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CAP High School Prize Exam
6 April 2009
Competitor’s Information Sheet
The following information will be used to inform competitors and schools of the exam results, to
determine 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:______________
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School: ____________________________________________________________ Grade:_____
Physics Teacher: _______________________________________________________________
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Immigration Status:_____________________________________________________________
For how many years have you studied in a Canadian school? ____________________________
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Sponsored by:
Canadian Association of Physicists
Canadian Chemistry and Physics Olympiads
Canadian Association of Physicists 2009 Prize Exam
This is a three-hour exam. National ranking and prizes will be based on a student’s performance on sections A, B, and C of the exam. Performance on the questions in part A will be used to determine whose written work in parts B and C will be marked for prize consideration by the CAP Exam National Committee. The marking scheme is: 40% for part A, 10% for part B, and 50% for part C. Part A consists of twenty multiple-choice questions; part B consists of five questions that require graphic solution. The problems in part C can also require graphing. The questions in part C 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 attempt 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 careful to answer the multiple-choice questions on the answer card/sheet provided; most importantly, write your solutions to the three long problems on three separate sheets as they will be marked by people in different parts of Canada. Good luck.
Data
Speed of light c = 3.00x10 8 m/s Gravitational constant G = 6.67x10 -11^ N·m^2 /kg 2 Acceleration due to gravity g = 9.80 m/s 2 Density of fresh water ρ = 1.00x10 3 kg/m^3 Specific heat capacity for water c = 4.19x10 3 J/(kg·K) The normal atmospheric pressure P 0 = 1.01x10 5 Pa Fundamental charge e =1.60x10 -19^ C Mass of electron m (^) e = 9.11x10 -31^ kg Mass of proton m (^) p = 1.67x 10 -27^ kg
Part A: Multiple Choice
Question 1 A ball falls to the earth from a height h and bounces to a
height h ′. Momentum is conserved in the ball-earth system:
(a) no matter what height h′ the ball reaches. (b) only if h′ < h. (c) only if h′ = h. (d) only if h′ > h. (e) only if h′ ≥ h.
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Question 2 A tap water pipe is bent as shown in the diagram. Sections 1 and 2 of the pipe are horizontal but section 2 is placed higher at a height of H. The diameter of the pipe of section 1 is 1.5 times larger than the diameter of section 2. Indicate which of the following is the most complete answer for the relationship between the hydrostatic pressures measured by the gauges in sections 1 and 2: (a) P 1 < P 2 because water flows slower in section 1. (b) P 1 > P 2 because water flows slower in section 1. (c) P 1 > P 2 because section 1 is lower than section 2. (d) P 1 > P 2 because water flows slower in section 1, and section 1 is lower than section 2. (e) For some value of H , P 1 = P 2 because the lower speed of the flowing water in section 1 is compensated by the hydrostatic pressure due to the difference H in the height of the two sections.
Question 3 We know that a person emits about 500 W of radiation. We also know that a person sitting still uses about 100W of chemical energy. Where is the rest of the energy mainly coming from? (a) Heat conducted from the air into our body. (b) Convection of the heat. (c) Radiation from objects around us. (d) The energy, emitted by the body does not have to have a source. (e) Burning fat that we have accumulated previously. ________________________________________________ Question 4
In the two circuits shown above, the batteries are identical and maintain constant voltage. The light bulbs A, B, C and D, are identical and have resistance R. Assume that the bulbs are brighter when there is more current flowing through them. Which of the following relationships correctly describe the brightness of the bulbs? (a) A = B > C = D (b) C = D > A = B (c) A = B = C = D (d) A = C > B = D
P
P
H
Question 13 A spacecraft of mass m orbits a planet of mass M in a circular orbit of radius R. What is the minimum energy required to send this spacecraft to a distant point in space where the gravitational force of the planet on the spacecraft is negligible?
(a) GmM /(4 R ) (b) GmM / R (c) GmM /(2 R ) (d) GmM /(3 R ) (e) 2 GmM /(5 R )
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Question 14
Two identical thermally isolated containers are separated by a valve. Initially, there is an ideal gas in container 1, and there is a vacuum in container 2. Some time after the valve is opened, the gas in the two containers comes to an equilibrium state. Which of the following statements about the gas during this process is true?
(a) The molar mass of the gas decreases. (b) The work produced by the gas is zero. (c) The temperature of the gas drops. (d) The work produced by the gas is positive and is equal to the absolute value of the change of the internal energy of the gas.
Question 15
During the winter vacation, children use snow and water to build frictionless slides of different shapes in order to conduct various experiments. The side view of one of them is shown in the figure: the linear segment of the slide is smoothly transferred to a circle with a circumference of radius R. A puck starts sliding down from rest at an initial height of 2 R. The acceleration of the puck at the lowest point of its trajectory is:
(a) g (b) 2 g (c) 3 g (d) 4 g (e) 0 ________________________________________________
Question 16
A star undergoes a supernova explosion. Just after the explosion, the material left behind forms a uniform sphere of radius 8.0x10^6 m with a rotation period of 15 hours. This remaining material eventually collapses into a neutron star of radius 4.0 km with a period of rotation T of:
(a) 14 s (b) 3.8 h (c) 0.021 s (d) 0.014 s (e) 0.0075 h
Question 17
An impulse laser may be treated as a source of photons that are emitted during the time interval of the pulse which is followed by a time interval when no photons are produced. Pulses are periodically repeated. A laser beam of diameter d = 10 microns is directed upward and is perpendicular to the thin foil surface which has an index of reflection ρ = 0.50 (see the sketch of the experiment). The index of reflection of the surface is the ratio of the reflected energy to the impact energy. A pulse with duration of 0.13 ms has a total energy of 10 J. What is the mass of the piece of foil that can be supported in the air solely by the light pressure of the laser beam?
(a) < 39 g (b) < 3.1 x 10 -12^ g (c) < 39 mg (d) < 3.7 g (e) < 0.38 g ________________________________________________
Question 18
Two sinusoidal waves traveling at the same speed in opposite directions interfere to produce a standing wave with the wave function y = (1.50 m) sin(0.400 x ) cos(200 t ), where x is in meters and t is in seconds. The speed of propagation of each of the interfering waves is
(a) 159 m/s (b) 200 m/s (c) 300 m/s (d) 47.7 m/s (e) 500 m/s
1 2
Laser
Question 19 A bar magnet is dropped from above and falls through a loop of wire as shown. A student measures the current in the loop between a time when the north pole of the magnet is above the plane of the loop and another time when the south pole of the magnet is below the plane of the loop. Which statement is correct about the result of the student’s measurement? (a) The current in the loop flows in one direction increasing steadily to its maximum value when the centre of the bar crosses the centre of the loop plane, after which the current begins to steadily decrease. (b) The current in the loop undergoes harmonic oscillations because the magnetic flux through the loop is changing. (c) The current in the loop flows first in one direction, then, after the centre of the bar crosses the centre of the loop plane, the current begins to flow in the opposite direction. (d) No current flows in the loop because both ends of the magnet move through the loop.
Question 20 Unpolarized light goes through three successive Polaroid filters, each with its transmission axis at 45° relative to the preceding filter. What percentage of the light gets through? (a) 0% (b) 12.5% (c) 25% (d) 50% (e) 33%
Part B: Questions that require graphical solutions
Question 1 The drag force due to air resistance on a falling object depends on the instantaneous velocity of the object as: D = -1/4 Av^2. Sketch a diagram of height vs. distance for the trajectory of two projectile objects launched from the same point at ground level with the same angle to the horizontal: a) the projectile for which the air resistance is negligible, and b) the projectile that is experiencing a drag force in the air.
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Question 2 A diagram below shows the potential energy of an object in an isolated mechanical system with total energy E and with conservative forces only. In the space below the given diagram, sketch a diagram for the x- component of the net force on the object as a function of x. Your diagram must show the correct trend of the function, zeros and vertex points.
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Question 3 A very thin stick is placed on the optical axis of a thin convex lens as shown in the diagram. Draw the image of the object. Show all rays used for the image construction.
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E
f f
