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Doing Science

Problems and tasks from a variety of sources intended to illustrate the way mathematics arises in life and work.

Drag Racing. Two cars are competing in a drag race. One has faster acceleration, the other a faster maximum speed. On an oval track, both cars have to drive below their maximums on the curve. Compare the performance of the two cars in races of various distances.

Astronomy. Examine Kepler's data on the period and mean orbital distance of the five inner planets to discover the relationship between these variables. Then extend this analysis to the outer planets to see how well the model works.

Circular to Linear Motion. A rod attached to the outside of a wheel rotating on a shaft drives a piston up and down as the wheel rotates. Describe the height of the piston in terms of the position of the wheel.

Wind Chill Factor. Explore the wind chill (WC) and temperature- humidity index (THI) data tables to determine the formulas used for their calculation.

Wooden Water Tanks. Analyze the flow of water into and out of a water tank with a spigot at the bottom.

Cooling Coffee. Some fast food restaurants were recently sued for serving scalding hot coffee which burned customers when spilled. How long after brewing should you wait to serve coffee?

Defrosting Food. Explore various strategies for defrosting food by subjecting ice cubes to several experiments: letting them sit on the cupboard, putting them under running water, putting them in a microwave, and putting them in an oven at 250 degrees.

Bounce-Back. Data are presented about the behavior of a ball that rests on the top of a vertical spring which is compressed and released. As the spring stretches to its normal height, it flings the ball in the air. The height the ball travels depends on the degree of compression of the spring at the time it is released. Given data on certain compressions, develop a theory to predict the behavior of the ball under other compressions.

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Last Update: 12/29/98