Download Electromagnetic Wave - Physics - Exam Paper and more Exams Physics in PDF only on Docsity!
CAP High School Prize Exam
11 April 2003
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·m^2 /kg^2 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/s^2 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 / 4 πo = 8. 99 × 109 J·m/C^2 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) 3 F/ 8 ; (b) F/ 2 ; (c) F/ 4 ; (d) F/ 16. Question 6 On the ground, the Earth exerts a force F 0 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 F 0 ; (b) a little more than F 0 ; (c) exactly F 0 ; (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) mv^2 / 2 ; (c) 2 πT ; (d) undetermined by the information given.
Question 18
Two carts, A and B, are placed on an air track. They are made of the same material and look identical. B is given a constant speed and collides elastically with A at rest. After the colli- sion, both carts move in the same direction. One concludes that
(a) A is hollow; (b) B is hollow; (c) A and B are identical; (d) any of the first three answers is possible.
Question 19
The smallest length scale known in physics is the Planck length. It is an important ingredient in some currrent cosmo- logical theories. Which of the following expressions could represent this Planck length? (see Data table.)
(a)
e^2 /hc ; (b)
hc/G ; (c)
Ghc ; (d)
hG/c^3.
Question 20
The Webb space telescope, scheduled to be launched in 2010, will have a mirror 6 m in diameter. Compared with the Hub- ble space telescope, whose mirror has a 2. 4 m diameter, it will be able to resolve objects whose angular separation is about
(a) 2.5 times smaller; (b) 5 times smaller; (c) an order of magnitude smaller; (d) the same: the larger mirror only increases the amount of light gathered.
Question 21
A simple pendulum of length L is suspended from the top of a flat beam of thickness L/ 2. The bob is pulled away from the beam so that it makes an angle θ < 30 ◦^ with the vertical, as shown in the figure. It is then released from rest. If φ is the maximum angular deflection to the right, then
L
L/ 2
θ φ
(a) φ = θ ; (b) φ < θ ; (c) θ < φ < 2 θ ; (d) φ ≥ 2 θ.
Question 22 In the diagram below, light is incident on the interface be- tween media 1 and 2 at exactly the critical angle, and is to- tally reflected. The light is then also totally reflected at the interface between media 1 and 3, after which it travels in a direction opposite to its initial direction. The two interfaces are perpendicular. The media must have a refraction index n such that
n 1 n 2
n 3
(a) n 1 < n 2 < n 3 ; (b) n^21 − n^23 ≥ n^22 ; (c) n^21 − n^22 ≥ n^23 ; (d) n^21 + n^22 ≥ n^23.
Question 23 For the sake of science a physicist jumps attached to the end of a bungee cord, carrying sound measuring equipment. As he swings up and down vertically with a period of 6. 0 s, he monitors the frequency of a sound source on the ground di- rectly below him, and observes a difference of 84 Hz between the maximum and minimum frequency of the source. If the source emits at a constant 1370 Hz, and assuming no signif- icant attenuation of his oscillations over the duration of the measurements, the amplitude of his oscillations is closest to (a) 10 m; (b) 20 m; (c) 32 m; (d) 15 m.
Question 24 A person pulls a box along the ground at constant speed. Con- sidering the Earth and the box together as a system, which of the following is true about the net force F exerted by the per- son on this system and the work W she does on it? (a) F = 0 and W = 0 ; (b) F 6 = 0 and W = 0 ; (c) F = 0 and W 6 = 0 ; (d) F 6 = 0 and W 6 = 0.
Question 25 A magnet moves inside a coil. Which of the following factors can affect the emf induced in the coil? I. the speed at which the magnet moves II. the strength of the magnet III. the number of turns in the coil (a) I only; (b) I and II only; (c) II and III only; (d) I, II and III.
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 38 K ions whose energy is 20 keV. 38 K has a mass of 6. 3 × 10 −^26 kg. Separa- tion should proceed in two steps, as illustrated below.
38 K
R
(1) Velocity Selector (2) Mass Separator
The figure shows the desired path of a 20 keV 38 K 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 (^38 K or not) entering the ve- locity selector from the left, only those that have a speed corresponding to a 20 keV 38 K 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 38 K 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, M 1 and M 2 , 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 M 1 and M 2 is constant. Since M 1 M 2 , the mo- tion of M 1 is not detectable at the scale of the figure below and can be neglected.
M 1 M 2
R
x
