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SAINT PATRICK’S HIGH SCHOOL PHYSICS 12 ADVANCED JANUARY 2002 EXAM Mrs. L. Clarke Instructions: 1. READ each question very carefully. There are no marks for answering a question not asked or for neglecting to answer a question. 2. Mark all answers directly on this paper. Use scrap paper if necessary, but it will not be marked. 3. Scientific calculators and rulers are allowed. 4. Write down as much as you can for each question, but be concise. There are partial marks for sections B and C. 5. In section B and C where there is choice, only complete the number of questions indicated (1 / 2 for Section B and 4/5 for Section C). If you do more than the required number of questions, your answers will be marked in the order that they appear, and the leftover questions will not be marked. GOOD LUCK! Name: ________________________________ Mark: SECTION A: MULTIPLE CHOICE Circle the correct answer. There is only one correct answer per question. If more than one answer is circled or the response is illegible, it will be marked wrong. (1 mark each, 40 marks total) 1. From the top of a cliff 50 m high, an object is thrown horizontally at a velocity of 20 m/s. What time does it take for the object to hit the ground below? a. 2.3 s b. 3.2 s c. 5.1 s d. 10 s 2. See the diagram below. The total energy of the projectile at point 3 is a. mgh b. ½ mv12 c. ½ mv12 + mgh d. ½ mv12 – mgh 3. See the diagram for #2. The kinetic energy of the projectile at point 3 is a. mgh b. ½ mv12 c. ½ mv12 + mgh d. ½ mv12 – mgh 4. See the diagram for #2. The total energy of the projectile at point 2 is a. mgh b. ½ mv12 c. ½ mv12 + mgh d. ½ mv12 – ½ mgh 5. A car is rounding a flat curve of radius 50 m with a speed of 20 m/s. The centripetal force provided by friction is 1.2 104 N. What is the mass of the car? a. 500 kg b. 1000 kg c. 1500 kg d. 2000 kg 6. A 0.50 kg mass is attached to the end of a 1.0 m string. The system is whirled in a horizontal circular path. If the maximum tension that the string can withstand is 350 N, what is the maximum speed that the mass can have if the string is not to break? a. 700 m/s b. 26 m/s c. 19 m/s d. 13 m/s 7. Let the average orbital radius of a planet be R. Let the orbital period of the planet be T. Which of the following is constant for all planets orbiting the same sun? a. T/R c. T2/R3 2 b. T/R d. T3/R2 8. A car goes around a curve of radius r at a constant speed of v. Then it goes around another curve, of radius 2r and at a constant speed of 2v. What is the centripetal acceleration of the car as it goes around the second curve, as compared to on the first curve? a. ½ as large b. the same c. twice as large d. four times as large 9. The speed of Halley’s comet, while traveling in its elliptical orbit around the sun, a. Is constant b. increases as it nears the sun c. decreases as it nears the sun d. is zero at two points in its orbit 10. Europa is one of the moons of Jupiter. It has an orbital radius 9.40 times the radius of Jupiter. Its period is 85.2 hours. Callisto, another of Jupiter’s moons, has an orbital radius 26.4 times the radius of Jupiter. What is Callisto’s period? a. 1.70 102 hr b. 2.39 102 hr c. 4.01 102 hr d. 1.61 105 hr 11. Which of the following can be used to calculate the acceleration due to gravity on any planet? a. Gmp/rp c. Grp2/mp b. Gmp/rp2 d. Grp2/mp2 12. The gravitational attractive force between two masses is F. If the masses are moved to half of their original distance, what is the new gravitational attractive force? a. F/4 b. F/2 c. 2F d. 4F 13. Who was the first person to realize that the planets move in elliptical orbits, and not circular ones, around the sun? a. Johannes Kepler b. Isaac Newton c. Albert Einstein d. Mrs. Clarke 14. A 500 kg elevator is pulled upward with a constant force of 5500 N for a distance of 50.0 m. What is the work done by the 5500 N force? a. 2.75 105 J b. – 2.45 105 J c. 3.00 104 J d. – 5.20 105 J 15. Does the centripetal force acting on an object moving in a circle at constant speed do work on the object? a. Yes, since a force acts and the object moves, and work is force times distance. b. Yes, since it takes energy to turn an object. c. No, because the object has constant speed. d. No, because the force and the displacement of the object are perpendicular. 16. What is the period of a pendulum with a length of 0.750 m? a. 0.481 s b. 1.74 s c. 4.71 s d. 5.44 s 17. A spring-driven dart gun propels a 10 g dart. Work is done on the dart by exerting an average force of 20 N over a distance of 5.0 cm. With what speed will the dart leave the gun, assuming the spring has negligible mass? a. 10 m/s b. 14 m/s c. 17 m/s d. 20 m/s 18. You slam on the brakes of your car in a panic, and skid a certain distance on a straight, level road. If you had been traveling twice as fast, what distance would the car have skidded, if all other conditions were the same? a. 4 times farther b. Twice as far c. 2 times farther d. Not enough information 19. Which of the following statements correctly expresses the value of Fnet on the box on the incline shown in the diagram? ([up the ramp] is positive.) a. -Fgsin - Ff +Fapp b. -Fgcos - Ff +Fapp c. Fapp + Ff – Fgsin d. Fapp + Ff + Fgcos Fapp 21. A brick is moving at a speed of 3 m/s and a pebble is moving at a speed of 5 m/s. If both objects have the same kinetic energy, what is the ratio of the brick’s mass to the pebble’s mass? a. 25 to 9 b. 5 to 3 c. 12.5 to 4.5 d. 3 to 5 22. A lightweight object and a very heavy object are sliding with equal speeds along a level frictionless surface. They both slide up the same frictionless hill. Which rises to a greater height? a. The heavy object, because it has greater kinetic energy. b. The lighter object, because it weighs less. c. They both slide to the same height. d. Not enough information. 23. A student standing on top of a building throws a ball with a horizontal velocity of 12 m/s. If the ball strikes the ground 45 m from the base of the building, how high is the building? a. 18 m b. 37 m c. 69 m d. 140 m 24. How many joules of energy are used by a 1.0 horsepower motor that runs for 1.0 hours? (Note: 1 h.p. = 746 W) a. 3.6 103 J b. 2.7 106 J c. 4.5 104 J d. 4.8 J 25. A person drops a ball while standing on a train moving at constant speed along a horizontal track. What path does a person at rest, off the train, see the ball take? a. A straight path down b. A parabolic path with motion in the direction opposite to that of the train’s motion c. A parabolic path with motion in the direction of the train’s motion d. A straight path angled forward in the direction of the train’s motion m θ Direction of motion 20. A skier, with mass 40 kg, pushes off the top of a hill with an initial speed of 4.0 m/s. Neglecting friction, how fast will she be moving after dropping 10 m in elevation? a. 7.3 m/s c. 49 m/s b. 14.5 m/s d. 196 m/s 26. A 0.060 kg tennis ball, initially moving at a speed of 12 m/s, is struck by a racket causing it to rebound in the opposite direction at a speed of 18 m/s. What is the ball’s change in momentum? a. 0.36 kgm/s b. 0.72 kgm/s c. 1.1 kgm/s d. 1.8 kgm/s 27. A 50 kg pitching machine (this mass is excluding the baseball) is placed on a frozen pond. The machine fires a 0.40 kg baseball with a speed of 35 m/s in the horizontal direction. What is the recoil speed of the pitching machine? (Assume friction is negligible.) a. 0.14 m/s b. 0.28 m/s c. 0.70 m/s d. 4.4 103 m/s 28. A 3.0 kg object moves to the right at 4.0 m/s. It collides head-on with a 6.0 kg object moving to the left at 2.0 m/s. Which statement is correct? a. The total momentum both before and after the collision is 24 kgm/s. b. The total momentum before the collision is 24 kgm/s and after the collision is 0 kgm/s. c. The total momentum both before and after the collision is 0 kgm/s. d. None of the above is correct. 29. A railroad freight car, mass 15 000 kg, is allowed to coast along a level track at a speed of 2.0 m/s. It collides and locks with a 50 000 kg second car, initially at rest and with brakes released. What is the speed of the two cars after they stick together? a. 0.46 m/s c. 1.2 m/s b. 0.60 m/s d. 1.8 m/s 30. A 4.0 N force acts for 3.0 s on an object. The force suddenly increases to 15 N and acts for one more second. What total impulse was imparted by these forces to the object? a. 12 Ns b. 15 Ns c. 16 Ns d. 27 Ns 31. A ping pong ball moving East at a speed of 4 m/s collides with a stationary bowling ball. The ping pong ball bounces back to the West, and the bowling ball moves very slowly to the East. Which object experienced the greater magnitude of impulse during the collision? a. Neither, both experienced the same magnitude of impulse. b. The ping pong ball c. The bowling ball d. Not enough information 32. In an elastic collision, which of the following statements is true? a. Kinetic energy is conserved b. Kinetic energy is gained c. Kinetic energy is lost d. None of the above 33. The distance from the Earth to our Sun is 8.3 light-minutes, which means a. 4.15 107 m b. 1.49 1011 m c. 1.66 10-6 m d. 6.02 105 m 34. Cosmology means a. Using physics to study the heavens b. The study of planets and stars c. The study of Kramer on Seinfeld d. The study of the universe as a whole 35. The term “nebula” currently refers to a. A glowing cloud of gas or dust b. A group of galaxies c. Something outside our galaxy d. A quasar 36. Einstein’s principle of equivalence says a. All frames of reference are equivalent b. An accelerating reference frame causes fictional forces c. Space is non-linear d. Gravitational mass is the same as inertial mass 37. A “closed universe” is most like: a. A sheet that folds back in on itself b. An infinite, never-ending sheet c. A rubber sheet with a heavy weight in the middle d. A sheet where the angles of a triangle add up to less than 180 38. The “missing mass” or dark matter might be found in a. WIMPS b. Quasars c. White dwarfs d. All of these 39. If the mass density of the universe is less than c 10 26 kg/m3, then a. The universe is contracting b. The universe is expanding c. The universe is staying the same size d. The universe is dying 40. The idea that life could not exist if any of the fundamental physical constants were even slightly different is called a. The deceleration parameter b. The radiation-dominated universe c. The big crunch d. The Anthropic principle SECTION B: ESSAY QUESTION Choose ONLY ONE of the following questions. Answer as completely as possible. If necessary, use the back of a page for extra space, but please indicate if you do so. (10 marks) 1. A metal ball is dropped at the same instant that a pellet is fired from a launcher as shown in the diagram. The pellet leaves the muzzle of the launcher at a velocity of 53.0 m/s in the direction of the metal ball. In a few sentences, describe the motion of the pellet, the motion of the ball, and why the pellet and the ball will collide. OR 2. Students set up a glider and some springs on an air track as shown. The glider is pulled in one direction away from the equilibrium position and released. In a sentence, describe what happens to each of the following in each case: a) What happens to the period of the glider if the initial displacement of the glider is increased? b) What happens to the restoring force of the system as the glider moves farther from the equilibrium position? c) What happens to the speed of the glider as it moves farther from the equilibrium position? d) What happens to the period of the glider if the mass of the glider is increased? SECTION C: PROBLEMS: Do ONLY four (4) of the five questions. YOU MUST ANSWER #1. Answer as fully as possible, using correct units and significant figures. It is helpful if a sentence is written to summarize the answer(s). (10 marks each, 40 marks total) YOU MUST ANSWER THIS QUESTION. 1. The diagram shows two vehicles about to collide. Car A has a mass of 1500 kg and a speed of 50.0 km/hr in the direction indicated. Car B has a mass of 1200 kg and a speed of 40.0 km/hr in the direction indicated. When they collide, the two cars remain stuck together. a. Draw a scale diagram showing the momentum of each vehicle before the impact, the total momentum before impact, and the total momentum after the impact. (3 pts) b. Determine the final velocity of the combined mass after the impact. (4 pts) c. How does the total kinetic energy after the impact compare quantitatively to the total kinetic energy before the impact? (i.e. give a percentage) (3 pts) NOW CHOOSE 3 OF THE REMAINING 4 QUESTIONS. 2. Determine the coefficient of friction on the table in the diagram below, if the system moves at constant, non-zero speed. Start with FBDs and show all necessary steps. (10 pts) 2.5 kg 1.5 kg 3. A 150 g pendulum bob is drawn aside from its equilibrium position to an angle of 15. The length of the pendulum string is 58 cm. Determine 4. a. The speed of the bob as it passes through its equilibrium position (4 pts) b. The period of the SHM of the bob (3 pts) c. The tension in the string as the bob passes through the equilibrium position. (4 pts) A 250 g ball is whirled in a horizontal circle on a 1.2 m long string. The tension in the string is 11.2 N. The string suddenly breaks and the ball becomes a projectile. a. Draw a diagram of what would happen to the ball after the string breaks, demonstrating what you know about circular motion and projectiles. (3 pts) b. Determine the horizontal distance the ball would land from the center of the circle, if it was released at a height of 1.8 m. (7 pts) 5. In the diagram shown, the mass m is released from the height h and travels around the circular, frictionless track. Derive a formula for the minimum height h from which the mass must be released to travel around the circle, in terms of only the radius r of the circle. Show all steps clearly. (10 marks) m h r SECTION D: BONUS QUESTION (3 pts possible) Show answer on back of this page. After a completely inelastic collision between two objects of equal mass, each having initial speed v, the two objects move off together with speed v/3. What was the angle between their initial velocities? -----------------------------------------------------------------------------------------------------In this space, you may make any reasonable suggestions or comments on the course, if you like: