(a) 6x kg (b) 6x kg (c)6x kg (d)6x kg (6) 質量為 m 之物體在地球表面的位能為 :( 設 R 為地球之半徑 ) The potential energy of an object of mass m at the surface of the earth i

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1 2015 年第三十二届全国华文独中数理学识比赛 - 物理适用的常數表 List of useful constants 光速 Speed of light: c = 3x10 8 m/s 普朗克常數 Plank constant: h = 6.626x10-34 Js 重力加速度 Gravitational acceleration on earth: 水的比熱 Specific heat of water: cwater = 4180 J/kg.K 声波在空气中的速度 Speed of sound in air = 343 m/s 重力常數 Gravitational constant: G=6.674x (1) 物體從粗糙的斜面下滑, 如果斜面與地面的角度為 θ, 摩擦係數為 μ, 則該物體之加速度為 :(g 為重力加速度 ) An object is sliding down from inclined rough plane surface. Suppose the angle of the plane with the floor is θ and the friction coefficient is μ. The acceleration of the object is: (g is gravitational acceleration) (a) μg(1+cosθ) (b) μgsinθ (c) μtanθ (d) g(sinθ-μcosθ) (2) 不掛重物時彈簧長度為當質量 m 之物體懸掛後它的長度變為, 如果 k 為力常數則為 : A spring has a length when it is unloaded. By hanging an object of mass m on the spring then its length is stretched to. If the mass of the object is m and the force constant of the spring is the length difference is: (a) mg (b) mg/k (c) mg /k (d) kgl (3) 一物體以水平速度從高度為 H 的建築物往下運動, 則在 H/2 高度時物體之速度為 : An object is free falling from the top of a building with height H and initial horizontal speed. The speed of the object when it is half way from the ground is: (4) 質量為 m 之物體在無摩擦力的平面上連結在彈簧的一端做簡偕振盪 ( 其另一端固定在牆上 ), 如果力常數為 k 則振盪的頻率為 : An object of mass m lying horizontally on a frictionless surface is connected to a spring which has its end fixed on the wall. What is the frequency of the harmonic motion if the spring s force constant is k? (5) 已知地球的半徑為 6400km, 則地球的質量約為 : By knowing that the radius of the earth is 6400km, the mass of the earth is approximate equal to: 1

2 (a) 6x kg (b) 6x kg (c)6x kg (d)6x kg (6) 質量為 m 之物體在地球表面的位能為 :( 設 R 為地球之半徑 ) The potential energy of an object of mass m at the surface of the earth is: (assuming R is the radius of the earth) (a) mgr (b) -mg/r (c) -GMm/R (d)- GM/R (7) 質量分別為 m 及 M 的兩物體如果它們之間的距離為 R, 則它們之間重力位能為 : The gravitational potential between two objects of masses m and M separated by a distance R is: (a) -GMmR (b) GMm/R (c) -GMm/R (d) GM/mR (8) 假設所有行星的軌道皆為圓形, 則在軌道上的速率 : (R 為軌道半徑 ) Assuming all planets are in circular orbits around the sun. Then the orbital speed : (where R is the orbital radius) (e). (9) 一顆子彈以速度 v 打在一塊靜止的木頭上 ( 設木頭的質量為 M), 假如子彈停在木頭內, 而且 m/m=0.1 則木頭的速度為 : A bullet of mass m moving with a speed v collides with a piece of wood at rest ( mass M). Suppose that the bullet stays inside the wood after the collision and their mass ratio m/m=0.1, the final speed of the wood is: (a) 0.9v (b) 10v/11 (c) v/11 (d) v/12 (e) 9v/10. (10) 把 10 公升的水由 273K 加熱至 373K 所需要的熱量為 : The amount of heat needed to raise the temperature of 10 liters water from 273K to 373K is : (a) cal (b) 80000J (c) 4180 J (d) 4180 cal (11) 一根 10 公尺長的金屬棍子夾在溫度為 600K 及 1000K 的兩個火爐中, 則離高溫爐子 4 公尺處的溫度為 : A 10m metal rod is placed between two furnaces with temperatures 600K and 1000K. The temperature at the position which is 4m away from the higher temperature furnace is: (a) 800K (b) 670K (c) 840K (d) 720K (e) 240K. (12) 聲速在空氣中的速率為 340m/s ( 在 303K 的溫度中 ), 則聲速在鋼鐵中約為 : The speed of sound in the air is about 340m/s at 303K. The speed of sound in steel is in the order of : (a) 500m/s (b) 5000m/s (c) 50000m/s (d) 50m/s (13) 急救車在靜止時它的警笛頻率為 f, 當它衝入醫院時, 門口等待的醫護人員 2

3 所聽到它頻率是 :( 為急救車的速率 ) (a) 一樣 (b) 低於 f (c) 高於 f (d) (e) 以上皆非 The siren of the ambulance at rest has a frequency f. When the ambulance is approaching toward the emergency center the medical staff will hear a different frequency which is: (a) the same as f (b) Lower then f (c) higher than f (d) (e) None of the above (14) 兩個相等的電荷 Q 被約束在距離 D 的位置上, 如果外力被去掉以後它們因互相排斥而在直線上分離, 假如它們也有一樣的質量 m, 則在遠處每一個物體的速率為 :(k 為常數 ) 2 positive charges( they carry the same charge Q) are held at rest with a distance D between them. When they are released then they will be flying apart on a straight line. If they have equal mass m then the speed at infinity for each mass is: ( k is a constant) (d) (e). (15) 三個相等的電荷 q 被放在一個等邊三角形的頂角上, 假如把另外一個電荷 -Q 放在三角形的中心上, 則以下敘述哪一個是正確的 : (a) 電位能為正的 (b) Q 上的力為 0 (c) Q 的力 0 (d) Q 上的電場 0 (e) 以上皆非 3 equal charges (denoted by q) are located at the vertices of a equilateral triangle. If another negative charge -Q is now sitting at the center of the triangle. Then which of the following statements is true: (a) the potential energy is positive (b) the force on -Q is zero (c) the force on -Q is non-vanishing (d) The electric field is not zero on -Q (e) none of the above. (16) 兩個電阻分別為 R 及 r 並聯並且與電池連接, 如果 r/r=0.25 則它們的功率比為 : Two resistors R and r are connected in parallel and attached to a battery. If r/r=0.25, then the ratio of their dissipated powers is : (a) 4 (b) 2 (c) 1/4 (d) 8 (e) 1/8. (17) 長的電荷線其電荷密度為 λ 其電場 : (a) 永遠與電荷線垂直 (b) r 為該點到電荷線的距 (c) (d) 平行於電荷線 (e) 以上皆非 The electric field of an infinite line charge with charge density λ is: (a) always perpendicular to the line charge (b) where r is the distance from the line charge (c) (d) always parallel to the line charge (18) 電荷 Q 在兩強度相同的平行電流 I 附近運動, 如果電流之間的距離為 D, 而 3

4 Q 與其中一電流之距離為 5D 而且它的運動方向也平行於電流, 則以下哪個敘述是正確的 : (a) Q 上的力 F 為 0 (b) F 平行於電流 (c) F 垂直於電流 (d) 電流之間的力為吸引力 (e) 以上皆非 A charge Q is moving parallel to two currents which are parallel and have the same magnitude I with a distance D between them. If Q is at a distance 5D from one of the current then which of the following statements is correct: (a) The force F on Q is zero (b) F is parallel to the currents (c) F is perpendicular to the currents (d) The force between the currents is attractive (19) 交流電流流過電阻 R, 則消耗的平均功率為 : An alternating current is passing through a resistor R. The average power dissipated on R is (20) 氫原子的能階為 : The energy level of hydrogen atom is given by: (d) (e) -3.4neV. (21) Einstein 引進光子來描述光, 則可見光所對應的能量範圍是 : Photon was introduced by Einstein in 1905 to describe light as particles. The energy range of visible light is: (d) (e). (22) 原子核的大小約為, 由此估計原子核中兩質子之平均位能約為 : The size of nucleus is about. From that what is the average potential energy between 2 protons in the nucleus? ~1 kev (d) ~100keV (e) ~1 Mev (23) 以下波的性質哪一個是正確的 (A, f, λ 及 I 分別是振幅頻率波長及強度 ): (a) I A (b) 波速 =λ/f (c) 波的疊加還是波 (d) 不同介質的波速都一樣 (e) 波沒有能量 Which of the following statements is correct for describing wave (where A, f, λ and I are the amplitude, frequency, wavelength and intensity respectively) : (a) I A (b) the wave speed = λ/f (c) waves can be added together as a wave 4

5 ( d) wave always has the same speed in different medium (e) waves do not carry energy. (24) 對光的繞射而言何者為正確 : (a) 光的頻率會改變 (b) 波長會變 (c) 繞射圖案與孔無關 (d) 有明亮及黑暗的區域 (e) 波長在繞射現象中不重要 What is the correct statement after light being diffracted? (a) light changes into a different frequency (b) The wave length has changed (c) The diffraction pattern is independent of the hole for diffraction (d) There are bright and dark regions (e) wave length is unimportant for the diffraction pattern. (25) 黑體輻射的強度 I 與溫度 T 的關係為 : For black body radiation at temperature T which of the following statement is correct for the intensity I: (e). 5

(6) 質量為 m 的流星離地球之距離為 R, 則他的動位能為 (G 為萬有引力常數,M 為地球質量 ): A comet of mass m is a distance R away from the earth then its gravitational potential energy is

(6) 質量為 m 的流星離地球之距離為 R, 則他的動位能為 (G 為萬有引力常數,M 為地球質量 ): A comet of mass m is a distance R away from the earth then its gravitational potential energy is 适用的常數表 List of useful constants 光速 Speed of light: c = 3x10 8 m/s 普朗克常數 Plank constant: h = 6.626x10-34 Js 重力加速度 Gravitational acceleration on earth: 水的比熱 Specific heat of water: c water = 4180 J/kg.K