Today, let's think about falling. The University of
Houston's College of Engineering presents this
series about the machines that make our
civilization run, and the people whose ingenuity
created them.

The concept of
*acceleration* is hard to see clearly without
calculus and graphs. Yet acceleration is with us
every waking moment. We all swim in the same sea of
uniform gravitational acceleration. We feel it all
the time. Every time we drop or toss an object,
gravity acts upon it in the same way. Jump from a
height of five feet, and you'll strike the earth at
eighteen feet per second. From a ten-foot wall,
that becomes twenty-five feet per second.

So when you double the height, you don't double the
speed you reach. Speed rises only as the square
root of the height of the fall. By the way, you
start endangering your limbs at about twenty feet
per second (depending on your age and physical
condition).

Gravity will accelerate any object at a rate of 32
feet per second per second. But what do we do with
that number? What it means is that if we fall for
one second we'll reach a speed of 32 feet per
second. After two seconds we reach 64 feet per
second. The speed rises as the *square root*
of height, but in *direct proportion* to time.

So acceleration is trickier than it might first
seem. Nothing accelerates until a force acts upon
it. Yet we feel no force as we fall. The force of
gravity is there, acting on every molecule in our
bodies -- but the force is unopposed, so we feel
nothing. Not until we stand on a solid floor do we
*feel* the force of gravity. The floor is what
resists gravity, and it acts only on our feet.

So an orbiting astronaut, who feels no gravity, is
in a perpetual free fall, constantly accelerating
toward Earth and hurtling forward at the same time.
The Space Shuttle keeps falling away from a
straight path, but just fast enough to stay a
constant height above Earth as it falls -- and
falls, and falls.

Swing a rock on a string, and it follows the same
kind of circular path as the Space Shuttle does.
But there's no significant force of gravity to
attract the rock toward you. That's why you had to
*replace* gravity with a string. Now you feel
just how much force it takes to accelerate the rock
away from straight flight.

Of course most accelerations don't have the
uniformity of gravity. A rising elevator
accelerates at first, and we feel our weight
increase by a few pounds. When we decelerate at the
18th floor, our weight drops just a tad. (That
*can be* a nice feeling.)

But too many people don't get it -- like motorists
who tailgate or don't slow down for a curve on an
icy road. Acceleration can deceive us. That's why
Isaac Newton, who first explained how force and
acceleration are related, was also an inventor of
calculus -- that special language for explaining
how things change in time and space. Acceleration
is so much clearer when we have that new language
to describe it. And I hear echoes of a fine old
saying about the language of math:
"Mathematics lets fools do what only geniuses could do without it."

I'm John Lienhard, at the University of Houston,
where we're interested in the way inventive minds
work.

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