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 Determining Center of Gravity (Level 2) Answers What is the length of a Boeing 747-400 domestic airplane? Length = 70.7 m Let us suppose that the approximate weight distribution (function) on a loaded 747-400 domestic airplane is given by the equation, w(x) = 700 sin(2px / L) + 42,850, where x is the distance measured from the nose of the airplane. Graph the weight distribution.   A sine wave oscillating for one period at the Y = 42, 850 level. The amplitude of the oscillation is small compared to the constant Y term of 42,850. What is the total weight W of the airplane?   Use the equation, to calculate the center of gravity of the airplane. The integration is calculated for x = 0 (nose) to Length (tail). [ Hint: Use integration by parts.] Let us suppose that the approximate weight distribution (function) on a loaded 747-400 domestic airplane is given by the equation, w(x) = 777 ( cos(2px / L) + sin(2px / L) ) + 42,850, where x is the distance measured from the nose of the airplane. Graph the weight distribution.    A sinusoidal curve oscillating for one period at the level of 42,850. The amplitude of the oscillation is minute compared to the height of the function. What is the total weight W of the airplane?    How does the weight calculated in Problem 3 compare with the weight in Problem 6? Explain why this is so. Use the equation, to calculate the center of gravity of the airplane with the new weight distribution. The integration is calculated for x = 0 (nose) to Length (tail). [ Hint: Use integration by parts.] (a) They are equal because the contributions to the integral by the sine and cosine average to zero. (b) = 35.15m Did the center of gravity move? If so, did it move toward the airplane's nose or tail?  Yes. (a) Toward the nose. If not, why did it stay in the same position?   If the airplane's center of gravity moved significantly during flight, do you think the pilot would notice it? Why or why not?   Yes. The airplane would begin to rotate about the cg because the plane would no longer be properly trimmed.

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