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TERMINAL VELOCITY
The Effects of Surface Area and Weight on the
Terminal Velocity of an Object
By Elliot Ensink and Andrew Peterson
“Does a heavier object fall faster than a lighter object?” This is the age old question that most
have heard ever since their years at elementary school. The first answer people usually come up with is
that the heavier object, such as a bowling ball, does fall faster than a smaller and lighter object such as a
baseball. But if the theory of gravity is considered, then the answer is that they should hit the ground at
the same time since the rate of gravity is the same on both objects.
This answer only works for a few of the cases. What if both objects were dropped from the top
of a very tall building, such as the Empire State Building? Now the answer depends on what the
maximum speed of the free-falling object can be. This maximum speed is known as terminal velocity.
Once an object reaches this speed, it cannot accelerate any faster unless an outside force acts on it. This
speed is dependent on three basic components: shape, weight caused by gravity, and the density of the
fluid it is falling through.
A falling object may seem to be chaotic with no order at all. But it is governed by natural laws to
the extent where it can be calculated and tested. God’s hand is guiding even chaotic things in the
creation such as falling. The creation is made by a wise God that has created order in every aspect of it.
So the question comes to mind: does weight affect terminal velocity more than surface area?
And what is the amount each factor affects the maximum velocity of a falling object. We believe that
surface area has a much greater affect than the weight of an object.
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Theory/ Scientific Principles
Terminal Velocity
Terminal velocity is the speed at which a falling object is no longer accelerating. The object is no
longer accelerating because there are no net forces acting on the object (Benson, Terminal Velocity
(gravity and drag), 2010). An object falling through a fluid accelerated by the force of gravity is counterbalanced by air resistance or drag so that it is travelling at a constant speed (Benson, Terminal Velocity
(gravity and drag), 2010).
Three basic factors affect the terminal velocity. The first of these is air resistance, otherwise
known as drag. Drag is the fore that opposes motion through a fluid (Elert, 2010). If a falling object has a
higher drag, then the terminal velocity will be slower. This is because air resistance is greater, causing
the object to reach a constant speed at a slower velocity.
Drag
The most important contributing factor to the terminal velocity is drag. In fact if there was no
drag there would be no terminal velocity (Benson, Terminal Velocity (gravity and drag), 2010). Drag is a
very complicated subject. It can take different forms such as aerodynamic drag (through a gas) and
hydrodynamic drag (through a liquid) (Elert, 2010).
There are also certain variables that affect the drag force. One of these is velocity. Unlike other
resistive forces the force of drag depends on velocity (Benson, What is Drag?, 2010). An object moving
at a higher velocity will have a higher drag than an object moving at a slower velocity (Elert, 2010).
Another variable that determines the drag force is surface area. The surface area of an object has a
great effect on drag. For example a sheet of paper that is falling horizontally will have a much greater
drag than a sheet of paper that is falling vertically. Why is this so? The answer is the effect of surface
area. The flat horizontal side of a paper has a much great surface area than the thin vertical side. The
larger surface area allows for more particles to resist motion and thus a greater amount of drag.
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Fluid Density
A second factor in determining the terminal velocity is the density of the fluid in which the
falling object is traveling through. The air is made of particles of oxygen, nitrogen, carbon dioxide, dust
particles, etc., and all of these exert force on a falling object. It is not very much force until the object
reaches high speeds. If the fluid is denser that means there are more of these particles in a certain
volume of that fluid. The greater the density of the fluid, the more the fluid will resist a force moving
through it (Elert, 2010).
This factor occurs because of the unique properties fluids have (Elert, 2010). Fluids have much
different characteristics than solids. Fluids let objects pass through them much easier than other
substances. Fluid material does not oppose a force through it for very long but there is a recordable
force opposing motion through it (Elert, 2010).
Gravity/Weight
The final major factor in terminal velocity is gravity and weight (Benson, Terminal Velocity
(gravity and drag), 2010). The force gravity is a major component to terminal velocity. This is obviously
true because if it were not for gravity an object would not fall to begin with. Gravity is a natural force
where two objects with mass are attracted to each other, as defined by Isaac Newton. It is the weakest
of the four fundamental forces in nature, but it is one of the most prevalent and dominant forces in the
universe (Nave, 2005). It can further be explained in Einstein’s theory of gravity. He said that gravity is a
property of matter where matter is able to bend space around it. It is not a type of magnetism. The
more matter an object has, the more space it bends. The earth, which has a huge amount of matter,
distorts space around it and creates a dimple around it. This is why the moon is in orbit around the
earth; it is stuck in this dimple (Layton).
Weight is the measure of gravity on a particular object, not to be confused with mass, which is
the measure of mass. The more weight an object has the more air resistance is needed to balance the
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object, thus giving it a higher terminal velocity (Benson, Terminal Velocity (gravity and drag), 2010). So
when people say “a lead ball and a Ping-Pong ball of a same size will hit the ground at the same time”,
this is true unless they are dropped from high enough off the ground. The Ping-Pong ball will reach a
terminal velocity first and stay at constant velocity, while the lead ball will continue accelerating until it
reaches its own terminal velocity.
Drag Coefficient
Basically terminal velocity is acted upon by the weight of the object caused by the acceleration
of gravity, the surface area which creates drag, and the density of the fluid it’s traveling through. These
major components make up the equation for determining the terminal velocity of an object. However,
there are important factors within these major factors that affect the terminal velocity. The drag
coefficient is one of these. The drag coefficient is a number used to describe the shape and air flow of
the drag of an object (Benson, What is Drag?, 2010).
Aerodynamicists use drag coefficients to take in account the shapes and angles of the object to
determine the drag. The drag coefficient is related to a particular surface area such as a cube or sphere.
When there is a higher drag coefficient the object will have a greater terminal velocity (Drag Coefficient,
2010).
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Works Cited
Drag (physics). (2010, December 6). Retrieved November 13, 2010, from Wikipedia:
http://en.wikipedia.org/w/index.php?title=Drag_(physics)&oldid=400939396
Drag Coefficient. (2010, November 14). Retrieved November 16, 2010, from Wikipedia: Free
Encyclopedia: http://en.wikipedia.org/wiki/Drag_coefficient
Fluid Dynamics. (2010, December 2). Retrieved November 13, 2010, from 2010:
http://en.wikipedia.org/w/index.php?title=Fluid_dynamics&oldid=400134249
Terminal Velocity. (2010, December 8). Retrieved November 13, 2010, from Wikipedia:
http://en.wikipedia.org/w/index.php?title=Terminal_velocity&oldid=401228214
Benson, T. (2010, August 18). Terminal Velocity (gravity and drag). Retrieved November 13, 2010, from
grc.nasa: http://www.grc.nasa.gov/WWW/K-12/airplane/termv.html
Benson, T. (2010, September 10). What is Drag? Retrieved November 13, 2010, from grc.nasa:
http://www.grc.nasa.gov/WWW/K-12/airplane/drag1.html
Elert, G. (2010). Aerodynamic Drag. Retrieved November 16, 2010, from Physics Hypertextbook:
http://physics.info/drag/
Layton, J. (n.d.). How Does Gravity Work. Retrieved November 16, 2010, from How Stuff Works:
http://science.howstuffworks.com/environmental/earth/geophysics/question232.htm
Nave, C. (2005). Gravity. Retrieved November 16, 2010, from HyperPhysics: http://hyperphysics.phyastr.gsu.edu/hbase/hph.html
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