Inextensible Rope of Length - Physics - Exam Paper, Exams of Physics

Download Inextensible Rope of Length - Physics - Exam Paper and more Exams Physics in PDF only on Docsity! CAP High School Prize Exam 8 April 2004 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 2004 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 care- ful 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 = 3.00 × 108 m/s Gravitational constant G = 6.67 × 10−11 N·m2/kg2 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 Boltzmann constant k = 1.38 × 10−23 J/K Part A: Multiple Choice Question 1 You are standing upright in a room in front of a vertical mir- ror. In this mirror, you can see from your position only the upper two-thirds of your body. You wish to see the entire length of your body reflected in the mirror. Which combi- nation of the following three courses of action will achieve this? (I) Move away from the mirror; (II) move toward the the mirror; (III) use a mirror whose height will allow you to see your whole image when you are at your initial position. (a) (I) only; (b) (II) only; (c) (III) only; (d) either (I) or (III). Question 2 A 5 kg cart collides on a horizontal surface with a 20 kg cart. Which cart experiences the smaller force because of the col- lision? (a) The 5 kg cart; (b) the forces are equal; (c) the 20 kg cart; (d) it depends if the collision is elastic. Question 3 Two monkeys with the same mass stand on a branch at height h above the horizontal jungle floor. Monkey A steps off the branch holding the end of an inextensible rope of length L whose other end is tied to another branch at height H , lets go at the bottom of the swing, and falls freely to the floor, as shown below. Monkey B steps off and falls straight down- ward. Then, neglecting air resistance but not the tension in the rope, the total work W done on each monkey and the speed v with which each hits the floor are as follows: BA H h L (a) WA < WB, vA < vB; (b) WA = WB, vA < vB; (c) WA = WB, vA = vB; (d) WA < WB, vA = vB. Question 4 A person, standing on a train that is accelerating forward at 3.3 m/s2, throws a ball vertically upward. Neglecting air re- sistance, the magnitude of the ball’s acceleration relative to the train is (a) 9.8 m/s2; (b) 10.3 m/s2; (c) 7.0 m/s2; (d) 13.1 m/s2. Question 5 I must cross a river in the shortest possible time. Water flows downstream at a constant 5.0 m/s between the two parallel shores. Taking the direction of the flow as reference, if my boat has a maximum speed of 10 m/s, it should head at (a) 90◦; (b) 120◦; (c) 150◦; (d) 27◦. Question 6 A hoop and a solid cylinder have the same mass and radius. They both roll, without slipping, on a horizontal surface. If their kinetic energies are equal, (a) the hoop has a greater translational speed than the cylin- der; (b) the cylinder has a greater translational speed than the hoop; (c) the hoop and the cylinder have the same translational speed; (d) the hoop has a greater rotational speed than the cylin- der.