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物理 高中

請問一下第10題的第四小題 解答是不是錯了??

W = 2x (B) aca hk 5 牛頓運動定律的應用 概念,地球自轉 若假設地球為正圓球體,且半徑為R、自轉週期為7.下列敘述何者正確?(多選) (A)地球上 任意一點對地軸的角速度皆為 GQ 處向心為 (D) 緯度0處因地球自轉的切向速度為2mRese辯度6歲的向心加速度為 會:20 T (TE) T 2元 (B)赤道處的向心加速度為 T 4元R ME S 0 三 Lsinst w ² =gtank Loosol w A T2 4R²R coso 概念,雖動擺 m mg-N=mão T2 9. 如圖所示為遊樂場中常見的旋轉吊椅示意圖,若鏈條與鉛直線夾37度,鏈條長 Lisinsh=R 度為L,則此時的角速度為6 T Tros 3% = ng tangha- g Tsihn = mac Rw =gtansh 10某彈簧的原長為45公分,將一端固定在天花板上,另一端懸一個質量為20公 斤的小球時,彈簧伸長4公分。今以通過固定端的鉛直線為軸,使該物體等速 率旋轉,如圖所示,此時彈簧伸長5公分。設重力加速度為10公尺/秒?,則: ,5 (1)彈簧和鉛直線的夾角= 3; 鉛 k.0,04 -> K = MAX 5000 " (2)彈簧之彈力為 2XU 牛頓; (3)圓周運動的向心力為10 牛頓; FC = Tsino = 250 x singh = 100N (4)圓周運動的速率為 公尺/秒,角速度為平弧度秒,週期為”及九秒。 a c=R 如圖所示,A、B兩球質量均為11,繞同一鉛垂線在同一水平面 (近的外貌的夾角為30度,B球與鉛垂線 200 e 2000 Tsino=mac Teoso = mg T = SORR X 0,05 = 250N 25000so =2000 caso = 4:39=0 | | 150-28 ac &c=25/615) 7,5x0,05 =1²

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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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