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CA M O S U N C O L L E G E PHYSICS DEPARTMENT Physics 115 Final Exam April 2008 Instructor: Julie Alexander Name _______________________ Show all of your work A single 8.5”X11” sheet of paper, handwritten on one side only is permitted. Total marks 100: (34 for long answers and 3 each for 22 multiple choice) 1) An amusement park ride consists of a rotating circular platform 8.00 m in diameter from which 10.0-kg seats are suspended at the end of 2.50-m massless chains as shown below. When the system rotates, the chains make an angle = 32.0 with the vertical. (a) What is the speed of each seat? (4 marks) Physics 115 Final Exam 2) A force F 4x iˆ 3y ˆj N 2 acts on an object as the object moves in the x direction from the origin to x = 8.00 m. Find the work done on the object by the force. (3 marks) 3) A toy cannon uses a spring to project a 5.60-g soft rubber ball. The spring is originally compressed by 5.10 cm and has a force constant of 8.00 N/m. When it is fired, the ball moves 15.0 cm through the horizontal barrel of the cannon, and there is a constant friction force of 0.032 0 N between the barrel and the ball. (a) With what speed does the ball leave the barrel of the cannon? (3 marks) (b) What is the maximum speed of the ball while it is still in the barrel? (3 marks) Physics 115 Final Exam 3 4) A billiard ball moving at 5.40 m/s strikes a stationary ball of the same mass. After the collision, the first ball moves at 4.33 m/s, at an angle of 30.0° with respect to the original line of motion. Assuming an elastic collision (and ignoring friction and rotational motion), find the struck ball's velocity after the collision.(4 marks) 5) A 10 000-N shark is supported by a cable attached to a 4.80-m rod that can pivot at the base. a) Calculate the tension in the tie-rope between the rod and the wall if it is holding the system in the position as shown below. (Neglect the weight of the rod.) (3 marks) b) Find the magnitude of the reaction force at the pivot. (3 marks) Physics 115 Final Exam 4 6) A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is 2.00 cm and the frequency is 1.50 Hz. a)Determine the maximum speed and the earliest time (t > 0) at which the particle has this speed, (3 marks) (c) the total distance traveled between t = 0 and t = 1.00 s.(3 marks) 7) A charged cork ball of mass 1.20 g is suspended on a light string in the presence of a uniform electric field as shown below. When E 3.00iˆ 5.00 ˆj 10 N / C , the ball is in equilibrium at θ=40o. a) Find the charge on the ball. (5 marks) 5 Physics 115 Final Exam 5 Answer sheet for Multiple Choice Problems (Please use lower case letters for your answers) 1. __________________ 2. __________________ 3. __________________ 4. __________________ 5. __________________ 6. __________________ 7. __________________ 8. __________________ 9. __________________ 10. __________________ 11. __________________ 12. __________________ 13. ___________________ 14. ___________________ 15. __________________ 16. ___________________ 17. ___________________ 18. ___________________ 19. ___________________ 20. ___________________ 21. ___________________ 22. ___________________ Physics 115 Final Exam 6 Physics 115 Final Exam. Write your answers on the answer sheet provided with the long answers. ____ 1. An object attached to the end of a string swings in a vertical circle (R = 1.2 m), as shown. At an instant when = 30, the speed of the object is 5.1 m/s and the tension in the string has a magnitude of 20 N. What is the mass of the object? a. b. c. d. e. 2.0 kg 1.5 kg 1.8 kg 1.2 kg 0.80 kg ____ 2. A race car traveling at 100 m/s enters an unbanked turn of 400 m radius. The coefficient of (static) friction between the tires and the track is 1.1. The track has both an inner and an outer wall. Which statement is correct? a. The race car will crash into the outer wall. b. The race car will crash into the inner wall. c. The car will stay in the center of the track. d. The car will stay in the center of the track if the driver speeds up. e. The car would stay in the center of the track if the radius were reduced to 200 m. ____ 3. A 2.0-kg projectile moves from its initial position to a point that is displaced 20 m horizontally and 15 m above its initial position. How much work is done by the gravitational force on the projectile? a. +0.29 kJ b. 0.29 kJ c. +30 J d. 30 J e. 50 J ____ Physics 115 Final Exam 7 4. The only force acting on a 1.6-kg body as it moves along the x axis is given in the figure. If the velocity of the body at x = 2.0 m is 5.0 m/s, what is its kinetic energy at x = 5.0 m? a. b. c. d. e. 52 J 44 J 36 J 60 J 25 J ____ 5. A 2.0-kg mass swings at the end of a light string (length = 3.0 m). Its speed at the lowest point on its circular path is 6.0 m/s. What is its kinetic energy at an instant when the string makes an angle of 50 with the vertical? a. 21 J b. 15 J c. 28 J d. 36 J e. 23 J ____ 6. A 1.0-kg block is released from rest at the top of a frictionless incline that makes an angle of 37 with the horizontal. An unknown distance down the incline from the point of release, there is a spring with k = 200 N/m. It is observed that the mass is brought momentarily to rest after compressing the spring 0.20 m. How far does the mass slide from the point of release until it is brought momentarily to rest? a. 0.98 m b. 0.68 m c. 0.82 m d. 0.55 m e. 0.20 m 7. A 1.5-kg playground ball is moving with a velocity of 3.0 m/s directed 30 below the horizontal just before it strikes a horizontal surface. The ball leaves this surface 0.50 s later with a velocity of 2.0 m/s directed 60 above the horizontal. What is the magnitude of the average resultant force on the ball? a. 14 N b. 11 N c. 18 N d. 22 N e. 3.0 N ____ Physics 115 Final Exam ____ 8. A 10-g bullet moving 1000 m/s strikes and passes through a 2.0-kg block initially at rest, as shown. The bullet emerges from the block with a speed of 400 m/s. To what maximum height will the block rise above its initial position? a. b. c. d. e. ____ 8 78 cm 66 cm 56 cm 46 cm 37 cm 9. A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval the angular velocity decreases to 10 rad/s. Assume that the angular acceleration is constant during the 5.0-s interval. How many radians does the wheel turn through during the 5.0-s interval? a. 95 rad b. 85 rad c. 65 rad d. 75 rad e. 125 rad ____ 10. A wheel (radius = 0.20 m) is mounted on a frictionless, horizontal axis. A light cord wrapped around the wheel supports a 0.50-kg object, as shown in the figure. When released from rest the object falls with a downward acceleration of 5.0 m/s2. What is the moment of inertia of the wheel? a. b. c. d. e. 0.023 kg m2 0.027 kg m2 0.016 kg m2 0.019 kg m2 0.032 kg m2 Physics 115 Final Exam 9 ____ 11. Particles (mass of each = 0.40 kg) are placed at the 60-cm and 100-cm marks of a meter stick of negligible mass. This rigid body is free to rotate about a frictionless pivot at the 0-cm end. The body is released from rest in the horizontal position. What is the magnitude of the initial linear acceleration of the end of the body opposite the pivot? a. 15 m/s2 b. 9.8 m/s2 c. 5.8 m/s2 d. 12 m/s2 e. 4.7 m/s2 ____ 12. A uniform ladder 15 ft long is leaning against a frictionless wall at an angle of 53 above the horizontal. The weight of the ladder is 30 pounds. A 75-lb boy climbs 6.0-ft up the ladder. What is the magnitude of the friction force exerted on the ladder by the floor? a. 43 lb b. 34 lb c. 38 lb d. 47 lb e. 24 lb ____ 13. A uniform 100-lb beam is held in a vertical position by a pin at its lower end and a cable at its upper end. A horizontal force (magnitude P) acts as shown in the figure. If P = 75 lb, what is the tension in the cable? a. b. c. d. e. 54 lb 69 lb 47 lb 61 lb 75 lb ____ 14. The motion of a particle connected to a spring is described by x = 10 sin (t). At what time (in s) is the potential energy equal to the kinetic energy? a. 0 b. 0.25 c. 0.50 d. 0.79 e. 1.0 Physics 115 Final Exam 10 ____ 15. The amplitude of a system moving with simple harmonic motion is doubled. The total energy will then be a. 4 times larger b. 3 times larger c. 2 times larger d. the same as it was e. half as much ____ 16. A 40-C charge is positioned on the x axis at x = 4.0 cm. Where should a 60-C charge be placed to produce a net electric field of zero at the origin? a. 5.3 cm b. 5.7 cm c. 4.9 cm d. 6.0 cm e. +6.0 cm ____ 17. A uniform linear charge density of 7.0 nC/m is distributed along the y axis from y = 2 m to y = 5 m. Which of the following integrals is correct for the magnitude (in N/C) of the electric field at y = 0 on the y axis? a. b. c. d. e. none of these ____ 18. A particle (m = 2.0 g, q = 5.0 nC) has a speed of 30 m/s at point A and moves (with only electric forces acting on it) to point B where its speed is 80 m/s. Determine the electric potential difference VA VB. a. 2.2 kV b. +1.1 kV c. 1.1 kV d. +2.2 kV e. +1.3 kV Physics 115 Final Exam 11 ____ 19. A particle (charge = 40 C) moves directly toward a second particle (charge = 80 C) which is held in a fixed position. At an instant when the distance between the two particles is 2.0 m, the kinetic energy of the moving particle is 16 J. Determine the distance separating the two particles when the moving particle is momentarily stopped. a. 0.75 m b. 0.84 m c. 0.95 m d. 0.68 m e. 0.56 m ____ 20. A particle (q = 5.0 nC, m = 3.0 g) moves in a region where the magnetic field has components Bx = 2.0 mT, By = 3.0 mT, and Bz = 4.0 mT. At an instant when the speed of the particle is 5.0 km/s and the direction of its velocity is 120 relative to the magnetic field, what is the magnitude of the acceleration of the particle? a. 33 m/s2 b. 17 m/s2 c. 39 m/s2 d. 25 m/s2 e. 45 m/s2 ____ 21. A straight wire is bent into the shape shown. Determine the net magnetic force on the wire when the current I travels in the direction shown in the magnetic field B. a. b. c. d. e. 2IBL in the z direction 2IBL in the +z direction 4IBL in the +z direction 4IBL in the z direction zero ____ 22. A proton is accelerated from rest through a potential difference of 150 V. It then enters a region of uniform magnetic field and moves in a circular path (radius = 12 cm). What is the magnitude of the magnetic field in this region? a. 18 mT b. 12 mT c. 15 mT d. 22 mT e. 10 mT