課程名稱︰普通物理學甲上 課程性質︰必修 課程教師︰趙治宇 開課學院：工學院 開課系所︰機械系 考試日期（年月日）︰2015/01/16 考試時限（分鐘）：170 是否發放獎勵金：Yes 試題 : http://imgur.com/If8hhUn 1. Prove that the speed v of a string wave with string tension τ and string density μ is given by τ ^(1/2) (10%) v = ( —─) μ 上課帶到的推導 2. Show that the intensity of sound wave is given by I = (1/2)ρvω^2(Sm)^2 (Sm is the displacement amplitude) (10%) 上課帶到的推導 3. (a) What's the principle and the application of a strain gauge; (b) Describe the principle of equivalence for general theory of relativity) (4%,4%) 上課提到的科技或定理 4. Derive the change in entropy delta S between the initial state(Vi,Ti) and final state (Vf,Tf) of an ideal gas in a reversible process (Fig.1). (Express your answer with Vi,Ti,Vf,Tf,n.) (10%) 上課帶到的推導 5. Derive the change in entropy delta S when n mole of an ideal gas doubles its volume in a free expansion. (You must derive the result by using statistical mechanisms.) (10%) 上課帶到的推導 6. In Fig.2, water stands at depth D = 30.0 m behind the vertical upstream face of a dam of width W = 250 m. Find (a) the net horizontal force on the dam from the gauge pressure of the water and (b) the net torque due to that force about a horizontal line through O parallel to the (long) width of the dam . (c) Find the moment arm of the torque. (12%) 習題 7. In Fig.3, a solid brass ball of mass 0.320 g will roll smoothly along a loop-the-loop track when released from rest along the straight section. The circular loop has radius R = 12.0 cm, and the ball has radius r << R. (a)What is h if the ball is on the verge of leaving the track when it reaches the top of the loop? If the ball is released at height h = 6.00R, what are the (b) magnitude and direction of the horizontal force component acting on the ball at point Q? (10%) 習題 8. The 0.800 kg cube in Fig.4 has edge lengths d = 6.00 cm and is mounted on an axle through its center.A spring (k = 3600 N/m) connects the cube's upper corner to a rigid wall.Initially the spring is at its rest length. If the cube is rotated 3° and released, what is the period of the resulting SHM? (10%) 習題 9. For an ideal gas. show that the relation between the gas temperature T and rms speed and molar mass M is given by 3RT ^(1/2) Vrms =( —─) M (10%) 上課帶到的推導 10. In Fig. 5, two blocks (m = 1.8 kg and M = 10 kg) and a spring (k = 200 N/m) are arranged on a horizontal,frictionless surface. The coefficient of static friction between the two blocks is 0.40. What amplitude of simple harmonic motion of the spring–blocks system puts the smaller block on the verge of slipping over the larger block? (10%) 習題 --

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