If you have an air hockey table, you know that the puck floats on a thin cushion of air when the table is turned on. With little friction, the puck can travel very fast. How much lift force is created by the air? Add small amounts of weight to the puck and see when it no longer floats to measure the lift force. How many air holes (on average) support the puck? How much force is generated by each air hole? Will a puck with a larger surface area, supported by more air holes (on average),…
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You can model this with an ice cube sliding down a plank: how high do you need to lift the end of the plank before the ice cube starts to slide? Try this with one side plain wood and the flip side waxed wood (use paraffin wax, candle wax or ski wax). Make sure both sides are equally smooth to start with. Do at least three trials. More advanced: using what you know about the forces acting on the ice cube, derive equations to calculate the coefficient of friction for each case. Variation:…
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How does ski wax affect the sliding friction of skis? You can model this with an ice cube sliding down a plank: how high do you need to lift the end of the plank before the ice cube starts to slide? Try this with one side plain wood and the flip side waxed wood (use paraffin wax, candle wax or ski wax). Make sure both sides are equally smooth to start with. Do at least three trials. More advanced: using what you know about the forces acting on the ice cube, derive equations to calculate the…
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What do knots, maps, mazes, driving directions, and doughnuts have in common? The answer is topology, a branch of mathematics that studies the spatial properties and connections of an object. Topology has sometimes been called rubber-sheet geometry because it does not distinguish between a circle and a square (a circle made out of a rubber band can be stretched into a square) but does distinguish between a circle and a figure eight (you cannot stretch a figure eight into a circle without…
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A fractal is, "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced/size copy of the whole" (Mandelbrot, 1982). There are many different fractal patterns, each with unique properties and typically named after the mathematician who discovered it. A fractal increases in complexity as it is generated through repeated sets of numbers called iterations. There are many interesting projects exploring fractal geometry that go beyond…
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Take shots at a set distance from the basket, but systematically vary the angle to the backboard. For a basic project: How do you think your success rate will vary with angle? Draw a conclusion from your experimental results. A bar graph showing success rate at different angles can help to illustrate your conclusion. For a more advanced project: Use your knowledge of geometry and basketball to come up with a mathematical expression to predict your success rate as a function of angle…
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Block off one-third of a soccer net with a cone, 5-gallon bucket or some other suitable object. Shoot into the smaller side from a set distance, but systematically varying the angle to the goal line. Take enough shots at each angle to get a reliable sample. How does success vary with angle? For a basic project: How do you think your success rate will vary with angle? Draw a conclusion from your experimental results. A bar graph showing success rate at different angles can help to…
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Block off one-third of a soccer net with a cone, 5-gallon bucket or some other suitable object. Shoot into the smaller side from a set distance, but systematically varying the angle to the goal line. Take enough shots at each angle to get a reliable sample. How does success vary with angle? For a basic project: How do you think your success rate will vary with angle? Draw a conclusion from your experimental results. A bar graph showing success rate at different angles can help to…
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Compare the strengths and weaknesses of different digital image formats. How does the amount of compression affect a JPEG image? What happens when you save a JPEG image multiple times?
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