Dropping Items While in Freefall
My question pertains to a scene in the movie "Shoot Em Up". I had an
argument with a friend about (in my opinion) an error in the movie. Two men had
fallen out of an airplane and one man released his gun. The gun fell faster than
the two men although they did not appear to be in a position where drag would
affect the rate at which they were falling. They also would have had enough time
to achieve maximum velocity. If two objects of different sizes and different
weights are dropped from and equal height would they fall at the same rate? This
excludes light items such as a feather or a balloon. I say they would fall at the
same rate. Please help with this and explain why.
I am afraid your friend may be right.
An object falling in air will, as you say, reach 'terminal velocity', but there is no position in which drag does not affect your rate of fall. Terminal Velocity is the speed at which the acceleration due to gravity is matched by the resistance caused by friction with the air. This resistance can also be called drag.
In a vacuum, there would be no terminal velocity, because there would be no friction to cause resistance - you would just fall faster and faster and faster.
Falling in air however, the density and the shape of the object have a lot to do with its terminal velocity. A dense compact item like a handgun would have a much higher terminal velocity than a relatively light and lumpy shape like a human. Changing the shape of the human can have a huge effect on terminal velocity too. The spread eagle shape that most free-fallers adopt has a much lower terminal velocity than if you tuck your arms to your side and make a torpedo shape.
If you dropped a handgun while you were in free-fall at terminal velocity, the gun would indeed fall away from you, and I suspect would do so quite rapidly because of the differences in density and shape.
Tennant Creek AUSTRALIA
In a vacuum, or on the moon where there is no atmosphere, two objects
will always fall at the same rate. Falling through the air can be
affected by your shape and by your size. The size that matters is the
area of your body as seen from below, often called the horizontal cross
section. How much these factors affect you are determined by air
density, body weight, and speed through the air. The official term for
this backwards force is air resistance. It is also called drag.
When speed is close to zero, there is no significant air resistance. As
a falling object speeds up, the air pushes harder against the motion.
For a very light object, this may already be enough to oppose the
object's weight (e.g. a feather). For a heavier object, it just begins
to oppose weight. The weight keeps pulling. For a slim object with
very little sticking out from its sides, sometimes called an aerodynamic
shape (e.g. an arrow), air resistance is smaller. When a parachutist
falls, speed is needed to build up air resistance that will balance
weight. When falling head first or feet first, greater speed occurs.
When falling "spread eagle", less speed occurs. When the parachute
opens, even smaller speed occurs. Which would fall faster (man or gun)
depends on the size and orientation of each, as well as weight of each.
Every object has a different maximum velocity in air. This maximum
velocity is achieved when all forces balance out. When falling through
the atmosphere, this is usually a balance of air resistance and weight.
Text books often give an average terminal velocity, correct for objects
of average shape, average size, and average density. They are good
approximations for objects composed mostly of water, such as rain drops
and human bodies. Most other objects have to be tested.
Dr. Ken Mellendorf
Illinois Central College
Maximum velocity is the compromise between the downward force of gravity
and the upward force of drag (air resistance) of a falling object.
Specifically, the force of drag increases with air speed, while the
force of gravity is pretty close to constant at different altitudes.
So, as an object falls, it accelerates from the force of gravity. As it
speeds up, the force of drag opposing gravity increases, until finally
the object is falling so fast that the force of drag exactly cancels the
force of gravity. At that point, the object no longer speeds up, so it
is falling at its maximum "terminal" velocity.
Without the force of drag, objects under the force of gravity all fall
at the same rate. This is because the more massive something is, the
more force is required to accelerate it, but simultaneously, the more
massive something is, the more force gravity exerts on it. So the two
effects of mass (increased resistance to force and increased force)
cancel each other out.
The kicker here is that the force of drag does not have any such
canceling of the effect of mass. Drag depends on the size, shape, and
air speed of the falling object, not specifically on its mass.
So the short answer to your question is that the falling people and the
falling gun might have different air speeds at which the force of drag
cancels the force of gravity. Actually, I would expect that the maximum
speed for a falling metal gun would be faster than the maximum speed of
a falling person, so the movie might have gotten it right.
Now, I have not seen that movie, so I cannot comment on whether it
unrealistically exaggerates the effect or not.
Richard Barrans, Ph.D., M.Ed.
Department of Physics and Astronomy
University of Wyoming
Sorry, Bill. But the gun, having a higher mass to surface ratio than a human,
would probably accelerate faster and achieve a higher terminal velocity. In
this case, air resistance is the controlling factor. The acceleration due to
gravity is the same, but the effect of the air in slowing the fall would be
greater on the human except in the initial few seconds of the jump.
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Update: June 2012