Bernoulli s Principle Air Resistance

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					Mr. Burtness                                                                      (adapted from Vernier Labs)
AP Physics

                                    Bernoulli’s Equation and Air Resistance
When studying motion, we often ignore air resistance as being negligible and for simplification. In many cases
this is valid* but not always. Acceleration is typically not always constant. Due to air resistance, objects do not
accelerate indefinitely at 9.8 m/s2. A piece of paper and a baseball do not fall at the same rate. Air has a much
greater effect on the motion of the paper than it does on the motion of the baseball. When paper falls, air
resistance very quickly becomes as large as its weight so that it moves at an almost constant velocity. When this
happens, the largest speed of an object is falling with is called terminal velocity, or vT . The paper reaches
terminal velocity very quickly, but on a short drop to the floor, the baseball does not. Air resistance is a drag
force, FDrag. From our study of Bernoulli:
                        Ptot= Pstatic + ½v2   (  = density of the fluid; air = 1.29kg/m3)
This suggests that aerodynamic lift and aerodynamic drag may be dependant on velocity2.
Since Pressure x Area = Force, the equations for lift and drag become:
                  FLift = ½v2(S)(CLift)          CL is the coefficient of Lift, S = Surface Area
                           FDrag = ½v2(S)(CDrag)      CD is the coefficient of Lift, S = Surface Area
   In this experiment, you will measure the terminal velocity as a function of weight for a falling object and use
   the data to determine the coefficient of drag.
      LabQuest with cables                                   Vernier Motion Detector
      Graphing calculator                                    Styrofoam bowl, basket-style coffee filters or
                                                             “high-drag” paper box & paper clip weights

           Identify the specific cases when it is valid to ignore air resistance. (Consider vel., mass, size)
           Sketch what the velocity vs. time graph will look like for an object as it: (1) starts from rest; (2)
            accelerates to its terminal velocity; (3) reaches terminal velocity; (4) hits the ground. Label these points
            on your sketch.
           Sketch the corresponding position vs. time graph.
           What is the net force on the object when it reaches terminal velocity? Compare the drag force to the
            weight when the object has reached terminal velocity.
            1. To help determine the coeffiecient of Drag, graph Drag force on the y- axis and terminal velocity
               on the x- axis. Choose the best fit curve for the data and state the relationship between the
               variables on the graph. (record equation and r value)

            2. Now plot a graph of Drag Force on the y- axis and (terminal velocity)2 on the x- axis. Choose
               the best fit curve for the data and state the relationship between the variables on the graph. (record
               equation and r value).

            3. The Coefficient of drag is related to the slope of this graph: FDrag = ½v2(S)(CDrag) Show the
               calculation for CD.

            4. CD for a blunt object can range from 1.0-1.5. Comment on your experimental results and discuss
               the validity of the equation for aerodynamic drag.

Procedure                                                                                              Motion
     1. Connect the Motion Detector to the DIG/SONIC 1 channel of the LabQuest                         Detector

     2. With the stylus, click on “RATE” and change the sampling rate to .02sec (50
        samples per second) before data collection.
     3. Support the Motion Detector up against the ceiling above the floor, pointing
        down, as shown in Figure 1.                                                                                          Interface

     4. Place a bowl (or drag box) in the palm of your hand and hold it 0.5 m under
        the Motion Detector.
     5. Click           to begin data collection. When the Motion Detector begins to
        click, release the bowl directly below the Motion Detector so that it falls
        toward the floor. Move your hand out of the beam of the Motion Detector as
        quickly as possible so that only the motion of the bowl is recorded on the
        graph.                                                                                                    Figure 1

     6. If the motion of the filter was too erratic to get a smooth graph, repeat the measurement. With practice,
        the filter will fall almost straight down with little sideways motionThe velocity of the coffee filter can be
        determined from the slope of the position vs. time graph. Terminal velocity is the asymptote of the
        velocity graph before the object hits the ground.
                    Drag your stylus to select the portion of the graph that represents the fall of the object. Click
                     Graph/Zoom in” to highlight that region.
               Drag your stylus again to select the terminal velocity region of the graph. (Note that your
               position vs. time graph is linear in this region).
            Either read the velocity graph if there is a clear terminal velocity or determine the slope of the
               position graph by clicking Analyze/curve fit/linear of the position-time graph.
     7. Repeat Steps 4-6 to confirm/average your results and record the terminal velocity.
     8. Repeat the above procedure for a total of 10 weights. Make sure the bowl falls without wobbling
        so the cross-sectional surface area does not change.
Data Table
Object cross-section dimensions__________ Cross-sectional (Surface) Area_________(m2)

Mass of filter(box)__________ Mass of paper clips_________
       Number of                Drag Force (N)     Terminal Velocity       (Terminal Velocity)        CD = FD/(½v 2S)
  filters/paper clips                                                             2   2 2
                                                     vT (m/s) trial            vT (m /s )


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