Omaha daily bee., 1917-04-03


shape OF a falling body should have
no effect whatever upon its increase
Of velocity it would be necessary to
remove the air and every other exter-
nal source Of resistance to the mo-
ton. The statement, as ordinarily
made, that aflarge and small body
fall with equal velocity neglects the
resistance OF the air, which is usually
hardly noticeable, but which may be-
come conspicuous under certain con-
ditions.
Suppose, for instance, that you take
two balls OF lead OF precisely the same
size, shape and weight and drop them
at the same instant. Then the air
resistance will be the same upon each,
and their velocities will be equal at
every point during their fall.
But if you hammer one of the balls
into the form of thin sheet then, al
though its weight remains equal to
the weight Of the other half, it will
on account of its shape, be more re-
tarded by the air, and will fall more
slowly.
Or you might imagine one OF the
balls transformed into a hollow
sphere, sort OF loaded soap bubble,
and again you would find that there
was difference OF velocity, the large
hollow ball being retarded more than
the small solid one of the same
weight. But ii you put the two into
perfect vacuum and let them fall
they would strike the bottom at the
same instant.
The reason is evidently because the
atmospheric resistance has more sur
face to act upon in proportion to the
weight when the falling body is in the
form of hollow sphere than when it
is solid bali. But when there is no
atmospheric resistance the size OF the
body makes no difference.
As far as the velocity acquired by
falling given length of time is con-
cerned, difference in weight has no
more effect than difference in shape.
A large, heavy body will fall just as
fast, ii, free space, as mere grain Of
sand. They would strike the earth's
surface, If the air were removed, with
the same velocity, but the effects they
produced at the point where they
struck would be very different, be-
cause the heavier body would strike
the harder blow.
Many persons appear to be puzzled
by the fact'that, while the velocity
acquired by d falling body is thirty
two feet Gin round numbers) per sec
ond, yet j. actually falls only sixteen
feet during the first second. This is
easily understood il you remember
that gravitation is constant force,
acting simultaneously, so that it is
able to impart the same velocity Of
thirty-two feet per second to body
whether that body starts from rest or
is already in motion.
Suppose it starts from rest; then
at the end of one second it will be
falling at the rate of thirty-two feet
per second; in other words, thirty
two feet per second is its velocity at
the end of the first second, while at
the beginning it was zero. ~
| In other words still, its velocity in
the course Of the second has increased
from zero to thirty-two feet. The
average velocity during the second
has, then, been half the sum Of the
initial and final velocities, or half the
sum OF nothing and thirty-two, which
is sixteen. Therefore, the distance
travelled is sixteen feet.
| Now consider the second second.
It starts this with velocity of thir-
| ty-two feet, and, in the course of the
second, acquires thirty-two feet. The
sum of the initial and final velocities
during the second second is ninety-six
feet, and half of this, forty-eight feet,
represents the average velocity during
| the second second, and, consequently,
is the measure of the distance fallen
during that second.
i Again, to make the subject perfectly
clear, take the third second. The body
starts this with velocity of sixty
four feet, and acquires another thirty
two feet during the second, so tina,
its final velocity is ninety-six feet
and its average velocity, or the dis.
lance during the third second, is one.
! half Of sixty-four plus ninety-six, OF
eighty.feet.
Il This is sufficient to show you how
the rules are derived which enable
anyone to calculate the velocity &C.
CURED by falling body during any
,, given number OF seconds, and the dis.
lance fallen during any one Of those
. seconds, or during all Of them to,
gether. =
For instance, you see that in three
seconds, the total distance fallen. |.
. sixteen plus forty-eight plus eighty
or ia feet altogether. Now this |.
equal to sixteen. the distance faller
during the first second, multiplied B,
the square Of the number of seconds
!, which Is nine, or 3x3. And this rul,
will tell you the distance fallen durins
any number Of seconds. II is only
! necessary to square that number ans
multiply by sixteen. To know wha
: the velocity will be at the end of an,
number OF seconds, multiply the mum
Der by thirty-two, since that is tn,
smount gained in each second.
But these rules do not strictly appl,
! when the distance from the earth be-
! comes measurable in miles instead o
: feet, because the force of gravit,
/ then decreases appreciably. Newtoi
: discovered that force at the distanc,
OF the moon requires minute insteat
: OF a second to cause body to fal
4 sixteen feet