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# History of exploration

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Solve these1. Pendulum clocks are very important for the history of exploration.   Accurate time was the best way to determine one’s longitude, since the time of sunrise or sunset depends sensitively on your longitude. In this regard, the great enemy of accuracy was thermal expansion of the pendulum used for the chronometer. (A) If a brass rod lengthens by 0.002% for a 1°C temperature rise, by how much would the period of a 1 m long brass-rod pendulum change if the temperature was changed 10°C? (B) How much error would that lead to in a day? (C) Given that 24 hours corresponds to 360 degrees of longitude, how many degrees of longitude error does your answer to B imply? (D) Using the radius of the earth from your book, and your answer above, how far away from your expected location would you be assuming you are at the equator?   (recall that this is the error in 1 day; the total will accumulate.) 3.   A horizontal spring of spring constant 100 N/m is attached to a wall, and a block (A) of mass 5 kg.   The block rests on a frictionless table.   It oscillates with an amplitude of 10 cm. On top of the block rests a second block (B), held in place only by friction.    (A) If block B slips, where is it most likely to do so:  near the center of the spring’s travel, or near the extremes?   Why?    (B)  How big should the coefficient of friction be so the block never slips?

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