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物理 高中

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BBAS11 是一個由二十多個密集星系團組成的超級星團。它總共包含超 過 10,000 個星系。它位於北斗七星的手柄正下方(向南)。它距離我 們大約十億光年。 恆星的核心發出連續的光譜。當這種光穿過恆星較冷的外層大氣時, 那裡的原子吸收了其中的一部分。這種光被電子吸收,這些電子被激 發到原子中的更高能級。由於能級是量子化的,因此只有具有相應能 量的光子才會被吸收。因此,光僅在某些波長處被吸收。這些在恆星 發出的連續光譜上表現為暗線,稱為吸收光譜。 下面的圖片顯示了太陽和 BAS 11 吸收光譜的模擬。紅色和藍色中的 暗線來自氢吸收原子。黄色的黑線來來自鈉原子。綠色中的黑線來自鎂 和鐵原子。紫色中的黑線來來自氫、鐵、鈣和原子。 可以清楚地 看到 BAS 11 的光譜與太陽光譜的偏移。來自 BAS 11 的 譜線都向光譜的紅端移動。這種偏移(稱為“紅移”)朝向更長的波長 (更小的頻率)並且是由由多普勒效應引起的。頻率偏移約為7%。這 意味著 BAS 11 正以大約7% 的光速遠離我們。 Absorption Lines from our Sun Absorption Lines from a supercluster of galaxies, BAS11 v=0.07 c, d = 1 billion light years 如果只考慮都卜勒效應,請問太陽的吸收光譜中,紅色暗線波長為 6562 埃,那麼超級星團BAS11的光譜中,相對應的波長是多少?

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物理 高中

18題,感謝

10. [2D and 3D motion] Show that the potential energy U(r) ofFa particle of nass jat aa distance r(> 員 from a planet of Inass 4 and radins 戶話 11. [The cross product] Caleulate the cross product A x B, assuming that A and B both lie in the x-y plane and have the respective nonzero components 4,, 4, and 妖,, 且, 12. [Angular momentum] Show that 主r, the instantaneous position ofa particle of mass mu with respect to a certain origin O, is parallel to its acceleration dv/吧, then the time Tate of change of the angular Inoimentum L with respect to the given origin vanishes 13. [Theorem 了 Show that the torque-angular momentum formnla _箇 7二 is also valid for a two-particle system 放 the origin lies at the center of mass 14. [Theorem IIH] Two particles of respective Inass ml and 2 are connected to the ends of amassless rod and Inove in the uniform gravitational field g ofthe earth. (a) What is the acceleration of their center of nass Telative to a Newtonian origin O? (b) Show that the angular Inomentum of the two particles about their center of nass 生 aconstant of the motion. 15. [Moments of inertia] Calculate the moment of inertia ofathin, uniform rod of mass m and length / about an axis perpendicular to the rod and at a distance q from one end. 16. [Rotation about a fixed axis] Consider the rotating cylinder in Figure, and suppose that A7 sg, Fo 三 0.6 Nt, and @ 二 0.2m, Calculate (a) The torque 7 acting on the cylinder (b) Ti ngular aceeleration q of the cylinder 17. [Work and kinet: instant Totat eenergy] A 40-kg homogeneous sphere of radius 10 cm is at acertain about ashaft through its center at 600 rpm. Assuining that a constant fric itude ets so that the sphere comes to rest in 10 seconds, Calculate th tional torque ofthis torque. 18. [The physical pendl end and allowed to oscillate freely in a horizontal plane (see Figure) m] A uniform Tod of Inass ru and length / is suspended at one (a) What is the period of this physic lpendulum for small amplitudes? (b) Ithe velocity u0 of the mass ce Hulum is initially released at rest in a horizontal position。what is the er at a subsequent instant when the Tod is vertical? (ec) Calculate the vertical and the horizontal components of the force on the rod at the point of suspensic 19 and rotations] Analyze the motion of a homogeneous sphere of mass 和7 and Tadius dq, which rolls without slipping down a fixed inclined plane of angle # 20. of angular momentum] A Inan has ainoment of inertia 五 about the = axis. He is originally at Test and standing on asinall platform which can turn freely. Ifhe is handed a wheel which is rotating at and has anoinent of inertia 了about its spinning axis, determine his angular velocity 放 (a) he holds the wheel upright, (b) turns the wheel out 9 二 90?, and (c) turns the wheel downward, 9 二 180?. Neglect the effect of holding the wheel a distance d away from the z axis

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