普物期中考考古題（林敏聰） 14.Nov.2002

看板NTUEE108HW作者Steggie (p2新板Tread_softly)時間21年前 (2004/11/10 16:37)推噓32(32推 0噓 20→)

留言52則, 12人參與討論串1/1

我知道現在才拿到有點晚 = =" 不過之前板上 90 年的那一份題目並沒有考到 Oscillation，所以應該還是有點參考價值的。 1. Please write down the three Newton's laws of motion in both translational and angular forms, including their "equivalent" expressions of Newton's second law. What are the assumptions for their application in classic mechanics? Are those "equivalent" forms really equivalent? Why? (20%) 2. Two particles, each of amss m and speed v, travel in opposite directions along parallel lines separated by a distance d. (a) In term of m, v and d find an expression for the magnitude L of angular momentum of the two-particle system around a point midway between the two lines. (b) Does the expression change if we change the point about which L is calculated? (c) Now reverse the direction of travel for one of the particles and repeat (a) and (b). (20%) 3. Please prove the parallel-axis theorem and calculate the rotational inertial of body (a), (b), (c), and (d) (see Fig.1). (20%) Fig.1 (a) Solid cylinder about central axis 圓柱，半徑 R，長 L，轉軸過柱面圓心，平行於 L (b) Solid cylinder about central diameter 圓柱，半徑 R，長 L，轉軸過柱面直徑，緊貼著圓柱的其中一個底面 (c) Solid sphere about any diameter 圓球，半徑 R，轉軸過球心 (d) Slab about perpendicular axis through center 矩形板子，長 a，寬 b，轉軸垂直於板面，過其中一個頂點 4. Please prove the TWO equivalent expressions of Newton's second law in angular forms from those in translational form. (10%) 5. Two blocks of masses m and 4m are connected by a spring and rest on a frictionless surface. They are given velocities toward each other such that the block with mass m travels initially at v1 toward the center of mass, which remains at rest. What is the initial velocity of the other block? (10%) 6. (10%) Consider a damped simple harmonic motion with the total force ΣF = - kx - bv, where k is force constant of the spring, x the displacement, v the velocity, b the damping constant. Please write down and solve the (differential) equation of motion from the Newton's second law. 7. (a) (5%) Two identical springs are attached to a block of mass m and to fixed supports as shown in Fig.2. Show that the frequency of oscillation on the frictionless surface is -1/2 <--上標 f = 1/2π(2k/m) (b) (5%) Suppose that the two springs in Fig.2 have different spring constants k1 and k2. Please state the frequency f of oscillation of the block in f1 and f2, where f1 and f2 are the frequencies at which the block would oscillate if connected only to spring 1 or only spring 2. Fig.2 | | ~~~~~ <--這是彈簧...||| | k1 m k2 | |~~~~~~~~~□~~~~~~~~~| <--這邊有個底面，有些 telnet 軟體顯示不出來 8. Good luck!!!! -- 感謝化學系 Raines 同學和她的學姊！ -- 請推 Steggie 好心會有好報￣︶￣謝謝大家！！ -- ...from *Vertopia*, somewhere over the rainbow... ★ ╭──╮╭─＊╮╭──╮╭──╮ ╭──╮╭──╮╭──╮ │ ╯ │ │ │ │ │ │ │ ╰──╮ │ ├── │ ─┬＊ ├──╮╰──╮╰──┤ ╰──╯ ┴ ╰──╯╰──╯ ╰──╯╰──╯╰──╯ -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 211.75.136.1

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