PHYS 124 Section A01 Final Examination Autumn 2006

Transcription

1 PHYS 14 Section A1 Final Examination Autumn 6 Name : S Student ID Number : Instructor : Marc de Montiny Time : Monday, December 18, 6 9: 11: AM Room : Tory Lecture (Turtle) TL-B Instructions : This booklet contains 1 paes (includin 1 blank sheet at the back). Items allowed : pen or pencil, calculator (prorammable or raphic allowed). Personal diital assistants not allowed. Please turn off your cell phones. This is a closed-book exam. You may use the formula sheet provided previously, with your own hand-written modifications. Specific rules have been explained in class. You may lose up to 1 marks (out of 45) if : 1. solutions are included, of if. the formula sheet is not returned with your exam. The exam is worth 45% of the course s final score. You can obtain a maximum of 1 marks out of the possible 14 marks. The exam contains two sections : Multiple-Choice Questions and Problems o 13 Multiple-Choice Questions. Not all questions have the same worth in marks. The total is 5 marks. No partial marks are iven. Circle the one best o answer. 6 Problems. They are worth a total of 9 marks. Partial marks will be iven. Show all work clearly and neatly. If you miss a result for a subsequent part of a question, then work alebraically. Please box your answers. You may use the back of paes for your own calculations. These will not be marked, unless you specify otherwise. When the exam is over, please stop writin immediately, or you may lose marks. Do not discuss with anyone while you are turnin it in. Examination rules apply until you have left the exam room.

2 Multiple-Choice Questions (Total of 5 marks). Circle the one best answer. MC-1. (3 marks) A baseball pitchin machine of mass M (includin the mass m of the baseball) rests on the pitcher s mound. What is the speed of recoil of the machine when it fires the baseball horizontally at speed v? A. mv /( M m) B. mv /( M + m) C. mv / M mv / M m D. ( ) MC-. (3 marks) A puck on a horizontal, frictionless surface is attached to a strin that passes throuh a hole in the surface, as shown below. As the puck rotates, the strin is pulled downward, brinin the puck closer to the hole. Durin this process, does the puck s anular speed A. decrease, B. stay the same, C. increase, or D. we do not have the appropriate information to answer. MC-3. (5 marks) ravitational force Rank the three objects shown below in increasin order of the net Gm1 m / r each object experiences. A. A < B < C B. A < C < B C. C < A < B D. None of the above

3 MC-4. (4 marks) If a projectile is launched vertically from the Earth s surface with a GM E speed equal to the escape speed ve =, how far from the Earth s centre will it R be when its speed is half the escape speed? A. RE B. RE C. 4RE D. None of the above MC-5. (3 marks) The velocity of an object underoin simple harmonic motion is described by v = C sin( Dt). What are the amplitude and period of this object s motion? A. Amplitude C, period D B. Amplitude C / D, period π / D C. Amplitude C / D, period π / D D. Amplitude C, period π / D MC-6. (4 marks) A randfather clock keeps correct time at sea level. If the clock (seen as a simple pendulum) is taken to the top of a nearby mountain, where the acceleration due to ravity is smaller, will the clock A. run slow, B. cease functionin, C. run fast, or D. keep correct time? E MC-7. (3 marks) end only. The fiure below shows a standin wave in a pipe closed at one By which factor is the frequency frequency f 1? A. One B. Four C. Five D. Nine f n of this harmonic reater than the fundamental MC-8. (5 marks) The frequencies of two successive harmonics in a pipe are 55 Hz and 45 Hz, respectively. Assumin that the speed of sound in this pipe is 34 m/s, what is the lenth of the pipe? A..5 m B. 1. m C.. m D. None of the above 3

4 MC-9. (5 marks) A skyrocket explodes 1 m above the round (Fiure below). Three observers are spaced 1 m apart, with observer A standin directly under the point of the explosion. What is the ratio of sound intensities I A / I C, heard by observers A and C? A. I A / I C =1/ 5 B. I A / I C =1/ 4 C. I A / I C = 4 D. I A / I C = 5 MC-1. (5 marks) Two in-phase loudspeakers, A and B, are separated by 3. m. A listener is stationed at point C, which is.4 m in front of speaker B. Assume that both speakers are playin tones with identical frequencies, and take the speed of sound equal to 343 m/s. 4

5 If the listener hears no sound as a result of destructive interference, what is the lowest possible frequency emitted by the loudspeakers? A. 17 Hz B. 14 Hz C. 49 Hz D. None of the above MC-11. (3 marks) A sinle-slit diffraction imae is formed on a distant screen. What effect does increasin the width of the slit have on the width of the central briht spot on the screen, assumin that the wavelenth and the distance between the slit and the screen both remain constant? A. The central briht spot will become wider. B. The central briht spot will become narrower. C. The central briht spot will not chane. D. The width of the slit has no effect on the diffraction pattern. MC-1. (3 marks) The blackbody spectrum from blackbody A peaks at a loner wavelenth than that of blackbody B. Does this means that : A. the temperature of A is reater than the temperature of B, B. the temperature of A is equal to the temperature of B, C. the temperature of A is lower than the temperature of B, or D. the wavelenth is not related to the temperature of the blackbody? MC-13. (4 marks) A beam of neutrons with a de Brolie wavelenth of.5 nm diffracts from a crystal of table salt, which has an inter-ionic spacin of.8 nm. What is the anle of the second interference maximum? A. 1.9º B. 6.3º C. 58.º D. 6.4º [Problems bein on next pae] 5

6 Problems (Total of 9 marks). Show all your calculations clearly. P-1. (17 marks) Rotational Enery A hollow sphere I CM = MR with a diameter of 1 cm is released from rest; it then 3 rolls without slippin down a ramp, droppin throuh a vertical heiht of 7 cm. When it leaves the bottom of the ramp, which is. m above the floor, it is movin horizontally. A. What is the speed v of the ball just as it leaves the ramp? [9 points] B. Throuh what horizontal distance d does the ball move before landin? [8 points] A. K i + U i = K f + U f 1 1 v mh i = mv + mr = 3 6 v = h =.87 m/s 5 r 5 6 mv B. y 1 t y t =, and = y ives d = x = vt = v y = 1.83 m 6

7 P-. (16 marks) Static Equilibrium A 3.-k uniform plank of lenth. m is supported by three ropes, as indicated below by the vectors T 1, T and T 3. What is the tension in each rope when a 7-N person is standin at.5 m from the left end? x y F : T1 cos 4 T3 = F : T 1 sin 4 + T ( m + M ) = τ :.5m + (1) M T1 () sin 4 = From these equations, we find T 1 = 51 N, T = 67 N, T = N 7

8 P-3. (1 marks) Simple Pendulum The strin of the pendulum displayed below is stopped by a pe when the bob swins to the left, but moves freely when the bob swins to the riht. A. Calculate the period of this pendulum in terms of L and l. [8 points] B. Evaluate your result for L =1. m and l =. 5 m. [ points] π A. T = = π ω Left half: Riht half: T l T L lenth 1 l = π = π 1 L = π = π l L Total period T = T + T = l L π l + L B. T =1.5 s 8

9 P-4. (17 marks) Standin Waves In the arranement shown below, a mass m = 5. k han from a strin around a liht pulley. The lenth of the strin between point P and the pulley is L =. m. When the vibrator is set to a frequency of 15 Hz, a standin waves with six loops is formed. A. What must be the linear mass density of the strin, in k/m? [11 points] B. How many loops (if any) will result if m is increased to 45 k? [6 points] A. 6 loops (or half-waves) means f = f 15 Hz, so that f 5 Hz F m v = = and μ μ f v L = = m m μ = = lead to 1 v ( f L) 1 1 = = k/m B. If m is multiplied by a factor 9, then v, and therefore, are multiplied by a factor 3. In other words, the new f1 is 75 Hz. Therefore, 15 Hz = (75 Hz) is f, so that there are two loops. f 1 9

10 P-5. (17 marks) Youn s Two-Slit Experiment In Youn s experiment, a mixture of orane liht (611 nm) and blue liht (471 nm) shines on the double slit. The first-order ( m = 1) briht blue frines lie at the outer edes of a screen that is located 5 cm away from the slits. However, the first-order orane frines fall off the screen. By how much and in which direction (toward or away from the slits) should the screen be moved, so that the first-order briht orane frines just appear on the screen? (It may be assumed that θ is small, so that sinθ tanθ.) Since θ (anular width of the interference pattern) is proportional to λ, the orane liht produces a wider pattern than the blue liht. Thus the screen should be moved toward the slits in order that the first-order briht orane frines just appear on the screen. From d sin θ = mλ and y = L tan θ, one finds, with sinθ tanθ, that yd m =1, we obtain L. Since y and d are the same, we find λ distance by which the screen should be moved is λorane Lblue λorane 471 blue Lorane = Lblue = Lblue 1 = 5 1 λblue λblue 611 L L blue orane y mλ. With L d λorane =. The λ L ( ) = 11.5 cm blue 1

11 P-6. (13 marks) Photoelectric Effect A metallic surface is illuminated with liht of wavelenth 3 nm. The work function for 19 the metal is.46 ev. (Note: 1 ev = J) A. Find the maximum kinetic enery (in ev) of the ejected photoelectrons. [9 points] B. Find the maximal wavelenth necessary to eject photoelectrons. [4 points] hc A. K max = hf W = W = J ou 1.68 ev λ B. W c hc = so that λ = = 55 nm h λ W f = 11