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Ch4-HW2-solutions

# Ch4-HW2-solutions - louey(cal2859 Ch4-HW2 florin(56930 This...

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louey (cal2859) – Ch4-HW2 – florin – (56930) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points If a chain of 40 identical short springs linked end to end has a stiffness of 200 N / m, what is the stiffness of one short spring? Correct answer: 8000 N / m. Explanation: Springs in series have the effective stiffness K , where K is given in terms of the stiffnesses of the individual springs as follows: 1 /K = 1 /k 1 + 1 /k 2 + ··· + 1 /k N . For identical springs, we have k = NK , where k is the stiffness of a single spring. Therefore k = (40)(200 N / m) = 8000 N / m . 002 10.0points You place 45 identical springs side by side (in parallel) and connect them to a large, massive block. The stiffness of the 45-spring combi- nation is 20295 N / m. What is the stiffness of one of the individual springs? Correct answer: 451 N / m. Explanation: Springs in parallel have an effective stiffness K , where K is given in terms of the stiffnesses of the individual springs as follows: K = k 1 + k 2 + ··· + k N . For identical springs, we have K = Nk , or k = K/N , where k is the stiffness of a single spring. Therefore, k = 20295 N / m 45 = 451 N / m . 003(part1of4)10.0points One mole of tungsten (6 . 02 × 10 23 atoms) has a mass of 184 g, and its density is 19 . 3 g / cm 3 , so the center-to-center distance between atoms is 2 . 51 × 10 - 10 m. You have a long, thin bar of tungsten, 2 . 1 m long, with a square cross section, 0 . 15 cm on a side. You hang the rod vertically and attach a 455 kg mass to the bottom, and you observe that the bar becomes 1 . 27 cm longer. From these measurements, it is possible to determine the stiffness of one interatomic bond in tungsten.

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