Electromagnetic Wave - Physics - Exam Paper, Exams of Physics

Download Electromagnetic Wave - Physics - Exam Paper and more Exams Physics in PDF only on Docsity! CAP High School Prize Exam 11 April 2003 9:00 – 12:00 Competitor’s Information Sheet The following information will be used to inform competitors and schools of the exam results, to deter- mine eligibility for some subsequent competitions, and for statistical purposes. Only the marking code, to be assigned by the local examination committee, will be used to identify papers for marking. Marking Code: This box must be left empty. PLEASE PRINT CLEARLY IN BLOCK LETTERS. Family Name: Given Name: Home Address: Postal Code: Telephone: ( ) E-mail: School: Grade: Physics Teacher: Date of Birth: Sex: Citizenship: For how many years have you studied in a Canadian school? Would you prefer further correspondence in French or English? Sponsored by: Canadian Association of Physicists Canadian Chemistry and Physics Olympiads Canadian Association of Physicists 2003 Prize Exam This is a three hour exam. National ranking and prizes will be based on a student’s performance on both sections A and B of the exam. Performance on the multiple-choice questions in part A will be used to determine whose written work in part B will be marked for prize consideration by the CAP Exam National Committee. The questions in part B have a range of difficulty. Do be careful to gather as many of the easier marks as possible before venturing into more difficult territory. If an answer to part (a) of a question is needed for part (b), and you are not able to solve part (a), assume a likely solution and at- tempt the rest of the question anyway. No student is expected to complete this exam and parts of each problem may be very challenging. Non-programmable calculators may be used. Please be very careful to answer the multiple-choice questions on the an- swer card/sheet provided; most importantly, write your so- lutions to the three long problems on separate sheets as they will be marked by people in different parts of Canada. Good luck. Data Speed of light c = 3.00 × 108 m/s Gravitational constant G = 6.67 × 10−11 N·m2/kg2 Radius of Earth RE = 6.38 × 103 km Mass of Earth ME = 6.0 × 1024 kg Mass of Sun MS = 2.0 × 1030 kg Radius of Earth’s orbit RES = 1.50 × 108 km Acceleration due to gravity g = 9.80 m/s2 Fundamental charge e = 1.60 × 10−19 C Mass of electron me = 9.11 × 10−31 kg Mass of proton mp = 1.673 × 10−27 kg Planck’s constant h = 6.63 × 10−34 J·s Coulomb’s constant 1/4πo = 8.99 × 109 J·m/C2 Speed of sound in air vs = 343 m/s Energy conversion 1 eV = 1.6 × 10−19 J Part A: Multiple Choice Question 1 A parallel-plate capacitor holds charge q and is not connected to anything. The distance between the plates is now in- creased. The electrical energy stored on the capacitor (a) decreases; (b) remains the same; (c) increases; (d) can do any of the above, depending on how the capaci- tance changes. Question 2 When a mechanical or electromagnetic wave goes from one medium to another, it undergoes a change in (a) amplitude only; (b) both speed and wavelength; (c) speed only; (d) wavelength only. Question 3 Two identical rooms in a perfectly insulated house are con- nected by an open doorway. The temperature in the two rooms are maintained at different values. The room which contains more air molecules is (a) the one with the higher temperature; (b) the one with the lower temperature; (c) the one with the higher pressure; (d) neither, since both have the same volume. Question 4 Three airplanes, A, B and C, each release an object from the same altitude and with the same initial speed v 0 with respect to the ground.. At the moment their object is released, A is flying horizontally, B is flying upward at an angle θ with re- spect to the horizontal, and C is flying at the same angle θ as B but downward with respect to the horizontal. Assuming the ground to be horizontal and neglecting any aerodynami- cal effect, the speeds v at which the three objects will hit the ground satisfy (a) vA = vB < vC; (b) vA > vB = vC; (c) vA < vB < vC; (d) vA = vB = vC. Question 5 Two identical conducting spheres, A and B, carry equal elec- tric charge. They are separated by a distance much larger than their diameter and exert an electrostatic force F on each other. A third identical conducting sphere C is initially un- charged and far away from A and B. Sphere C is then brought briefly into contact with sphere A, then with sphere B, and finally removed far away. The electrostatic force between A and B is now (a) 3F/8 ; (b) F/2 ; (c) F/4 ; (d) F/16 . Question 6 On the ground, the Earth exerts a force F0 on an astronaut. The force that the Earth exerts on this astronaut inside the Space Shuttle in low Earth orbit, 300 km above the ground, is (a) a little less than F0; (b) a little more than F0; (c) exactly F0; (d) zero, since the astronaut is weightless when in orbit. Question 7 A person is swinging a ball at the end of a string of length ` with constant speed v. The work done by the tension T in the string over one revolution is (a) 0; (b) mv2/2; (c) 2π`T ; (d) undetermined by the information given. Canadian Association of Physicists Prize Exam 2003 Part B Problem 1 At TRIUMF, a large experimental particle and nuclear physics research facility on the campus of the University of British Columbia, one major programme involves the production of intense beams of unstable isotopes of alkali atoms (potassium K, rubidium Rb, francium Fr). These have the advantage that since their valence shell contains only one electron, their closed shell structure when they are ionised simplifies calcu- lations. Many isotopes are produced when bombarding a calcium oxide target with 0.5 GeV protons from the TRIUMF accel- erator. Until recently, the desired isotope was selected by means of the TRIUMF Isotope Separator On-Line (TISOL)— now decommissioned and replaced by a combined separa- tor/accelerator called ISAC—and sent as a low-speed beam to experimental areas. You are asked to design a (much) simplified version of TI- SOL. More specifically, you want to select 38K ions whose energy is 20 keV. 38K has a mass of 6.3 × 10−26 kg. Separa- tion should proceed in two steps, as illustrated below. 38K R (1) Velocity Selector (2) Mass Separator The figure shows the desired path of a 20 keV 38K ion through the system. This path is to be achieved by means of suit- able uniform time-independent electromagnetic fields. Inter- actions between ions can be neglected here. (a) In the first step, out of all ions (38K or not) entering the ve- locity selector from the left, only those that have a speed corresponding to a 20 keV 38K ion should be undeflected. Suggest a field configuration that can do this, draw a sketch showing the direction of the field(s), and derive as much information as you can about the magnitude of the field(s). (b) In the second step, only 38K ions should be deflected so that the radius R of their trajectory is 2.1 m. Again, suggest a suitable field configuration for this, draw a sketch showing the direction of the field(s), and derive as much information as you can about the magnitude of the field(s). Problem 2 Tides are mainly caused by the gradient (or variation) of the gravitational force of the Moon and of the Sun across the Earth’s diameter. Large water masses, such as Earth’s oceans, bulge along the direction of the gradient and are pinched in the perpendicular direction. As the Earth rotates, the bulges (high tide regions) move across the surface of the Earth. Now the Bay of Fundy, between New Brunswick and Nova Scotia, is reputed to have the highest tides in the world. Their amplitude is only about a metre at the mouth, or entrance, of the bay, whereas at the other end, 260 km away, the ampli- tude reaches up to 16 m. You may assume that the relevant speed of water waves in the bay (for very long wavelengths and shallow enough depth) is about 25 m/s. The bay is nar- row compared to its length. Using the above data, investigate whether the unusually high tides could be the result of a resonance excited by the Moon in the bay. Assume that the depth of the bay is uniform, and neglect the influence of the Sun. Hint: calculate the period of the water oscillations in the bay. Problem 3 The next-generation large space telescope is scheduled for launch in 2010. It will be put in orbit around the Sun, in a special zone where its distance relative to the Earth and to the Sun can remain constant. The location of such zones was first calculated in the XVIIIth century by the French-Italian mathematician Joseph-Louis Lagrange. Even though it relies on approximations, Lagrange’s full so- lution is fairly involved, but you should still be able to make a good qualitative guess at a partial solution. Consider two point masses, M1 and M2, referring respectively to the Sun and the Earth. Both orbit around their common centre of mass at angular velocity ω and with a period of one year. These or- bits are circular to a good approximation, and the distance R between M1 and M2 is constant. Since M1  M2, the mo- tion of M1 is not detectable at the scale of the figure below and can be neglected. M 1 M 2 R x 4 Canadian Association of Physicists Prize Exam 2003 We wish to find where, on the line that joins M1 and M2, an object of mass m can sit so that it also orbits the centre of mass (which we can take to be at M1’s position) with the same, constant, angular velocity ω. We can also safely as- sume that m is so small that it does not influence the motion of M1 and M2. (a) Write down the equation that must be satisfied by the forces acting on the orbiting m in terms of ω, M1, M2, R and x, where x is the distance between m and M1. (b) Show that in the limit M2  M1, this condition can be written u3 − 1 = ± α u 2 (1 ± u)2 where u ≡ x/R, and α ≡ M2/M1. (c) Do not attempt to solve this algebraic equation. Instead, use physical arguments to find how many solutions there are for x and where roughly the Lagrange zones are po- sitioned on the x axis. Provide a qualitative sketch based on the above figure, and explain your reasoning. (d) The Webb space telescope (as it is called) will operate at a temperature of about 35 K and, therefore, it should be shielded from heat sources at all times, while having as unobstructed a view of the sky as possible. Discuss which (if any) of your solutions is most suitable for the Webb telescope. (e) If there are other Lagrange zones off the x axis, they can- not be found from the equation in (b), but what would be their minimum number? Justify your answer. Hint: To a good approximation Kepler’s Third Law for the system is ω2R3 = GM1. ∗ ∗ ∗ ∗ 5