Drag Force
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Drag Force: Position vs. Time, Dependent vs. Independent, and Graphing Rules & Calculation, Slides of Civil Engineering
Rules for graphing position versus time and dependent versus independent variables. It also explains the concept of drag force, the relationship between velocity and drag force, and the calculation of drag force using a free body diagram. Instructions for loading data into excel and plotting graphs, as well as finding the slope of the drag force versus velocity squared to determine the constant k.
Typology: Slides
2012/2013
1 / 19
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Drag Force
Rules
for
Graphing
Position versus Time Dependent versus Independent Y
Axis versus
X
Axis
Drag
Force
The slope of F D versus v 2 will give us k. 2 D kv F 2 p D
Av
C
F
C
p = Drag coefficient = density of air A = cross sectional area of the object v = speed of the object
Project
One
Hints
Speed
Distance/Time 1 2 1 2
t
t
d
d
v
Acceleration =
v/
t 1 2 1 2 t t v v a
Drag
Force…on
the
way
down?
Free Body Diagram
ma
F
F
D
F
g
ma
F
F
D g
g D
F
ma
F
mg
ma
F
D
) g a ( m F
D
Procedure
Load tennis02a.txt into Excel
Plot the position versus time - Compute the velocity in the third column - Use v = (d 2 ‐ d 1 )/(t 2 ‐ t 1 ) - Plot the velocity versus time - Compute the acceleration in the forth column - Use a = (v 2 ‐ v 1 )/(t 2 ‐ t 1 ) - Plot the acceleration versus time
Find the slope of
F
D versus v 2
In Excel, select Chart>Add Trendline… - Use the Options tab to set the y ‐ intercept to zero and “Display equation on chart” - Click OK
Double click on the equation that appears on the chart and change its appearance to Scientific Notation
Record the slope from this equation on your handout. - Notice that the slope is our constant k. - y = m x + b - F D = k v 2
Note that since the plot is
F
D versus v 2
that the units for the slope (k) is Newtons/(m 2 /s 2
Terminal
Velocity
Notice in this animation that the accelerationbecomes zero at the terminal velocity.
Terminal
Velocity
At the terminal velocity a=0.
Therefore…
ma
F
F
F
D g
g D
F
F
mg
kv
2 t
k
mg
t
v
velocity
terminal
Drag
Coefficient
Note that we could compute the drag coefficient
C
D now using the following:
A
k
C
A
C
k
v
A
C
F
D D 1 2 2 D 1 2 D
Drag
Coefficient
The density of dry air at sea level is about 1/800th the density of water. So the density of air is about
kg/m 3
The diameter of a tennis ball is about
cm
inches).
We could now see how
C
D that we determined experimentally
(C
D =2k/A
compares to the theoretical value of a sphere
(C
D
for a smooth sphere and
C
D
for a rough sphere).
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