EC air drag - 1. (b): __________ 2. (mg/b) : __________...

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Name ______________________________ Phy 2425 EC - Air Drag and Terminal Velocity A. Free-fall exercise. If the vertical direction is denoted by y, the instantaneous position of a body that starts from height y o with initial velocity v o is given by y t y v t gt o o ( ) = + - 1 2 2 (1) Newton's second law can be written for this case as follows. F ma m dv dt mg = = = - (2) Task 1: Demonstrate that the function defined by eq. (1) is a solution to eq (2). [Hint: Differentiate eq. (1) with respect to time to find v(t). Then find dv/dt and substitute it into eq (2).] Task 2: Use Excel to plot v(t) over the range (0 t 10 s) for the special case v o = 0. Use a step size t = 0.25s. Print out the plot and attach it. B. Falling body in the presence of a resistive force proportional to v(t). In this case Newton's 2nd law can be written: F ma m dv dt F mg r = = = - where F r = -bv, b is a constant, and v < 0. Thus F ma m dv dt bv mg = = = - - (3) Task 3: Determine the dimensions of
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Unformatted text preview: 1. (b): __________ 2. (mg/b) : __________ Task 4: By referencing eq. (3) describe what you think will happen to the downward accelerating body as v approaches (-mg/b). Consider the following function: v t mg b e bt m ( ) =- -1 (4) Task 5: Use an analogous procedure to that described in Task 1 to determine if eq. (4) defines a solution to eq. (3). Task 6: Use Excel to plot eq. (4) over the range (0 t 10 s) for the special case b/m = 1. Repeat this procedure for b/m = 2 and b/m = 3. Display all three curves on a common graph. Compare these graphs with the one you made in Task 2. Use a step size t = 0.25s. Print out the plot and attach it. Task 7: Is the conclusion you drew in Task 4 supported by these graphs? Would &quot;terminal velocity&quot; be an apt name for the quantity mg/b? Why?...
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EC air drag - 1. (b): __________ 2. (mg/b) : __________...

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