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Question: One important performance measure of a commercial airliner is "dollars per seat-mile," or the cost to fly one passenger one mile. The smaller this number, the better the aircraft performs. This number is not just a function of the shape of the wing and the engine; it depends on how heavily the aircraft is loaded. If you can sail a small balsa wood or foam glider from a repeatable height (ladder, balcony, hilltop, etc.), you can optimize the "dollars per seat-mile" for it. Maximizing dollars per seat-mile for the glider is a task of minimizing the denominator: seats times miles, or the product of payload and distance. Load your glider with varying payloads and record the distance it travels (you must retain good trim, so tape on weights at the glider's center of mass). What payload provides you the maximum payload-range product? The minimum?
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
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