物理 高中 5年以上以前

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

物理 高中 約6年以前

第五題

品 242 = 0中 X7 【單元練習】 二砰 和 1 某大樓樓高 320 。 公尺,所使用之升降機可載重 1500 公斤重,並在 4 秒由自地面邊 1還 摩擦不計,則滿載時該升降機之平均輸出功率為 瓦特。 、一真量 60 公斤的人,搭乘一斜角30"的電動扶梯,正以02m/s 的壩繼 皆率上樓,則該 相 朋全人 說 3、當引擎輸出功率為 時, 穩可在水中以速鸞 V 等飄 前從 , 陛 有和喲 2 ,所受平均阻力大小為 。 若髓在水中航行時所受陽力與般 全HERE 匡 的 陣輸出功說 2P 時, 。船可在水中 和 語 等速前進 ?2 和 (4 六 @ 慾使船在水中以速率 2V 等速前進,則引擎輸出功率需增為 4、邑知飛機在空氣中飛行時所受空氣阻力與其終端速度的平方成正比 ,則欲使飛機的8 端速度加倍時,則引擎輸出功率需增為_》 _倍。 2 5 說生用 ME SA 以0 myS 了了駛,此時汽車引谷和 二 es C 若汽車與斜坡間的摩探力 為汽車重量的 )旦與汽車的可 課率無關,當汽和 以想同的引擎輸出功率洛斜坡向下行駛時 , 人 m/S 。 6、質量 5SKg 的物體自距地面高 40 公尺的塔頂以 10m/s 水平拋出,則: 02秒內,重訖對物體作功的平均功率為 瓦特。 @ 第2秒末, 重力對物體作功的瞬時功率為 瓦特。 , 7、質量 m 的質點自高處水平拋出,著地時,其運動方向俗與地面成53" 俯角, 若全和 對質點所施衝量之大小為了J,則 : @ 全程,重力對物體作功 @@ 金怪, Ni 。 @ 著地前之瞬間, 重力對物體作功之瞬時功率為 。 8、質量 m 的物體自地面處以初速V 鉻直上拋,若空氣阻力f的大小為一 G@ 物體可達最大高度為 。 @ 物體落回地面時的瞬時速率為 。 9、將質量 m 的物體置於倖角@的固定光滑斜面上,並由高刀處自由 髓下滑人至斜面底時: @ 全程重施對物體作功之下均功率訪 - , @ 承@,物體下滑至斜面底之瞬間,重力對物體作功之瞬時功率 WWWV