Air resistance factors (math help)

The wind resistance of a fabric is an important factor in determining its various end uses. In this paper the appropriate drag is punched needle fabrics from 16 different fibers of 140 examined. An empirical relationship is to MEA confident air resistance on the data used gradually multiple regression analysis. The regression analysis of air resistance refers to the material parameters of the weight per unit area, thickness, porosity, and fineness of the fiber. This empirical relationship of air resistance is shown, exactly to predict.

Objectives

* Develop a physical model, that an object with a parachute drop simulated.
* Analyze the relationship between mass and terminal velocity of a falling object with data from the model to.
* Assess two mathematical models in connection with air resistance to terminal speed with data in the simulation.
* A for the model to calculate the air resistance.
* Tell her, the air resistance for the parachute and the maximum permissible load for the decline.

Materials

* Graphing Calculator link cable
* CBL 2? or LabPro? system
* DATAMATE application loaded into the computer
* Vernier motion detector
* Coffee filters, (5 basket-style)
* Balance
* Graph paper

DEVELOPMENT OF THE MODEL

To determine a mathematical model for air resistance in the lab, can delete an object that is similar to a parachute and to collect data, as it is a motion detector to use. To simulate a parachute in this experiment, use coffee filter deleted right side up. The factors which are upward force of air resistance on the filter in a single number called "air resistance". summarized

Answer the following questions before starting this activity.

1. For a falling object, what is the mathematical expression, down trading force describes the object?

2. If an object reaches terminal speed, what is the net force acting on? Explain your answer.

3. Sketch a graph of speed over time for a parachute, which is carry a small load and it falls through the air. Label the points in the diagram on the terminal speed is carried out. On the same set of axes, sketch a diagram with a parachute with a much greater weight attached. How affects the weight of the cargo terminal speed, reaches the parachute?

(4) A possible mathematical model for air resistance on a parachute is that the drag is directly proportional to the speed is (FR = - kv). Assuming that this is the case, you find vT, an expression for terminal speed in g, m and k, where g is the acceleration freefall, m is mass, and k is a constant air resistance. (Note: set FR = FG and calculate V.)

5. A further possible mathematical model for air resistance on a parachute is that drag is directly proportional to the square of the velocity (FR = - kv2). Assuming that this is the case, see vT an expression for terminal velocity, g, m and k.
vT, 2 (m2/s2) in the data table record each terminal in the data table to speed up and the results under the heading.

6. Graphing data on a separate diagram, terminal, speed squared plot, vT 2, against mass, m. Again, scaling of the axes through the origin. Seems this is a better fit than the linear model? Explain why or
Why not.

7 Base interpret graphs on your data and graphs representing mathematical model at best the relationship between the force of air resistance and the speed of the coffee filter? (Choose (a) or (b).)
a. FR = – kv (linear model) B. FR = - kv2 (square model)

8 Evaluation results to take air resistance k, for every coffee-filter studies. If you determine that your data a linear model fit better, use the following equation: k = mg/vT

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