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Transcript
SAINT PATRICK’S HIGH SCHOOL PHYSICS 12 ADVANCED JANUARY 2003 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 where there is choice, only complete the number of questions indicated (1 / 2). 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 if 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 7. A 65 kg person is standing in an elevator and on top of a scale. The scale reads 71 kg. What is the acceleration of the elevator? a. 21 m/s2 [up] b. 0.90 m/s2 [up] c. 21 m/s2 [down] d. 0.90 m/s2 [down] 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 8. The coefficient of friction between an object and the ground is 0.32. What is the acceleration of the object if the ground is flat and no other horizontal forces act? a. 0.32 m/s2 b. 3.1 m/s2 c. 1.8 m/s2 d. not enough information 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. A projectile is shot from a certain height above the ground at a velocity of 7.3 m/s [30 degrees up from horizontal]. How long will it be before the projectile returns to its original height? a. 0.32 s b. 0.74 s c. 0.86 s d. 7.3 s 5. A ball is thrown straight upwards at a velocity of +12 m/s. It reaches its maximum height and then begins its descent. Which statement is true about the ball while it is descending? a. The ball has positive velocity and positive acceleration. b. The ball has negative velocity and positive acceleration c. The ball has negative velocity and negative acceleration d. The ball has positive velocity and negative acceleration 6. When the ball in the previous question is at its maximum height, it has a. Non-zero velocity and non-zero acceleration b. Zero velocity and non-zero acceleration c. Zero velocity and zero acceleration d. Non-zero velocity and zero acceleration 9. 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. 2500 kg 10. 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 11. 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 12. 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 13. 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 14. 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 15. Which of the following can be used to calculate the acceleration due to gravity on any planet? a. Gmp/rp b. Grp2/mp c. Gmp/rp2 d. Grp2/mp2 16. 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 c. F/2 b. 2F d. 4F 17. 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 18. 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 always perpendicular. 19. What is the period of a pendulum with a length of 0.750 m? a. 0.481 s c. 1.74 s b. 4.71 s d. 5.44 s 20. A 2.0 kg mass is hung from a vertical spring, extending the spring by 3.0 kg. The force constant for this spring is a. 650 N/m c. 6.5 N/m b. 67 N/m d. 0.67 N/m 21. The period of oscillation for the system in the previous question, once set in motion, would be a. 0.49 s c. 110 s b. 0.49 Hz d. 110 Hz 22. The period of a pendulum’s oscillation on the moon, compared to its oscillation on Earth, would be a. Smaller b. Larger c. The same d. Not enough information 23. If a pendulum is displaced to a large initial angle, its period, as compared to the period with a small initial angle, would be a. Smaller b. Larger c. The same d. Not enough information 24. 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 c. 14 m/s b. 17 m/s d. 20 m/s 25. 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 26. 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 27. A merry-go-round of radius 6.5 m is rotating at an angular speed of 1.1 rad/s when it begins to slow down at a rate of 0.49 rad/s2. How long will it take to stop? a. 0.54 s c. 0.47 s b. 2.2 s d. 0.22 s 28. What is the linear speed of a point on the outer edge of the merry-go-round in the previous question? a. 0.16 m/s c. 5.9 m/s b. 7.2 m/s d. 9.8 m/s 29. What was the initial frequency of the merry-go-round’s rotation in the previous question? a. 0.18 Hz c. 0.91 Hz b. 1.1 Hz d. 0.14 Hz 30. 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. 1 to 6 d. 3 to 5 31. 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. 32. A torque of 230 mN acts on a point. At what distance from the point should a force of 99 N act in order to produce static equilibrium at the point? Assume no other forces act. a. 0.43 m c. 22 cm b. 23 km d. 2.3 m 33. Which combination of circumstances would give the most torque on the fulcrum of a seesaw? a. A light person sitting far from the fulcrum b. A light person sitting close to the fulcrum c. A heavy person sitting far from the fulcrum d. A heavy person sitting close to the fulcrum 34. 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 c. 37 m b. 69 m d. 140 m 35. 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 36. 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 c. 0.72 kgm/s b. 1.1 kgm/s d. 1.8 kgm/s 37. 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 38. 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 c. 15 Ns b. 16 Ns d. 27 Ns 39. 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 40. 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 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. 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? (2 pts) b) What happens to the restoring force of the system as the glider moves farther from the equilibrium position? (3 pts) c) What happens to the speed of the glider as it moves farther from the equilibrium position? (3 pts) d) What happens to the period of the glider if the mass of the glider is increased? (2 pts) OR 2. 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, a) describe the motion of the pellet, (3 pts) b) describe the motion of the ball (3 pts) c) explain why the pellet and the ball will collide (4 pts) SECTION C: PROBLEMS: Answer all FOUR problems. Answer as fully as possible, using correct units and significant figures, and demonstrating what you have learned in class. (10 marks each, 40 marks total) 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) 2. Determine the coefficient of friction on the ramp in the diagram below, if the system moves at constant, positive speed. Start with FBDs and show all necessary steps. (10 pts) 2.5 kg 8.5 1.5 kg 3. A 250 g ball is whirled in a horizontal circle on a 1.2 m long string. The tension in the string is 112 N. The string suddenly breaks and the ball becomes a projectile. a. Draw a diagram (or possibly 2 diagrams) of what will happen to the ball after the string breaks, demonstrating what you know about BOTH circular motion AND projectiles. Include a word explanation of each diagram. (3 pts) b. Determine the distance the ball would land from the center of the circle, if it was released at a height of 1.8 m. (7 pts) 4. In the diagram shown, the mass m is released from the height h and travels around the circular, frictionless track. (a) Derive a formula for the minimum speed needed for the mass to stay on the circle. (5 pts) (b) Derive a formula for the minimum height h from which the mass must be released to travel around the circle, using what you found in part (a), in terms of only the radius r of the circle. Show all steps clearly. (5 pts) m (not to scale) h r SECTION D: BONUS QUESTION (2 pts possible) Show all work on the back of this page. No work, no marks! 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?