Joel Dorman Steele.

Answers to the practical questions and problems contained in the fourteen week courses: in physiology, philosophy, astronomy, and chemistry (old and new edition) online

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ANSWERS



PRACTICAL QUESTIONS AND PROBLEMS



CONTAINED IN



THE FOURTEEN WEEKS COURSES



Physiology, Philosophy, Astronomy, and

Chemistry (Old and New Edition),



BY

;pDORMAN STEELE, PH.D., F.G.S.,

AUTHOR OF THE FOURTEEN WEEKS SERIES If! PHYSIOLOGY, PHILOSOPHY,
fl ASTRONOMY, AND* (JEOLOGY.



A. S. BARNES & COMPANY,
NEW YORK AND CHICAGO.



THE FOURTEEN WEEKS' COURSES

IN

NATURAL SCIENC

BY

J. DORMAN STEELE, A.M., Pn.D.

Fourteeij Weeks iij Natural Ptylosopty,
Fourteeij Weeks iij Cljenjistry,
Fourteeij Weeks iij Descriptive Astroijonjy,
Fourteeij Weeks iij Popular Geology,
Fourteeij Weeks iij Human Physiology,
Fourteeij Weeks iij Zoology,
Fourteerj Weeks in Botany,

A Key, containing Answers to the Questions
and Problems in Steele's 14 Weeks' Courses,




SERIES,

ON THE PLAN OF STEELE'S 14 WEEKS IN THE SCIENCES.

A Brief hjistory of the United States,
A Brief F|istory of Fraijce,



The same publishers also offer the following standard scientific
works, being more extended or difficult treatises than those of
Prof. Steele, though still of Academic grade.

Peck's Ganot's Natural Philosophy,
Porter's Principles of Chemistry,
Jarvis' Physiology and Laws of Healtfy
Wood's Botanist and Florist,
djanjbers' Elements of Zoology,
tyclij tyre's ^stro$)tfty and
Page's Elenjents of GeologJ, * s



tDUCATJON DEPT.



Entered according to Act of Congress, in the year 1869, by

A. S. BARNES & CO.,

In the Clerk's Office of the District Court of the United States
for the Southern District of New York.

STEELS' s JCPY.



PREFACE.



THIS little work is designed to aid teachers who are using
the Fourteen Weeks Course. The problems contained in
all the books are fully, and, it is thought, accurately solved.
Great pains have been taken to revise and compare them
carefully. The practical questions are answered, often not
in full, yet enough so to give the key to the more perfect
reply. The use of the text-books is presupposed, and the
statements merely supplement, or apply the fuller theories
therein contained and explained. On many points there
may be a difference of opinion. The author often finds in
his own classes a wide diversity. On mooted questions he
has merely advanced one view, leaving the subject open
for the discussion of other theories. Minute directions are
given, pages 71-82 inclusive, for performing a course of
experiments in Chemistry. It is hoped that these may be
of service to teachers who, with incomplete apparatus, are
trying to illustrate to their pupils some of the principles cf
that science. In all cases of doubt or misunderstanding
with regard to the answers or solutions, the author will be
pleased to correspond with any teacher using the Series

ELMIRA, March 19, 1870



ANSWERS

TO THE PEACTICAL QUESTIONS

m THE

FOURTEEN WEEKS COURSE

IN

NATURAL PHILOSOPHY.



|.The bold-faced figures refer to the pages of the Philosophy ; the others to
the number of th. Practical Questions.]



INERTIA.

26. I. If one is riding rapidly, in which direction will he
be thrown when the horse is suddenly stopped ?

In the same direction in which he is going. He has the
motion of the carriage, and his inertia carries him forward.

2. When standing in a boat, why, as it starts, are we thrown
backward ?

Because the inertia of our bodies keeps them stationary,
while the boat carries our feet forward.

3. When carrying a cup of tea, if we move or stop quickly,
why is the liquid liable to spill?

The inertia of the tea tends to keep it still or in motion, as
the case may be. If we move the cup quickly, the motion is
not imparted to the liquid soon enough to overcome the
inertia. When, therefore, we start, the tea spills out back-
ward; or, when we stop, it spills out forward. We under-
stand this if we can tell why a cup of tea is more liable to spill
than one of sugar.



ANS^JKS TO PRAVT1VAL QUESTIONS



4. Why &>,fofrlo.d$*pfr'r'sued, \cctn we. escape by dodging?
We turn sharply. ' O'ur pursuer, ignorant of our design,

cannot overcome his inertia so as to turn as quickly, and
hence is carried past.

5. Why is a carriage or sleigh , when sharply turning a
corner, liable to tip over f

Because its inertia tends to carry it directly forward. A
puzzling question in this connection is Why is a sleigh more
liable to tip over than a wagon ?

6. Why, if you place a card on your finger, and on top of it
a cent, can you snap the card from under the cent 'without
knocking the latter off your finger?

Because the friction between the card and the cent is so
slight that, by a quick snap, you can overcome the inertia of
the former without imparting any force to the latter.

7. Why } after the sails of a vessel are furled, does it still
continue to move; and why, after the sails are all spread,
does it require some time to get under full headway?

Its inertia must be overcome in the one case by the resist-
ance of the air and water, and in the other by the force of the
wind.

COHESION.

4O. i . Why can we not weld a piece of copper to one of
iron ?

Cohesion acts only between molecules of the same kind.

2. Why is a bar of iron stronger than one of wood?
Because its force of cohesion is stronger.

3. Why is a piece of iron, when perfectly welded, stronger
than before it was broken f

By the hammering, more particles are brought within the
range of cohesion.

4. Why do drops of different liquids vary in size f
Because they vary in cohesive force.

5. Why, when you drop medicine, will the last few drops
contained in the bottle be of a larger size than the others ?



/2V NATUKAL PHILOSOPHY. 7

The pressure of the liquid in the bottle is less, and therefore*
they form more slowly.

6. Why are drops larger if you drop them slowly ?

There is more time for the adhesive force of the bottle to
act on the liquid, and so a larger drop can be gathered.

7. Why is a tube stronger than a rod of the same weight?
Let a rod supported at both ends be broken in the middle.

We shall see that it yields first on the circumference. So true
is this, that long beams heavily loaded have been broken by a
mere scratch of a pin on the lower side. The particles along
the centre break last. They rather aid in the fracture, since
they afford a fulcrum for the rest of the rod, acting as the long
arms of a lever, to act upon. In a tube the particles at the
centre are removed and all concentrated at the outside, where
the first strain is felt. (See Physiology, p. 20).

8. Why, if you melt scraps of zinc ', will they form a solid
mass when cooled?

The heat overcomes, in part, the attraction of cohesion, so
that the particles flow freely on each other. They now all
come within the range of cohesion, so that when the metal
cools they are held by that force in a solid mass.

9. In what liquids is the force of cohesion greatest?
Mercury, molasses, etc.

10. Name some solids that will volatilize without melting f
Arsenic, camphor.

ADHESION.

47. i. Why does cloth shrink when wet?

By capillary attraction the water is drawn into the pores 01
the cloth. The fibres are thus expanded sidewise and short-
ened lengthwise. The cloth "fulls up" or thickens while it
shortens and narrows (shrinks) in the process.

2. Why do sailors at a boat-race wet the sails ?
The pores being full and expanded make the sails more com-
pact. They will therefore hold the wind better.



8 ANSWERS TO PRACTICAL QUESTIONS

3. Why does not writing-paper blot?

Because the pores are filled with size. (See Chemistry,
p. 161.)

4. Why does paint prevent wood from shrinking?
Because it fills the pores of the wood.

5. What is the shape of the surface of a glass of water and
one of mercury f

Ordinarily the former is concave and the latter convex.

6. Why can we not dry a towel perfectly by wringing ?
Because of the strength of the capillary force by which the

water is held in the pores of the cloth.

x

7. Why will not water run through a fine sieve when the
wires have been greased?

Because the grease repels the water and so prevents capil-
lary action.

8. Why will camphor dissolve in alcohol and not in water?
Because there is a strong adhesion between the alcohol and

camphor, and little, if any, between the water and camphor.

9. Why will mercury rise in zinc tubes as water does in
glass tubes ?

Because of the strong adhesion between zinc and mercury.

10. Why is it so difficult to lift a board out of water ?
Because of the adhesion between the board and the water.

1 1 . Why will ink spilled on the edge of a book extend further
inside than if spilled on the side of the leaves?

Because the capillary pores of the paper are short, being
only the thickness of a leaf, while the capillary spaces between
the leaves are longer and continuous.

12. If you should happen to spill some ink on the edge of
y cur book, ought you to press the leaves together?

No. Because you would make the capillary spaces between
the leaves smaller, and so the ink would rise in them further.

13. Why can you not mix oil and water ?
Because there is no adhesion between them.



IN NATURAL PHILOSOPHY. 9

15. Why will water wet your hand while mercury will not?
Because in the former case there is an adhesion, in the
latter none.

1 6 Why is a tub or pail liable to fall to pieces if not filled
with water or kept in the cellar?

Because the moisture dries out of the pores, and the wood
shrinks so as to let the hoops fall off.

17. Name instances where the attraction of adhesion h
stronger than that of cohesion.

Wood fastened by glue will often split before the glue will
yield. Paper stuck with paste, and bricks with mortar, are also
examples.

GRAVITATION.

63. i. When an apple falls to the ground ^ how much does
the earth rise to meet it?

The earth falls as much less distance than the apple, as its
weight is greater.

2. What causes the sawdust in a mill-pond to collect in large
masses ?

The attraction of gravity which exists between all bodies,
whereby they attract each other. All bodies on the earth
would tend to approach each other, and the big ones would
gather all the little ones around them were they as free to move
as the sawdust floating on water.

3. Will a body weigh more in a valley than on a mountain f
It will, because the attraction of the earth is greater.

4. Will a pound weight fall more slowly than a two-pound
weight ?

They will both fall in the same time, except the slight
difference which is caused by the resistance of the air. Galileo
propounded this view and proved it, in the presence of a vast
crowd, by letting unequal weights fall from the leaning tower
of Pisa.



IO ANSWERS TO PRACTICAL QUESTIONS

5. How deep is a well, if it takes three seconds for a stone to
fall to the bottom of it ?

(2) equation of falling bodies, d = 1W ; hence d = 16 x 3 a a 144 feet.

_6. Is the centre of gravity always within a body as ', for
example, a ring?

It is not. In the case given it is at the centre of the circle.

7. If two bodies, weighing respectively i and 4 pounds, be
connected by a rod 24 inches long, where is the centre of gravity ?

To be In equilibrium the weight of one multiplied by its distance from the
c:nt-re of gravity must equal the weight of the other multiplied by its distance.
24 -+- 6 = 4 ; hence 4 in. is the unit for each pound. Therefore the centre of
gravity is 8 in. from the larger weight and 16 in. from the smaller.

- 8. In a ball of equal density throughout, where is the centre
of gravity ?

At the centre of the ball.

9. Why does a ball roll down hill?

Because the line of direction falls without the small base of the
ball.

10. Why is it easier to roll a round body than a square one f
Because the base of the ball is so much smaller, and therefore

the centre of gravity need not be raised to bring the line of di-
rection without.

1 1. Why is it easier to tip over a load of hay than one of
stone ?

Because the centre of gravity in a load of hay is very high,
and in a load of stone very low. Therefore the centre of
gravity in the former need not be raised much to bring the
line of direction without the base, while in the latter it must be.

12. Why is a pyramid the stablest of structures ?

Because the base is so broad and the centre of gravity so
low. The centre of gravity must therefore be lifted very high
before the line of direction will fall without the base.

13. When a hammer is thrown, on which end does it always
strike f

On the heavy end or head, because that part is attracted by
the earth more strongly.



IN NATURAL PHILOSOPHY. I J

14. Why does a rope-walker carry a heavy balancing-pole ?
Because in this way he can easily shift his centre of gravity.

15. What would become of a ball if dropped i*ito a hole
bored through the centre of the earth ?

In falling, it would gain a momentum which would carry it
past the centre of the earth. But as it is constantly coming
to a part having a slower axial revolution than itself, it would
scrape on the east side of the hole until it reached the centre ;
beyond that point it would scrape on the west side. This
friction would prevent its reaching the opposite side of the
earth. It would therefore vibrate to and fro, each time through
a shorter distance, until, at last, it would come to rest at the
centre of the earth.

1 6. Would a clock lose or gain time if carried to the top of
J a mountain ?

It would lose time, because the force of gravity would be
lessened. At the North Pole it would gain time, because there
the force of gravity would be increased.

1 7. In the winter, would you raise or lower the pendulum-
bob of your clock ?

I would lower it, since the cold of winter shortens the pen-
dulum, and this movement of the bob would counteract that
change.

1 8. Why is the pendulum-bob always made flat?
To decrease the friction of the air.

19. What beats off the time in a watch f
The vibration of the balance-wheel.

20. Is solved in the book.

21. What should be the length of a pendulum at New YorA
to vibrate half-seconds ?

(1 sec.) : (V a sec.) 2 : : 39.1 in. : x = 9.7 + inches.
To vibrate quarter-seconds ?

(1 sec.)' : (V 4 sec.)' : : 39.1 in. : x = 2.4 + inches.
To vibrate hours f

(1 sec.) 3 : (3600 sec.) 3 : : 39.1 in. : x - 7997.7 miles.*

* Nearly the diametor of the earth.



12 ANSWERS TO PRACTICAL QUESTIONS

22. What is the proportionate time of vibration of two pen*
dulutns^ 1 6 and 64 inches long, respectively ?

According to the third law of pendulums,
Time of vib. of 1st : Time of vib. of 2d : : v/16 : v/64 : : 4 : 8 : : 1 : 2.

23. Why, when you are standing erect against a wall, and
a piece of money is placed between your feet, can you not stoop
forward and pick it up ?

By leaning forward you bring the centre of gravity in front
of your feet, and, as on account of the wall, you cannot throw
any part of your body back to preserve the balance, you fall
forward.

24. If a tower were 198 feet high, with what velocity would
a stone dropped from the summit, strike the ground f

According to equation (3), t> 2 = 64 d. t? 2 = 64 x 198. 0=112.5 feet.

25. A body falls in 5 seconds : with what velocity does it
strike the ground?

According to equation (1), v = 32 t. v =32 x 5. v =160 feet.

26. How far will a body fall in 10 seconds ?

According to equation (2), d = 16 2 . d = 16 x 10 2 = 1600 feet.
With what velocity will it strike the ground?

According to equation (1), v = 32 t. v = 32 x 10 = 320 feet.

27. A body is thrown upward with a velocity of 192 feet the
first second ; to what height will it rise ?

Equation (1), v = 32 t. 192 = 32 t. t = Q sec.

(2), d = 16 P. d = 16 x 6 2 =576 feet.

28. A ball is shot upward with a velocity of 256 feet ; to
what height will it rise ? How long will it contin ue to ascend f

Using equations (1) and (2), as in the last problem, we hare :

t = 8 sec.
d = 1024 feet.

30. Are any two plumb-lines parallel?
They are not, since they all point to the centre of the earth.
No two spokes of a wheel can be parallel



IN NATURAL PHILOSOPHY. 13

31. A stone let fall from a bridge strikes the water in three
seconds. What is the height ?

Equation (2), d = 16t\ d = 16 x 3 9 = 144 feet.

32. A stone falls from a church steeple in 4 seconds. What
is the height?

Equation (2), d = 16* a . d = 16 x 4 s = 256 feet.

33. How far would a body fall the first second at a height
of 12,000 miles above the earth's surface?

(16,000 mi.) a : (4000 mi,) 2 : : 16 feet : x = 1 foot.

34. A body at the surf ace of the earth weighs 100 tons :
what would be its weight 1 ,000 miles above ?

,(5000 mi.) 3 : (4000 mi.) 2 : : 100 tons : x = 64 tons.

35. A boy wishing to find the height of a steeple lets fly an
arrow that just reaches the top and then falls to the ground.
It is in the air 6 seconds. Required the height.

Equation (2), d = 16< a . d = 16 x 3* = 144 ft.

36. A cat let fall from a balloon reaches the ground in 10
seconds. Required the distance.

Equation (2), d = 16 x 10 a = 1600 ft,

37. In what time will a pendulum 40 feet long make a
vibration f

According 1o the third law of pendulums, and taking the length of a seconds
pendulum as 39 in., we have :

1 sec. : x : : V9 : 1/40x12 in.



x = 3.5+ sec.



In what time will a pendulum 52 feet long make a vi
bration?




14 ANSWERS TO PRACTICAL QUESTIONS

How long would it take for a pendulum one mile in length
to make, a vibration ?

How long would it take for a pendulum reac king from
the earth to the moon to make a vibration ?

Required the length of a pendulum that would vibrate
centuries. ( 70 be solved like problem 20. )

38. Two meteoric bodies in space are 12 miles apart. They
weigh 100 and 200 Ibs. respectively. If they should fall
together by force of their mutual attraction, what portion of
the distance would be passed over by each body ?

The distance passed over by the two bodies is inversely as
their mass; hence one moves 8 miles and the other 4 miles.

39. If a body weighs 2,000 Ibs. upon the surface of the earth,
what would it weigh 2,000 miles above ?

(6000 mi.) 2 : (4000 mi.) 3 : : 2000 Ibs. : x = 888*/ Ibs.
How much 500 miles above?

(4500 mi.)2 : (4000 mi.) 3 : : 2000 Ibs. : x = 1580+ Ibs.
The weight of bodies below the surface of the earth de-
creases as the distance increases. Ex. : What would the above
body weigh if carried 2 , ooo miles below the surface ? I , ooo Ibs.
i , ooo m iles below ? i , 5 oo Ibs.

40. At what distance above the surface of the earth will a
body fall, the first second, 2 1 \ inches ?

A body falls 16 ft.* (192 inches) at the surface of the earth. 21 1 / 3 inches are
: /9 of 192 inches : Now as the attraction is inversely as the square of the dis-
tance, the distance must be v/9, or 3 times that at the surface. Hence the body
must be 12,000 miles from the centre, or 8,000 miles from the surface of the
earth. The problem may be solved directly by proportion, thus :

a 2 : 4000 2 : : 192 inches : 21 Vs inches.

* = 12000 miles (distance from the centre)

12000 miles 4000 miles =8000 miles.

41. How far will a body fall in 8 seconds? 1,024 ft. In
the %th second? 240 ft. In 10 seconds? 1,600 ft. In th*
30^ second? 944 ft.

* According to the best authorities the distance is more exactly 16 l /ir ft.



IN NA TUB A L PHILOSOPHY. I 5



MOTION.

8O. i. Can a rifle-ball be fired through a handkerchief sus-
pended loosely from one corner?

Yes. The wind of the ball will lift the handkerchief somewhat.

2. A rifle-ball thrown against a board standing edgewise
will knock it down j the same bullet fired at the board will
pass through it "without disturbing its position. Why is this?

The ball which is thrown has time to impart its motion to
the board ; the one fired has not.

3. Why can a boy skate, safely over a piece of thin ice, when,
if he should pause, it would break under him directly ?

In the former case there is time for the weight of his body to
be communicated to the ice ; in the latter, there is not.

4. Why can a cannon-ball be fired through a door standing
ajar, without moving it on its hinges ?

Because the cannon-ball is moving so quickly that its motion
is not imparted to the door.

5. Why can we drive on the head of a hammer by simply
striking the end of the handle ?

This can only be done by a quick, sharp blow which will
drive the wooden handle through the socket before the motion
has time to overcome the inertia of the iron head. A slow,
steady blow will be imparted to the head, and so fail of the
desired effect.

6. Suppose you were on a train of cars moving at the rate
oj '30 miles per hour : with what force would you be thrown
forward if the train were stopped instantly?

With the same velocity which the train had, 01 44 feet pet
second. Your momentum would be your weight avoirdupois
multiplied by this velocity.

7. In what line does a stone fall from the mast-head of a
vessel in motion ?

In a curved line, produced by the two forces gravity and
the forward motion of the vessel.



1 6 ANSWERS TO PRACTICAL qUESTlONS

8. If a ball be dropped from a high tower it will strike the
earth a little east of a vertical line. IV hy is this ?

In the daily revolution of the earth on its axis, from west to
east, the top of the tower moves faster than the bottom, be-
cause it passes through a larger circle. When, therefore, the
ball falls, it retains that swifter easterly motion and so strikes
east of the vertical.

9. // is stated that a suit was once brought by the driver of
a light-wagon against the owner of a coach for damages caused
by a collision. The complaint was that the latter was driving
so fast, that when the two carriages struck, the driver of the
former was thrown forward over the dash-board. Show how
his own testimony proved him to have been at fault.

When the light-wagon was suddenly stopped, its driver went
on by his inertia with the same speed at which the wagon was
moving. That this threw him forward over the dash-board,
proves his speed to have been unusual.

10. Suppose a train moving at the rate of '30 miles per hour ;
on the rear platform is a cannon aimed parallel with the track
and in a direction precisely opposite to the motion of the car.
Let a ball be discharged with the exact speed of the train,
where would it fall?

In a vertical line to the track. The two equal, opposite
motions would exactly destroy each other.

11. Suppose a steamer in rapid motion and on its deck a
man jumping. Can he jump further by leaping the way the
boat is moving or in the opposite direction ?

It will make no difference as long as he jumps on the deck.
Should he jump off the boat, then the effect would be different.

12. Why is a running jump longer than a standing one?
Because the motion gained in running is retained in the

jump and adds to its distance.

13. If a stone be dropped from the mast-head of a vesselin
motion, will it strike the same spot on the deck that it would if
the vessel were at rest ?

It will. It falls with the motion of the vessel, and goes just
as far forward while falling as the vessel does.



IN NATURAL PHILOSOPHY. 17

\

14. Could a party play ball on the deck of the Great Eastern
when steaming along at the rate of 20 miles per hour, without
making allowance for the motion of the ship?

They could. The ball would have the motion of the ship,
and would move with it in whatever direction they might
throw it.

15. Since "action is equal to reaction," why is it not as dan-
gerous to receive the " kick" of a gun as the force of the bullet?

The striking force is as the square of the velocity; and the
velocity with which the gun moves backward is as much less
than that with which the bullet moves forward, as the gun is
heavier than the bullet. For this reason a heavy gun will
kick much less than a light one.

1 6. If you were to jump from a carriage in rapid motion,
would you leap directly toward the spot on which you wished
to alight?

No ; because as one jumps from the wagon he has its for-
ward motion, and will go just as far ahead, while leaping, as
he would if he had remained in the carriage. He should,
therefore, aim a little back of the desired alighting-place.

1.7. If you wished to shoot a bird in swift flight, would you
aim directly at it ?

No. The bird will fly forward while the bullet is going to
it. One should, therefore, aim a little in advance.

1 8. At what parts of the earth is the centrifugal force the
least?

The poles. They simply turn around in 24 hours.

19. What causes the mud to fly from the wheels of a carriage
in rapid motion ?

The centrifugal force.


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Online LibraryJoel Dorman SteeleAnswers to the practical questions and problems contained in the fourteen week courses: in physiology, philosophy, astronomy, and chemistry (old and new edition) → online text (page 1 of 15)