課程名稱︰普通物理學甲上 課程性質︰大一必修 課程教師︰李慶德 開課學院：電資學院 開課系所︰電機工程學系 考試日期（年月日）︰2015/1/15 考試時限（分鐘）：110分鐘 試題 : =============================================================================== General Physics A0 ── Final Exam( January 15, 2015 ) 1 Multiple-choice Problems: (5 points each) 1. The displacement of an object oscillating on a spring is given by X(t) = Xm cos(ωt+ψ). If the object is initially displaced in the negative x direction and given a negative initial velocity, then the phase constant ψ is between: (A) 0 and π/2 radians (B) π/2 and π radians (C) π and 3π/2 radians (D) 3π/2 and 2π radians (E) none of the above ( ψ is exactly 0,π/2,π,or 3π/2 radians ) 2. A window washer attemps to lean a ladder against a frictionless wall. He finds that the ladder slips on the ground when it is placed at an angle of less than 75°to the ground but remains in place when the angle is greater than 75°. The coefficient of static friction between the ladder and the ground: (A) is about 0.13 (B) is about 0.27 (C) is about 1.3 (D) depends on the mass of the ladder (E) depends on the length of the ladder 3. A stationary source S generates circular outgoing waves on a lake. The wave speed is 5.0 m/s and the crest-to-crest distance is 2.0 m. A person in a motor boat heads directly toward S at 3.0 m/s. To this person, the frequency of these waves is: (A) 1.0 Hz (B) 1.5 Hz (C) 2.0 Hz (D) 4.0 Hz (E) 8.0 Hz 4. The orbit of a certain satellite has a semi-major axis of 1.5 * 10^7 m and an eccentricity of 0.20. Its perigee( minimum distance from Earth ) and apogee( maximum distance from Earth ) are respectively: (A) 1.2 * 10^7 m, 1.8 * 10^7 m (B) 3.0 * 10^6 m, 1.2 * 10^7 m (C) 9.6 * 10^6 m, 1.0 * 10^7 m (D) 1.0 * 10^7 m, 1.2 * 10^7 m (E) 9.6 * 10^6 m, 1.8 * 10^7 m 5. Two pipes are each open at one end and closed at the other. Pipe A has length L and pipe B has length 2L. Which harmonic of pipe B matches in frequency the fundamental of pipe A? (A) The fundamental (B) The second (C) The third (D) The fourth (E) There are none 6. Take the mechanical equivalent of heat as 4 J/cal. A 10-gram bullet moving at 2000 m/s plunges into 1 kg of paraffin wax( specific heat 0.7 cal/g°C ). The wax was initially at 20°C. Assuming that all the bullet's energy heats the wax, its final temperature( °C ) is: (A) 20.14 (B) 23.5 (C) 20.006 (D) 27.1 (E) 30.23 7. Ten grams of ice at -20°C is to be changed to steam at 130°C. The specific heat of both ice and steam is 0.5 cal/g°C. The heat of fusion is 80 cal/g and the heat of vaporization is 540 cal/g. The entire process requires: (A) 750 cal (B) 1250 cal (C) 6950 cal (D) 7450 cal (E) 7700 cal 8. In a certain process a gas ends in its original thermodynamic state. Of the following, which is possible as the net result of the process? (A) It is adiabatic and the gas does 50 J of work (B) The gas does no work but absorbs 50 J of energy as heat (C) The gas does no work but rejects 50 J of energy as heat (D) The gas rejects 50 J of heat and does 50 J of work (E) The gas absorbs 50 J of energy as heat and does 50 J of work 2 Calculation Problems: (20 points each) 1. Comet Halley orbits the Sun with a period of 76 years. and in 1986, had a distance of closet approach to the Sun, its perihelion distance Rp of 8.9 * 10^10 m. This shows the comet was between the orbits of Mercury and Venus then. (a) Use a circular orbit to find the relation between the period of a planet and the radius of its orbit. The relation holds also for elliptical orbits provided you replace the radius of the circular orbit with the semi-major axis of the ellipse. (b) Find the comet's farthest distance from the Sun, which is called its aphelion distance Ra. (c) What is the eccentricity e of the orbit of comet Halley? Note that the mass M of the Sun is 1.99 * 10^30 kg and the gravitational constant is G = 6.67 * 10^(-11) N m^2/(kg^2). 2. A harmonic oscillator consisting of a block with mass m and a spring with spring constant k is damped by a damping force that is proportional to the velocity v, i.e., Fd = -bv. Thus, the displacement function x(t) satisfies the equation 2 d x dx m ─── + b ── + kx = 0 2 dt dt The solution of this equation is 2 -bt/2m k b X(t) = Xm e cos(ω't+ψ), with ω' = √( ─ - ── ) m 2 4m where Xm is the amplitude and ω' is the angular frequency of the damped oscillator. Assume that m = 250 g, k = 81 N/m, and b = 50 g/s for this damped oscillator. (a) What is the period of the motion? (b) How long does it take for the amplitude of the damped oscillator to half its initial value? (c) How long does it take for the mechanical energy to drop to half its initial value? 3. The temperature of 4.00 moles of an ideal monatomic gas is raised 24.0 K at constant volume. (a) What is the work done by the gas? (b) What is the energy transferred as heat? (c) What is the change ΔEint in the internal energy of the gas? (d) What is the change ΔK in the average kinetic energy per atom? Note that the Boltzmann constant k = R / NA = 1.38 * 10^(-23) J/K and the Avogadro's number NA = 6.02 * 10^23 mol^(-1). =============================== 試題完 ==================================== 備註： 試卷分A0、A1兩份，僅選擇題順序不同，此份為A0卷。 --

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