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Name ________________________________________________________________________ Final Exam Physics I Spring 2003 If you took all three unit exams, this Final Exam is optional. It may bring your grade up, but it may also bring your grade down. If this exam is optional for you, you may decide at any time before you hand it in that you do not want it graded. If you do not want this graded, check here and sign your name __ ________________________________________________________ If you would like to get credit for having taken this exam, we need your name (printed clearly) at the top and section number below. Section # _____ 1 _____ 2 _____ 3 _____ 4 _____ 14 _____ 5 _____ 7 _____ 10 _____ 11 _____ 15 _____ 12 M/R 8-10 (Washington) M/R 10-12 (Schroeder) M/R 10-12 (Zhang) M/R 12-2 (Bedrosian) M/R 12-2 (Adams) M/R 2-4 (Hayes) M/R 4-6 (Bedrosian) T/F 10-12 (Wilke) T/F 12-2 (Sperber) T/F 12-2 (Adams) T/F 2-4 (Wilke) Questions Part A Value 28 B-1,2,3 18 B-4,5 16 B-6,7 16 B-8,9 18 B-10,11 16 B-12 14 C-1 16 C-2 16 C-3,4 8 C-5 16 C-6 18 Total 200 Score If we catch you cheating on this exam, you will be given an F in the course. Sharing information about this exam with people who have not yet taken it is cheating on the exam for both parties involved. The Formula Sheets are the last two pages. Detach carefully for easier reference if you wish. 1 Name ________________________________________________________________________ On this exam, please neglect any relativistic and/or quantum mechanical effects. If you don’t know what those are, don’t worry, we are neglecting them! On all multiple choice questions, choose the best answer in the context of what we have learned in Physics I. On numerical questions, show all work to receive credit. Part A – Warm-Ups – 28 Points Total (7 at 4 Points Each) Write your choice on the line to the left of the question number. _______1. Which of the following statements is not one of Newton’s Laws of Motion? A) All objects fall with equal acceleration regardless of mass. B) Objects at rest tend to stay at rest and objects moving with a constant velocity maintain that velocity unless acted on by a force. C) F Fnet m a D) For every action there is an equal and opposite reaction. _______2. A) B) C) D) E) Your weight and the force of gravity pulling on the earth due to your mass. Your weight and the normal force from the seat holding you up. The weight of an airplane and the lift from its wings holding it up. All of the above. None of the above. _______3. A) B) C) D) A competitor in the Olympics springs off a diving board and attempts a triplesomersault dive. While she is in the air, neglecting air resistance, she cannot change her Angular velocity. Angular momentum. Rotational kinetic energy. Rotational inertia. _______4. A) B) C) D) E) F) Which of the following are Newton’s Third Law Pairs? A car is heading north at 100 km/hr when the driver steps on the brakes. While the car is slowing down, what is the direction of the net torque on the wheels? Up (Toward the Sky). Down (Toward the Ground). North. South. East. West. N W E S 2 Name ________________________________________________________________________ _______5. A) B) C) D) For this question, take right as the positive direction. A 0.25 kg rubber ball traveling horizontally to the left at 12 m/s hits a wall and bounces back at 8 m/s to the right. The total impulse exerted by the wall on the ball is +5.0 N s. –5.0 N s. +3.0 N s. –3.0 N s. E) F) G) H) +2.0 N s. –2.0 N s. +1.0 N s. –1.0 N s. _______6. A) B) C) D) E) F) An electron is moving East in a uniform magnetic field directed North. What is the direction of the Lorentz force on the electron? N B Up (Out of the Page). Down (Into the Page). W E North. South. v East. S electron West. _______7. A) B) C) D) E) An electron is moving in a region of space with a static electric field and a static magnetic field. The electron begins with a kinetic energy of 6.0 x 10–17 J at point P where the electric potential is +100 V. It moves to point Q where the electric potential is –100 V. All forces but the electric force and the magnetic force can be neglected. What is the electron’s kinetic energy at Q (to two significant digits)? 2.8 x 10–17 J 4.4 x 10–17 J 6.0 x 10–17 J 7.6 x 10–17 J 9.2 x 10–17 J 3 Name ________________________________________________________________________ Part B – Short Questions and Problems – 84 Points Total B-1 (8 Points) Starting at rest, a car accelerated in the +X direction for 2.0 seconds with an acceleration of +a. It continued for an additional 8.0 seconds with an acceleration of +a/2 in the +X direction, reaching a final speed of 30 m/s. How far did the car travel in the total time of 10.0 seconds? Answer: _____________________ units ________ B-2 (6 Points) Jack threw a ball straight up into the air and caught it some time later. It reached a maximum height of 19.6 meters above the height of his hand. Assuming he caught it at the same height he released it, how long was it in the air? Use g = 9.8 m/s2 and neglect air resistance. Answer: _____________________ units ________ B-3 (4 Points) _______ A) B) C) D) Jack threw a ball straight up into the air and caught it. He then threw it a second time to his sister, Jill, who was standing some distance away. The ball reached the same maximum height both times. Jack and Jill both caught the ball at the same height above the ground. Compared to the first throw, how long was the ball in the air on the second throw? Neglect air resistance. It was in the air for less time on the second throw. It was in the air for the same time on the second throw. It was in the air for more time on the second throw. There is not enough information to answer this question. 4 Name ________________________________________________________________________ B-4 (8 Points) A block of mass 2.0 kg moving on a horizontal surface starts with a velocity of 5.0 m/s in the +X direction and 0.0 m/s in the +Y direction. It experiences a net impulse of 18.0 N s in the –X direction and 6.0 N s in the +Y direction. What is the velocity of the block after the impulse? X Component: _____________________ units ________ Y Component: _____________________ units ________ B-5 (8 Points) A block of unknown mass on a horizontal surface experiences a constant force of 8 N in the +X direction and 6 N in the –Y direction. It moves from X = 2 m, Y = –2 m to X = 5 m, Y = 2 m. How much work does the force do on the block during the move? Answer: _____________________ units ________ 5 Name ________________________________________________________________________ B-6 (10 Points) A hockey puck (Puck A) sliding on frictionless ice initially at 12 m/s collided with two other pucks of the same mass initially at rest (Pucks B and C). What is the speed of the center of mass of the system consisting of Pucks A, B, and C after the collision? Answer: _____________________ units ________ B-7 (6 Points) A wheel initially spinning at 10 rev/s took 100 revolutions to come to a stop. What was the magnitude of its angular acceleration assuming it was constant? Answer: _____________________ units ________ 6 Name ________________________________________________________________________ B-8 (6 Points) A rod with a mass of 0.60 kg and a length of 0.50 meters has two 0.50 kg masses attached, one at each end. It is rotating about its center. What is the rotational inertia of the system consisting of the rod and the two attached masses? The rotational inertia of the rod is 121 M L2 . center of rotation 0.50 meters Answer: _____________________ units ________ B-9 (12 Points) An ice skater began a spin with her arms out. Her rotational inertia was 1.25 kg m2 and her angular speed was 12.0 rad/s. She changed her rotational inertia to 0.75 kg m2 by pulling her arms in. How much work did the skater do while pulling her arms in? Neglect the friction of her ice skates on the ice and neglect air resistance. Answer: _____________________ units ________ 7 Name ________________________________________________________________________ B-10 (8 Points) An electron is traveling in a vacuum tube at 5.6 x 10+6 m/s in a horizontal direction toward the south. There is a constant magnetic field in the tube with a magnitude of 2.5 x 10–4 T. The direction of the magnetic field is 30º from vertical toward the north, as shown. What is the magnitude of the magnetic force on the electron? B Up 30° v S N -e Down Answer: _____________________ units ________ B-11 (8 Points) An ion with the same charge as a proton but unknown mass is moving in a circular path in a magnetic field. The magnetic field is 1.0 T at a right angle to the path of the ion and the radius of the path of the ion is 0.5 meters. What is the magnitude of the linear momentum of the ion? Answer: _____________________ units ________ 8 Name ________________________________________________________________________ B-12 (14 Points) Concept and Equation Matching In this question, you will match important concepts in Physics I will their corresponding equations on the Formula Sheet. In each case, you will pick the equation number that best exemplifies the concept. In some cases, there are two equations with the same number, like 48a and 48b. In that case, we want only the number and we will assume you mean either or both of the equations as appropriate for the correct answer. Example: (You would put “1” as the correct equation from the sheet for this concept.) 1 Relationship of Time Interval and Change of Velocity for Constant Acceleration ____ The Impulse-Momentum Theorem ____ The Work-Kinetic Energy Theorem ____ Change in Mechanical Energy from Non-Conservative Forces ____ Potential Energy of an Ideal Spring ____ Newton’s 2nd Law of Motion ____ Newton’s Law of Universal Gravitation ____ Coulomb’s Law ____ The Magnetic or Lorentz Force on a Moving Charged Particle ____ Finding the Scalar or Dot Product of Two Vectors ____ Finding the Vector or Cross Product (Magnitude) of Two Vectors ____ Collision in Two Dimensions with Conservation of Momentum ____ Elastic Collision in One Dimension ____ Definition of Torque ____ Definition of Angular Momentum for a Particle 9 Name ________________________________________________________________________ Part C – Extended Problems – 88 Points Total C-1 (16 points) A toy gun fires a plastic pellet with a mass of 0.5 g. The pellet is propelled by a spring with a spring constant of 1.25 N/cm which is compressed 2.0 cm before firing. The plastic pellet travels horizontally 10 cm down the barrel (from its compressed position) with a constant friction force of 0.0475 N opposing the motion of the pellet. k = 1.25 N/cm d = 10 cm travel x = 2 cm compression The toy gun is held 1.0 m above the floor. How far does the pellet go horizontally from the point it leaves the barrel until it hits the floor? Use g = 9.8 m/s2 and neglect air resistance. Answer: _____________________ units ________ 10 Name ________________________________________________________________________ C-2 (16 points) A small ball of mass 300 g is given a charge of +2.0 x 10–3 C. It is suspended by a nearly massless string in an electric field of 735 V/m in the horizontal direction. The only forces on the ball are the electric force, gravity, and string tension. The ball is at rest in equilibrium. What is the angle of the string with respect to vertical (shown as )? Treat the ball as a point mass and charge. Use g = 9.8 m/s2. Answer: _____________________ units ________ 11 Name ________________________________________________________________________ C-3 (4 points) For questions C-3, C-4, and C-5, we will refer to the two-particle system shown below. It consists of an electron and a positron. A positron has the same mass as an electron but a positive charge (+e). The center of mass of the electron-positron system is located at (0,0) and the center of mass is not moving. At the instant shown in the figure below, the location of the electron is (4.0 x 10–12 , 3.0 x 10–12) m and its velocity is 6.0 x 10+6 m/s in the +X direction. electron Y 6.0 x 10+6 m/s Location: (4.0 x 10–12 , 3.0 x 10–12) m X Center of Mass (not moving) location = ? velocity = ? positron Important Note: In C-3 and C-4, if you think you can write down the answer without doing a calculation with equations, state why in a complete sentence. First question: What is the location of the positron at the instant shown above? X Coordinate: _________________________ m Y Coordinate: _________________________ m C-4 (4 points) What is the velocity of the positron at the instant shown above? X Component: _________________________ m/s Y Component: _________________________ m/s 12 Name ________________________________________________________________________ C-5 (16 points) What is the angular momentum of the electron about the center of mass? Give all 3 components. (Note: The +Z axis is out of the page in the diagram on page 11.) Angular Momentum: X Component: ___________________ units ________ Y Component: ___________________ units ________ Z Component: ___________________ units ________ 13 Name ________________________________________________________________________ C-6 (18 points) The figure below shows two charged spheres, A and B. Sphere A is directly above sphere B. The initial distance between their centers is d = 4.0 cm. Sphere A has a weight: W = 0.90 N. Both have the same charge: q = 2.0 x 10–6 C. Initially, both spheres are held in place. Then sphere A is released while sphere B remains held in place. Neglecting air resistance, treating the spheres as point charges, considering only the electric and gravitational forces on sphere A, and assuming only vertical motion, what is the maximum height of sphere A above the height of sphere B after being released? Do not try to use “F = m a” to solve the problem. ax bx c 0 x 2 force of gravity A b b2 4 a c 2a d = 4.0 cm B Maximum Height: ___________________ units ________ 14 Name ________________________________________________________________________ Formula Sheet for Exam 3 and Final – Page 1 of 2 1. v v 0 a t t 0 21. 2. x x 0 v 0 ( t t 0 ) 12 a ( t t 0 ) 2 K 12 m v 2 12 m (v x v y ) 22. 3. x x 0 12 ( v0 v)( t t 0 ) 23. K f K i Wnet U Fcons dx 4. x x 0 v( t t 0 ) 12 a ( t t 0 ) 2 24. U g m g (y y 0 ) 25. U s 12 k ( x x 0 ) 2 26. 27. 28. K U Wnoncons s r v tangential r a tangential r 2 2 6. v 2 v 02 2a x x 0 F Fnet m a 7. T 8. a centripetal 29. 30. 0 t t 0 Fcentripetal p mv dp F Fnet d t J Fnet dt p P pi dP Fext dt 31. 0 0 ( t t 0 ) 12 ( t t 0 ) 2 32. 0 12 (0 )( t t 0 ) 33. 0 ( t t 0 ) 12 ( t t 0 ) 2 M mi 38. 5. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 2r v v2 2 r r v2 m m 2 r r 35. 2 02 2 0 a b a b sin( ) 36. I m i ri 34. 37. 39. 1 1 x cm m i x i y cm m i y i M M P M v cm a b a b cos() a x b x a y b y W Fd W F dx 40. 41. 42. 43. 44x. m1 v1, x ,before m 2 v 2, x ,before m1 v1, x ,after m 2 v 2, x ,after 44y. m1 v1, y ,before m 2 v 2, y ,before m1 v1, y ,after m 2 v 2, y,after m1 m 2 2 m2 v1,i v 2 ,i m1 m 2 m1 m 2 2 m1 m m1 v1,i 2 v 2 ,i m1 m 2 m1 m 2 45a. v1,f 45b. v 2,f 15 2 K rot 12 I 2 W d r F dL I d t l r p L l i L I Name ________________________________________________________________________ Formula Sheet for Exam 3 and Final – Page 2 of 2 m m 46a. | F | G 1 2 2 r m m 46b. F G 1 2 2 r̂ r 1 | q1 || q 2 | 47a. | F | 4 0 r2 1 q1 q 2 47b. F (r̂ ) 4 0 r 2 1 | qi | 48a. | E i | 4 0 ri 2 1 qi (r̂i ) 48b. E 4 0 ri 2 49. F q E 50. 51. 52. 1 qi 4 0 ri U qV V E dx V V x V 53y. E y y 54. F q v B mv 55. r qB 53x. E x Useful Constants (You can use the approximate values on tests.) Universal Gravitation Constant G 6.67310 11 N m 2 kg 2 6.67 10 11 Electrostatic Force Constant 1 8.987551788 10 9 N m 2 C 2 9.0 10 9 4 0 Magnetic Constant 0 4 10 7 H m 1 1.26 10 6 Speed of Light in Vacuum c 2.99792458 10 8 m s 1 3.010 8 Charge of a Proton e 1.602176462 10 19 C 1.6 10 19 Electron-Volt Conversion Constant 1eV 1.602176462 10 19 J 1.6 10 19 Mass of a Proton m p 1.6726215810 27 kg 1.67 10 27 Mass of an Electron m e 9.10938188 10 31 kg 9.110 31 16