a freely suspended magnet P I llustrate the earth’saction by means ofa bar-magnet.
1475. What is meant by magnetic inclination or dip P1476. What is meant by the declination and inclination of
the magnetic needle P What is meant by the terms magneticdip
,magnetic poles, and magnetic equator ? (T .)
1477. What do you think causes a magnetic needle to set
north and south P Does its direc tion ever vary P Ifso, statewhat you know regard ing the variation. (T . )
1478. S tate what you know regarding the use ofthe magnetic needle in the steering ofships. (T . )
1479. T he marked end ofa magnet is attrac ted by theearth’s north magnetic pole ; but ifthe magnet be set floatingon a cork it does not move toward the pole. Why P (T .)
1480 . What is the meaning ofthe term geographical meridian ? What is the meaning ofmagnetic meridian P Whatname is given to the angle between the two meridians P (T .)
148 1 . A bar-magnet, freely suspended horizontally, sets inthe mag net meridian. Supposing a second bar-magnet to besuspended by the side ofthe first, how will they ac t uponeachotherP Make your answer clear by a dw IT .)
1482 . Y ou carry with you a dipping needle from the
earth’s north magnetic pole across the equator to the southmagnetic pole ; how will the dipping needle behave duringthis exc ursion P
1483. H ow would you demonstrate that the earth behaveslike a magnet P
1484. H ow am I to hold an iron bar so that it shall tec eive its maximum ofmagnetization from the earth P H ow,
when held in this position, is such a bar to be tested P1485. Give the law ofmagnetic intensity.
1486. H ow maymagnetic force be measured P
150 can nons um m enu s 1: P H YS IC S .
1487. A smallmagnetic needlefreelysuspended, and actcd
upon by the earth alone, executes 1 20 vibrations m a minute;
plac ed near the pole ofa steelmagnet 1t osc illates 250 timesin a minute ; compare the forc e which the earth exerts upon
the needle with that exerted by the magnetic pole, and givethe numbers which express the forc es. (T .)
1488. You have two barmagnets ofdifierent powers, anda smallmagnetic needle. You are required to detennine andexpress numerically the relative powers ofthe two magnets.
How willyou do it P (T .)1489. A magnetic needle is plac ed obliquely to the mag
netic meridian ; show by a sketch the charac ter ofthe forcesac ting upon the needle, and tending to turn it into the meri
(T .)1490 . You hearofthe magnetic meridian and ofthe geo
graphical meridian ; what is the difl'
erenc e between them?T o what changes, ifany, have they been observed to be sub
jec t P (T .)149 1 . T he end of a magnetic needle brought near the
middle ofa bar-magnet is, to allappearance, not acted uponat all by the magnet. Does the magnet really exercise no
ac tionon the needle inthis position P Ifso, what action P (T .)
151 0 . A strip ofpaper rubhed with india—mbher is hrought
near a glass rod which has been mbhed with silk ; whatfol
lows ? Deduce from the experiment the qnali y of the elec
tric ityupon the paper. (12)151 1 . Explain fullywhat takes plac e when light bodies are
attrac ted bya stic kofsealing-wax rubbed with flannel. (T .)151 2 . When you think ofan elec trified body, in what n y
do you picture i t to your mind P (T .)1 513. A collodion balloon simply stroked with the hand
becomes negatively electrified . Supposing you were asked to
prove the truth of this statement, how would you proc eed?(T )
1514. An egg-shell is placed on a table, and a glass rod
which has been rubbed with silk is brought near the shell ; theshell rolls after the rod . Describe the condition of the rod
and the shell during the motion of the latter. (T .)1515. Ifyou take an insulator in your hand and rub it
properly you electrify it ; ifyou do the same with a c onductor
you obtain no signsofelectricity ; what is the reason P Bod
ies were formerly divided into electrics and non-elec tries ;
why P (T .)1516. C an a solid body be electrified by fi'ic tion with a
liquid or gas P Ifso, mention an instance ofeach .
1517. When is water a bad conductor ofelectricity P1518. Distinguish between conductors and non-conduc t
ors ofelectricity. Is this distinction absolute P1519. Mention three conducting substanc es and three non
conducting ones.
1520 . When is air a good conductorofelectric ity P152 1 . Mention two causes why electrified bodies, even
when plac ed on insulators, gradually lose their electric ity.
1522. H as climate any influence on insulators P Illustratebysiau
1 3101 10 1141. m om . 158
1523. Ifyou rub a stick ofsealing-wax held in the handwith flannel, it becomes electrified ; ifyou rub a rod ofbram,
you do not electrify it. What is the reason of this difl'
er
ence P (T . )1524. What happens when two conducting bodies are
brought in contac t with each other, the one being electrified ,the othernot P1525. H ow is the conductivity ofglass altered when the
glass is heated to rednessP1526. T wo strings are given to you, and you are required
to test whether they insulate or conduct electricity ; how willyou proceed P (T .)
1527. Prove that there are two kinds ofelectricity.
1528. What do the signs and mean in elec tricityP
1529. Why is repulsion a surer test of the electric condition ofa body than attraction P
1530 . When two bodies are rubbed together, which ofthetwo kinds ofelectricities is generated first P
1531 . Mention three substances arranged in such an orderthat ofthe first two each bec omes positively electrified whenrubbed with the body following, and that the last becomesnegatively elec trified when rubbed with the substance preceding.
1 532 . When you rub a stick of sealing-wax with flannel,what is the state of the rubber? When you rub a stick ofglass with silk, what is the state ofthe rubber P (T .)
1533. Iftwo persons stand, each on an insulating stool,and one strike the other with a well-dried cat’s fur severaltimes, which of them will be M b! electrified, and whic hW M
1 534. What is meant by the term “ insulated P” I bringa glass rod which has been rubbed with silk near an insulated
154 QUI BT IOR S 4111) 1130311 113 111 Pmrsms.
brass sphere ; what is the cond ition of the sphere while theglass is near it ? What oc curs when the glass is removed?
T.
1 535. S tate the laws offi'ic tional electricity.
1536. What is an elec trosc Ope P What an elec tronomer?
1537. I grind sulphur in a mortar and thus electrify it. Iplace some of the electrified powder on the plate ofa goldleafelectroscope ; the leaves diverge ; why P sinc e the sul
phur is an insulator and does not part w ith its electricity. Iremove the powder by means ofan insulator ; what will ccc ur, and why will it oc curP (T .)
1538. Describe an experiment to prove that free staticalelectricity shows itselfonly on the surface of bodies.
1539. Does the form ofa body exert any influenc e on theac c umulation ofelec tric ity P (T .)
1540 . T wo insulated conductors, of the same size, andc harged with unlike electricities, attract eac h other with a
c ertain amount offorce or tension. Find the relative amonmt
of this force when eac h conductor is charged with six timesthe previous quantity ofelectricity ? Answer : 36.
1 541 . T wo insulated conductors, of the same siz e, and
c harged with like electric ities, repel each other with a certainamount offorce. Find the amount of the forc e when one of
the c onductors is charged w ith 3% times, the other with 554times the previous quantity ofelectric ity.
1541 . T wo insulated conductors, of the same siz e, and
c harged with like elec tricities, repel eac h other with a certainamount offorc e. Each is then charged with three times theprevious quantity ofelectric ity. H ow many times as farmustthey now be apart from each other, in order that the force ofrepulsion remain the same as before ?
1543. What amount ofrepulsive or attractive force will be
lfitl 11111151 10113 4111) m m 1! ram
1557. l‘lxplainthe commonmode ofc h g'
h g a lc wfln jl .
15510. lletine electric density, elec tric (m in ,and d unk
intensity.
What in an elec tric condenser ? M i s c .
15011. You are provided with a sheet of v-h m'
nu l I-istttbluu nml two sheets oftin-foil, and are required tnmthumno ttll to obtain from them a shoc k simflar m dnt d
’
a
Lawton Jm'
. How will you do it ? (11)u5m. 0 11 a sheet oftin-foil I lay a pla te of glass-hid
mo be llllml bymeans of100ps ; and on the glass I by:
not'
oml shoot oftin-foil . T he lower sheet is c onnected with
the emth, uml the upper one with the c ond uc tor ofan dec"ht lllttt‘lllllt‘.nml also with a gold-leaf elec trosc ope. I turnthe mm-bhm c arefully, and find the amount ofM g neces
saryto t-mtun the. gold leaves to diverge greater than whenthe
t otnlttt lot'
and the elec troscope are connec ted without the in
lntvnulhm ol the sheetsoftin-foil . Explain this. I also find
tlmt. wlmn tho about and the upper sheet are lifted from the
lowmmm. the goltl lc ttvcs suddenly diverge. Why P (T .)
A lmytlcnlot ishung up in the air by a silk string;
tho knobol'
the jar is connected with an elec tric machine, and
its mum routing is connected by '
a wire with a large gas pipe.
What tlt‘t‘tlllt in this outerwire when the machine is worked,
llllllwhy tlomt it oc cur? (11)
1563. Why do I employ a silk string to suspend the jar
In the but experiment? What would happen, supposing the
string to be ordinary twine P (T .)
1564. You are provided with an electric machine and a
battery often Leyden jars, and are required to charge and
discharge the battery ; how will you proc eed P Describesome of the effects and appearances of the electric dis
charge.(T .)
1 11101 101141. E LE CT R IC ITY. 157
1 565. In charging a Leyden jar, some time ago, I hearda crack. An elec trometer attached to the conductor of themachine instantly fell, and showed no further signs ofelectrit ity. When the jar was examined it was found perforated.
Explain these effects. T. )1 566. Y ou hold the knob ofa Leyden jar against the con
ductor ofan electric machine, and stand on one foot uponan insulating stool, placing the otherfoot on the knob of a
Leyden iar whic h stands on the earth . S tate exactly whatoccurs when the machine is worked . (T . )1567. I furnish you with two Leyden jars, and ask you
to charge one ofthem in the usual way ; how will you proneed ? I then ask you to charge the second jar by electricityfrom the external coating ofthe first. H ow is this electricitygenerated, and what arrangement will you make to send itinto the second jar P (T . )
1568 . Describe an experiment to prove that when a L ey
den jar is c harged with positive electricity, positive electricitya capes from the outer coating ofthe jar. (T . )
1569 . A needle is attached to a prime conductor, so as to
project fiom it, ofan electric machine. Why is it that thesparks are shorter than when the needle is absent P
1 570 . Explain the ac tion of electrified points. (T1571 . A bundle of cotton wool is hung by a common
thread from the c onductor ofan electric mac hine, and thenelectrified. I present my c losed hand, which c ontains a sew
ing needle within it, to the wool ; the wool is attracted . Inow open my hand so as to uncover the point ofthe needle ,
the wool is repelled . Why ? Connect this action with thatofa lightning conduc tor upon a cloud. (T.
1572 . Name some ofthe changes on which atmosphericelec tricity depends.
168 commons A N D PnoBLm 1 ! m m
1573. What is lightning1574. What maybe considered the safest pod iumduring
a thunder storm1575. Describe and explain Franklin’
ss experimmt ' ith the
kite, by which he demonstrated the exis tenc e ofm osphaic
elet tric ity. (T .
1576. What influence may atmospheric elec tricityhaveonthe wires ofthe electric telegraph
1577. What are the purposes of lightning rods
1578. A common prejudice against lightning rods maybe
stated thus : Lightning rods invite the elec tric fluid and, with
it, also its damages. H ow will you refute it1579. Describe the action ofa pointed lightning conduc
tor ou a cloud charged with positive elec tricity.
160 oums'rrorrs u rn P aonnm 111 m ares .
1591 . What happens when a strip ofz inc and c opperare
placed disconnected in the same body ofwater159 1 . What happens when the same strips are in water,
d isconnected , but the z inc has a conduc tor soldered to it,
connecting it with the c 0pper1593. I dip a strip of pure platinum and of pure zinc
into waterwhich has been rendered sour by sulphuric acid.S tate what occurs when the metals do not touc h each other,and also what occurs when theydo touch each other. (T .)
1594. Supposing the two strips to be half in the sourwa
ter and halfout ofit, and that their two outer ends are unitedby a wire, what oc curs? (See preceding example. ) (T .)
1595. What law holds good ofa series of c ells, or oftheelectro-motive force in general ?
1596. What is meant by contact-electricity1597. Ofpotassium, z inc, iron, c opper, gold, which be
c ome positive when in contact with tin and silver, and
which bec ome negative1598. Desc ribe the Sand battery.
1599. Describe Smee’s battery, and tell how Walker’s differs from it.
1600 . S tate th1ee defects ofsingle-fluid batteries.
160 1 . Tell clearly what is meant by a two-fluid battery.
160 2 . Describe Daniell’s battery .
1603. Desc ribe Marie Davy’s battery.
1604. Give a sketch ofa cell ofGrove’s battery, and state
the uses of its various parts.
1605. What is the part played by the nitric acid in Grove’sbattery ?
1606. Describe the bi-chromate battery.1607. Describe Lec lanc hé ’s cell.1608. I give you platinum, z inc and brine, and ask
ounmoan sn ows torm . 161
you to produce, by means of them, an electric current ; howwill you do it ? (T .)
1609 . What are the chiefmerits ofa galvanic cell ?161 0 . What does the strengr/z ofa galvanic cell depend
upon P161 1 . P latinum is a bad , silver a good, conduc tor of elec
tric ity which of the two offers the greater resistanc e to a
current161 2 . T he same electric c urrent is sent in succession
through two spirals ofplatinum wire Both feel warm to the
hand . Y ou then heat one of the spirals to bright rednesswith a spirit lamp. What is the effec t upon the temperatureofthe other? (T . )
1613. Suppose that, in the previous example, instead of
heating one of the wires by means ofa spirit lamp, you had
c ooled it with ic e. What would have happened ?1614. Give the law ofelectric resistance ; also state it by
an equation.
161 5. T he same current from a Grove’s battery is sentthrough two pieces ofwire, one ofsilver, the other ofplatinum , of the same length and thic kness. T he silver remainscool, the platinum is heated to redness. Why (T . )
1616. Give Ohm’s law.
1617. What does the thermo-electric current dependupon
161 8. H ow will you produce a thermo-electric current ?(T
161 9. Define and describe a galvanometer.1620 . What is an astatic galvanometer(or the astatic
needle) ?162 1 . S tate the four c ases inwhich an electric c urrent may
deflect a magnetic needle.
162 QUES T I ON S A N D P R OBL EM S I N P H Y S I C S .
1622 . Youm sh to convert a poker into an electrom agnet,with its knob as a north-pole. Show by a sketch how it istobe done. (T .)
1623. What are the principles ofthe elec tric telegraph?1624. In what particulars does an electro-magnet differ
from an ord inary steel magnet P1625. You are required to prove that a current ofelec
tric ity is passing through a telegraphic w ire to which youhave access. (T
1 626. What are the effec ts of chemical electri c ity P1627. Explain and illustrate the thermal ” effects of
chemical elec tric ity . A re these confined to thin wire, ormaythey occur also in thick wire P
1628. Y ou are required to fire gunpowder by means ofa
voltaic c urrent ; how will you proceed P1629. Explain the principles of the electric lamp
,and
state in the explanation how the two carbon points are affectedby the passage of the c urrent. (T .)
1630 . A voltaic current is sent through water, the waterisdecomposed and two gasesformed ; what are they, and wheredo they make their appearanc e P (T .)
1631 . If a strong voltaic current is sent in successionthrough a thin platinum wire through acidulated water, andthen through a w ire which surrounds a common poker, whatis the effect produced in each case P (T .)
1632 . A glass cell contains a solution of common tablesalt, colored by indigo. A voltaic current is sent through thesolution, the blue color is observed to grow gradually paler,and finally to disappear; explain this effect. (T .)
1633. Describe and illustrate by an example the processof electrotyping.
1634. Define electrolysis.
A P P E N D I X .
T H E METRIC SYSTEM OF WEIGHTS ANDMEASURES .
I .—M EA SUR E S OF L E N GT H .
BA SE —I M eter=39.37079 inches, nearly.
T A BL E . T H E T ABL E I S T HUS R EAD.
I M yriameter. Io M illimeters make I c entimeter.I Kilometer. Io C entimeter I dec imeter.I H ec tometer. I o Decimeters
I Dec imeter. 10 M eters I dec ameter.I M eter—Unit. Io Dec ameters I hectometer.
Io H ectometers I kilometer.l Dec imeter.
10 Kilometers l myriameter.1 C entimeter.
I M illimeter.
One foot=o~
3o47945meter. One centimeter=o.3937079 inch.
11.—M EA S UR E S OF S UR FA C E , OR SQUA R E M EA SUR E .
BA SE .—l Are=the square whose side is 10 meters
= 1 square yards, nearly,: 4, perches or square rods, nearly.
T H E T ABL E 18 T HUS READ.
I H ec tare makes Ioo ares.
1 A re 100 c enuares.
uare centim.=o. 155 square inch.
uare inch=6.4516 sq. cent.
uare foot=9 . 2899683sq. decim.
uare yard=o.83609715sq. meter.
165
I I I . —M EASUR E S OF VOLUM E .
BASL —I L iter=the cube on the dec imeter= Iooo c . c.
=61 °0 27+eubic inches,=a little more than a wine quart.
TABLE. T H E T ABL E I S THUS R EAD.
l K ilioliter. Io M illiliters make I centiliter.I H ed oliter. 10 C entiliters 1 dec iliter.1 Decaliter. 10 Decoliters' 1 liter—1000 cubic centim.
l L iter—Unit. Io L iters I decaliter.I Deciliter. Io Decoliters 1 hec toliter.I C entiliter. to H ectoliters I kilioliter, or stere.
I M illiliter.
l Gallon=4.54345797liters=277.25cub. in.
I C ubic inch= 16.386176 ch. cen.
1 C ubic foot=28.315312 eh. decim.
IV.—M EA S UR E S OF WE IGH T .
BAS E .—I Gram=weight ofa cubic centimeter ofdistilled water at4°C.
— 1 grains T roy, nearly.
=o°o352746 ounc es A voirdupois, nearly.
T ABL E . TA BLE 18 THUS R EA D.
I M illier, or tonneau. Io M illigrams make 1 centigram.
I Quinta!. I o C entigrams I dec igram.
I M yriagr Io Dec igrams I gram.
1 Kilogram, 2. 10 Grants 1 decagram.
l H ec togram. Io Dec agrams 1
1 Dec agram. 10 H ec tograms 1
1 Gram—Unit. 10 Kilog'rams I
1 lo M yri s I
1 10 Quingm
1 01 1111111.
One pound Avoirdupois=o.45359265kilo.
TABLE OF VELOCITIES (P ER Sacosm).
to
3toWinds and 3oand
L ight(approximately).E lectricity on copper
168 AP P EN DI X.
C ON DUCTION OF HEAT.
THERMAL OON DUC T IVI TY IN VA C UO.
(Wz'
edensan 6 ’ Franz . )
Organic substances have a low power ofconduc tion.
REMARKABLE TEMPERATURES (DEGR . C).
Greatest artificial cold 140 degreesM ercuryfreez es
I c e melts 0
Greatest density ofwater. 4Blood heat
Water boils 100
R ed heat 526C ast ironmelts 1530
COEFF. OF LINEAR AND CUBICAL EXPANS ION.
L inearM eanfor 1° C entigrade Cnbt
'
ealM eanfor C entigrade
(between 1°and (between 1°and
o.oooo36
A P P E N DIX . 169
EXPANS ION OF MERCURY AND WATER.
Vol. ofWater Unity at
T emperature C°
. Vol. ofM ere.=-Unz'
ty at 4°c=399 5;
MELTING POINTS (DEGR . C). BOILING POINTS
Solid C arb. A c id . .—87deg. ! inc 423 deg . (DEGR . C ) .
M ercury—39 S ilver I OOO
Phosphorus 43 C o per 1090 A lcohol. 79 deg.
S ulphur 109 Go (1 1250 Water . 1 00
228 Iron 1600 M ercury . 350
325 Platinum. ! inc 1040
I 0 05393
5
Vol. at 100° C
(unityat 0° C ) of
H ydrochl’ic A c id . 1 .o37
170 A P P E N DIX .
LATENT HEAT.
C6
Sulphur 1 1
N itrate of 794N itrate ofPotass 0 .598
0 179Bismuth 159
067
. o. 172
Vapors (equal tw ig/its; steam=1 ).
Bisulphide ofC arbon .6. 162Oxalic E ther . . . o. 136
A c etic E ther. .
33Iodide ofE thyl 0 . 7Iodide ofM ethyl.
Bromine.
P erchloride ofT in.
Formiate ofM ethyl.A c etate ofM ethyl 206P erchloride ofPhosphorus
LATENT HEAT OF WATER VAPOR (R egnault.)
T emperature C9.
00
10
TotalH eat. P ressnrd inpdsz per sq. in. )
0 . 173o.
0 .
1 .78
4. 1
10 . 1614.20 .
52 .52
F O R
B y m ore 0 . L . 220m
FIR ST L ESSO N S IN P HY S IC S, 176Pages,
Illustrated, Price forIntroduction,65Cents.
FIR ST L ESSO N S IN P HYS IOLOGY,
192Pages, Illustrated PriceforIntroduction 60Cents.
P ram . E d u c a t ion ,
For, Ieavin out only
played in ? T e are cm
tribution ofcommgd ities.
preparation and d istributionuse ofmethod s fitted to the
reservation, or the
owledge is-S c ienc
'
ning a livelihood .true d tscharge of
found in—S c ience.
sent, without whtch the citizen cannot rightlyregulateindispensable key is- Science ! yet this Is the kindonlynow receiving a grudging recognition.
”
Prom Prof. Chas. R . Allen,
P rin N orma l S elim!, S an yore, 641.
We like Hotz e’s Physics,
’as an elementarywork, muc h.
”
C OM M E N D A T I O N S .
Hotz e’s ‘ First Lessons in Ph is exc ellent for the commonschools and for children
’s reading at me, bec ause it is a judicious selec
tion of the wonders ofthe world—the -daywonders—explained in
simple, clear language. S uch books make t e world around us a
like a glorious paradise to youth.
”pp“ :
P rom Hon. Andrew J. R iokofl ,
We have ado ed Prof. H otze’
s First L essons in Physic s for use b
pupils in the 11d and T hird Grades ofourGrammar Schools, anhave found that the interest ofthe pupils in this study is such that it leadsthem to the reading oflargerworks upon the same subjects to the con
ofsimple apparatus illustrative ofthe text, and, finally, to indeexperiment and discussion.
"From Hon. 1 . Ormond Wilson,
S upt. P ublic S elim , Warsism , D . C .
Hotze’s Fimt Lessons in Physics and Physiology are used in the
Public Schools ofWashington, andgives good satisfac tion to teachers and
pm T heyare excellent text and suc cessfully do the work fortheywere designed.
"M W. P . Atkinson,
“ Very well adapted from its aim licity and rac ticali to hel
about a reform inour schoolinstruc tionin the dizc tion aimrelorm is most um needed , by the introduc tion into them ofPhysical
recogn'
branch ofstudy.
”
FromJohn Lockwood.
P rin. L aeh awd’: N ew A cademy, Bmoklyn, L . 1 .
a copyofH otz e’s First Lessons in Physio
logy.
’ L ike its predecessor, First Lessons in Ph sic s,’this willbe wel
comed by every teacher who found , as manymust ve done in the other,
just what he wanted. T he method ofthese books I think admirable.
S upt. qfm ac scams, N ew York a s .
I have received a copyofH otze’s First Lessons in Phy
much eased with its general characteristics. T he treatment seems tobe well pted to the purpose Ofelementary instruction.
”
I have examined H otz e’s ‘F’
rrst L essons in Physi i ugy’v ith a great
oi
scholar.
“ M L V . ”
lam pleased with the arrangement of H ome’s‘Physiology
'
,
’and csn
cheerfullyrecommend it.”
M W.W. Janie-n,
The Board of Education of this c ity have adopted Home’s‘Fint
Lesson in Physics as a textb ook in our grammar-schools.”
Prom B . B. N eely,
S upt. P ublic S elzoob , S t. yosepb, H o.
lintze’l First Lessons in P hysiology was adopted as a text
-book inour Public S chools—as a text-book in the hands ofthe peri ls, to beused
by the first grade durin the last halfyear of the course. We use tin
same author’
s Physics with increased pleasure and profit each year.”
Prom George L . Osborne,
P rise. N ormal S elma!, Warrem bueg, N o.
We use Hotzc ’s Physic s in the N ormal.”
From Geo. 3. Sears,
S upt. P ublic S elzools, N ewark , JV. 7.
I think Hotze’s First Lessons in Physics’ is a book admirabl
gamed to elementary instruction in a very important branch ofknowgo.
From Hon. E . 8. Carr,
S tate S uperintendent, S acramento, Cal.
Our estimation of H otz e’s Physic s is ex ressed in the fact that it is
ted as a text-book in the public schools 0 the S tate.
H otze’s Physiology seems well adapted to the purpose
was designed.
"
BY C . L. HOT! E,
AUT H OR or“FIR S T L ES S ON S m P H YS IC S ,
"ET C .
A n E lementary work written spec iallyfor the upper grades ofour Con e
mon Schools after years ofexperience in these grades C ontaining mpages, over fortyengravings, Glossary ofT erms. Questions for T eachers,Index, etc .
T o T sac asas son Em rm rrox
Address
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