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>> Terminal velocity. So we've discussed that when objects are falling and there's some
air resistance, at first the motion is accelerating motion due to the force of gravity, but as
the object goes faster and faster the air resistance force gets larger and at some point
we have this transition, and after the transition, the object falls with uniform motion so it's
moving at constant speed. So what happens is when the air resistance force is large
enough that it balances the force of gravity then the net force is zero and so by the law
of acceleration, the acceleration will be zero and so the speed stops changing and we've
reached the maximum velocity for falling, so we call that the terminal velocity. So,
terminal velocity depends on various things. One of the obvious ones would be for a given
size and shape, the more an object weighs the higher the terminal velocity because the
more air resistance force we need to match that weight. So if we have a block of wood
that has the same size and shape as a brick, the brick weighs more so when we drop the
two the terminal velocity for the wooden block is going to be slower than the terminal velocity
for the brick, which will be higher. Now for a given weight, the larger the surface area
the slower the terminal velocity. So the skydiver before opening the parachute has a rather
high terminal velocity, but after opening the parachute the weight hasn't changed but
the surface area has increased quite a bit, and so to match the parachutist's weight,
the parachutist doesn't have to move very fast because air resistance is large when
the surface area is large. So let's look at something simple like a falling coffee filter.
So here's a little quick video, and if we track the distance fallen we see that at first
it's a bit of a parabolic curve, but then rather quickly, it becomes a straight line
and we know that in the motion graph, when we have a straight line we're traveling with
constant speed. So for a sheet of paper or a leaf, the terminal velocity is about five
feet per second, which translates to two to three inches per frame, and that terminal
velocity is reached rather quickly, so the accelerating motion is only for about the
first four frames, and then the something like a leaf or sheet of paper travels if it's
falling just straight down under the force of air resistance. Let's look at a different
object: a cat. So this is some video reference that one of my students shot. They were asked
to record a falling object, and do some data analysis, and he chose his cat. They had to
do five drops for reference. The cat's tail is up so it seems to be enjoying that. So
doing some frame by frame analysis of the falling motion, we see pretty much a parabolic
arc, and it turns out for distance of just a few feet air resistance is not significant
for a cat. On the other hand, if a cat fell out an 8 floor window in a building, so falling
from a height of about 100 feet, then after falling about 50 feet the cat would be falling
fast enough that it would reach its terminal velocity, which for an average size cat is
roughly 40 miles an hour and so after falling about 4, maybe 5 floors the cat reaches its
maximum speed and continues traveling at that same speed. So you see that it doesn't matter
whether a cat falls out of a 4th floor window or a 40th floor window because it reaches
terminal velocity after about 50 feet, it just continues traveling at constant speed
until it reaches the ground. Now that was for an average sized cat, but if we have a
small cat versus a large cat, the large cat will have a higher terminal velocity than
the small cat. In fact, if we have two things that have similar shape and composition then
the larger one has the higher terminal velocity. Of course the larger one weighs more, but
you might also wonder well the larger one also has a larger area so perhaps that compensates
for the weight but it doesn't. The larger weight of the larger cat has a more significant
affect than its size on surface area so it does indeed fall faster than the small cat.
Now very small animals like squirrels, they reach their terminal velocity after falling
about one floor and that speed is normally not fast enough to be fatal so squirrels are
rather fearless in terms of falls because they seem to know that a fall, no matter what
the height, normally won't be fatal. On the other hand, cats survive high falls about
half the time and humans rarely survive if we reach terminal velocity because that terminal
velocity is 120 to 140 miles an hour. So unless you fall into something very soft like a net,
a fall from traveling at that speed is normally lethal. Now you can estimate the terminal
velocity for an object if you can estimate the wind speed that would be needed to support
it. So here's a little example with a ping pong ball.
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So you see that the hair dryer is blowing at a speed, air speed, that is fast enough
that it is supporting the ping pong ball, so that means that the ping pong ball has
a terminal velocity roughly equal to that air speed. We can do a similar thing with
people. We have a very large fan. So this is an indoor facility where there's a chamber
and beneath the floor there's a very large fan that blow air at high speed, about 100
to 140 miles an hour and that provides enough force to support the weight of people. So
this is very similar to skydiving, and you see that by changing your area you can either
increase the force or decrease the force and move up and down. So in summary, when the
force of air resistance on a falling object balances the object's weight, that object
will fall at a constant speed, and we call that the terminal velocity. For a given size
and shape the object that weighs more has a higher terminal velocity. So the wooden
board has a slower terminal velocity than the brick if the two are the same size and
shape. For a given weight, the object with the smaller surface area has a higher terminal
velocity. So the parachutist, or the skydiver before opening the parachute, has a higher
terminal velocity; after opening the parachute they have more surface area so they have a
slower terminal velocity. Two things of similar composition and shape, the larger one has
the higher terminal velocity so the larger cat has the higher terminal velocity than
the small cat or the squirrel. And you can estimate the terminal velocity as the wind
speed needed to support an object's weight. So hopefully that helps you understand falling
motion when terminal velocity is reached. So we'll continue looking more about motion
through air and even through water in some of the upcoming tutorials where we'll be talking
about pressure and we'll also talk about aerodynamic lift in those. So see you then.