Please wait for the animation to completely load.
In this Illustration we compare the motion of a red projectile
launched upward to that of an identical green projectile launched upward but
subjected to the force of air friction. To make the motion easier to see,
we have given both projectiles a slight horizontal velocity and do not consider
frictional effects in this direction either. In addition,
we show the free-body diagrams for each projectile (the force of gravity is
drawn with a fatter vector so it is easier to see). Restart.
Watch the Position Graph animation and look
at the free-body diagram.
First, what is the direction of the force of air friction? It opposes motion, just
as static and kinetic friction do. Consider the Velocity Graph
animation.
If we look at the motion on the way up, the velocity is positive, and therefore
the force of friction opposes the motion and is downward, hence |ay| > g on the way
up. At the top of the arc, the velocity is zero, and hence |ay| = g. On the descent,
the velocity is downward, and the force of air friction is therefore upward and
hence |ay| < g. Therefore, |ay| is greater on the way up! This is borne out by
the Acceleration Graph. At some point,
the frictional force has exactly the same size as the force of gravity. When
this occurs there is no longer a net force, and the acceleration
of the projectile is zero. The velocity corresponding to this situation is
called the terminal velocity.
These animations are valid at low speeds. We can experimentally determine
that the force of air friction is proportional to the velocity at low speeds,
with R = -b v, where
R is the resistive or drag force and b is a constant that depends on the
properties of the air and the size and shape of the object. One benefit of
this model is that the mathematics is a little easier to handle than for the
high-speed case.
For massive small objects at high speeds (not depicted, but you can look at
Exploration 5.6 to view this model) we can experimentally determine that the force of air friction is
proportional to the velocity squared. The magnitude of the drag force can
be represented as R = 1/2 Dρ Av2, where ρ is the density of
air (mass/volume), A is the cross sectional area of the object, v is the
magnitude of the velocity, and D is the drag coefficient (0.2–2.0). Sometimes
the drag force is written as bv2 with the assignment that b = 1/2DρA. We can solve for the velocity as a function of time, but it is harder. We
must be careful in this model if we have two-dimensional motion, since the x and y
motions are no longer independent.
Instructor's Resource CD Edition: Do not post or distribute.
The complete version of Physlet Physics is available as a text with CD; Physlet Physics can be bundled with this Prentice Hall textbook.
© 2004 by Prentice-Hall, Inc. A Pearson Company