Download Lab Writeup Air Resistance

Air Resistance
LBS 164
Objectives:
Most experiments and derivations in physics classes and labs ignore the friction of an
object moving through air. In this lab, we will study experimentally the various parameters
governing air resistance including speed and cross sectional area.
Theory:
If you drop a ping pong ball and a baseball at the same time, the baseball will hit the
ground first. Large raindrops fall faster than small raindrops. These effects are due to air
resistance. Without air resistance, the objects will all fall with the same acceleration, g, and hit
the ground at the same time. Air resistance acts like a frictional force. However, air resistance
does not behave like the frictional forces we have been studying such as kinetic friction. The
force of kinetic friction does not depend on the speed of the object or the area of the object in
contact with the sliding surface. Instead, the force of kinetic friction, Fk, depends only on the
normal force , N, and the coefficient of kinetic friction µk:
F = µkN.
(1)
The force of air resistance results from air molecules colliding with the moving object.
The number of collisions depends on the area of the object . In addition, the faster the object is
moving, the more collisions occur. Thus one can write the force due to air resistance, Fa, as
Fa = CAv2
(2)
where C is a constant, A is the cross sectional area of the object, and v is the velocity of the
object. Note that the force depends on the square of the velocity. One factor of v arises because
the average momentum of each molecule is proportional to v and the other factor comes from the
fact that the number of molecules striking the object per second is also proportional to v. The
constant C for air is about 1 kg/m3.
One can see from equation 2 that the force of air resistance will increase as the speed of
the object increases. At a certain velocity, the force of air resistance will balance the force of
gravity for a falling object and the speed will remain constant. This velocity is termed the
terminal velocity. Suppose the object is moving down an inclined plane that makes an angle 
with the horizontal. The force of gravity is Fgrav = mgsin and the force of air resistance is Fa =
CAv2. The terminal velocity then is
vt 
mg sin
.
CA
(3)
and the acceleration would be zero.
Before the terminal velocity is reached, the object will accelerate. The acceleration can
be obtained using F = ma:
F = Fgrav - Fa = mgsin - CAv2 = ma
Air Resistance Lab Write-up
(4)
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We can rewrite equation (4) as
a 
CA 2
v  mg sin
m
(5)
Procedure:
Setup
Set up the dynamics track, motion sensor, and sail cart as shown below.
Measure the angle  that the track makes with respect to the horizontal. Make sure that the
motion sensor is connected to the Pasco interface and that the power is turned on. Open the
Science Workshop document “Air Resistance”.
Measurements
Measure the velocity of the sail cart as a function of time for two different angles. Export
the velocity versus time tables to Excel. Use Excel to calculate v2 and a. The resulting table
should resemble the following table:
t (s)
v (m/s)
v2 (m2/s2)
a (m/s2).
Plots
Make plots of v vs. t for two angles.
Make plots of a vs. v2 for the two angles.
Questions and Exercises
1. Is the acceleration of the sail cart constant? Give an explanation for your observation.
2. Is a terminal velocity reached by the sail cart?
3. Is the graph of a vs. v2 for the sail cart a straight line? Give an explanation for your
observation.
4. Extract a value of C from your data. Compare your result for C with 1 kg/m3.
5. Apply your newly-gained knowledge of air resistance as a function of velocity to a real-life
situation.
Air Resistance Lab Write-up
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