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Canadian Association of Physicists 1997 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. However, 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 consider- ation by the National Committee. The questions in part B of the exam have a range of difficulty. Please be careful to gather as many of the easier marks as possible before venturing into more difficult territory. In some cases an an- swer to part (a) of a question is needed for part (b). Should you not be able to solve part (a), assume a likely solution and attempt the rest of the question anyway. No student is expected to completely finish this exam and parts of each question are very challenging. Non-programmable calculators may be used. Please be very careful to answer the multiple choice questions on the answer card/sheet provided to you and, most impor- tantly, write your solutions to the three written problems on separate sheets as they will be marked by different peo ple in different parts of Canada. Good luck. Data Speed of light Gravitational constant c = 3.00 x 10° m/s G = 6.67 x 107"! Nm?/kg? Radius of Earth Rg = 6.38 x 10°m Radius of Moon Ry = 1.70 x 10°m Mass of Earth Mz = 5.98 x 1074 kg Mass of Moon My = 7.35 x 107? kg Mass of Sun Radius of Moon’s orbit Radius of Earth’s orbit Acceleration due to gravity Fundamental charge Mass of electron Mass of proton Mass of neutron Planck’s constant Coulomb’s constant Permeability of free space Speed of sound in air Boltzmann constant Absolute zero Ms = 1.99 x 10° kg Rem = 3.84x 10° m Res = 1.50 x 10% m g = 9.81 m/s? e=1.60x 10-1 C me = 9.11 x 1073! kg mp = 1.673 x 10-27 kg Mn = 1.675 x 10777 ke h = 6.63 x 10-%4 Js 1/4x€ = 8.99 x 10° Nm?/C? Ho = 4m x 10-7 N/A? v, = 340 m/s k= 1.38 x 10-73 J/K T=0K,T =~273C Part A: Multiple Choice Question 1 Two astronauts, each of mass 75 kg, are floating next to each other in space, outside the space shuttle. One of them pushes the other through a distance of 1 m (an arm’s length) with a force of 300 N. What is the final relative velocity of the two? (a) 2.0 m/s (b) 2.83 m/s (c) 4.0 m/s {d) 16.0 m/s Question 2 Twelve identical resistors (each of resistance R) are placed along the 12 edges of a cube. What is the effective resistance between opposite corners of the cube? (a) 2R/3 (b) 5R/6 () BR {d) 12R Question 3 A heavy wooden beam of length Z lies on the ground. You must carry it with a friend who happens to be twice as strong as you are (she can carry twice as much weight with the same effort). If you pick up the beam at one end, at what distance from your end should your friend carry it in order to be fair? (a) 2£/3 (b) 3L/5 (c) 32/4 (d) E Question 4 A car travelling at 80 km/h needs a braking distance of 50 m to come to a complete stop. What braking distance should the same car need if its initial speed were 160 km/h? You may assume that the same braking force can be applied in both cases. (a) 70.7 m {b) 100m (c) 141m (4) 200 m Question 5 What would the length of the earth’s day be if a pen- dulum suspended at some point along the equator did not swing (i.e., when it is pulled from its equilibrium point, it does not swing down again)? (a) 24 br (b) 1.2 br (c) 1.4 br (d) 2.4 hr 
