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### ch08

Course: PHYSICS 108, Spring 2008
School: SUNY Buffalo
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Word Count: 3750

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8: POTENTIAL Chapter ENERGY AND CONSERVATION OF ENERGY 1. Only if a force on a particle is conservative: A. is its work zero when the particle moves exactly once around any closed path B. is its work always equal to the change in the kinetic energy of the particle C. does it obey Newton's second law D. does it obey Newton's third law E. is it not a frictional force ans: A 2. A nonconservative force: A. violates...

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8: POTENTIAL Chapter ENERGY AND CONSERVATION OF ENERGY 1. Only if a force on a particle is conservative: A. is its work zero when the particle moves exactly once around any closed path B. is its work always equal to the change in the kinetic energy of the particle C. does it obey Newton's second law D. does it obey Newton's third law E. is it not a frictional force ans: A 2. A nonconservative force: A. violates Newton's second law B. violates Newton's third law C. cannot do any work D. must be perpendicular to the velocity of the particle on which it acts E. none of the above ans: E 3. The sum of the kinetic and potential energies of a system of objects is conserved: A. only when no external force acts on the objects B. only when the objects move along closed paths C. only when the work done by the resultant external force is zero D. always E. none of the above ans: E 4. A force on a particle is conservative if: A. its work equals the change in the kinetic energy of the particle B. it obeys Newton's second law C. it obeys Newton's third law D. its work depends on the end points of every motion, not on the path between E. it is not a frictional force ans: D 5. Two particles interact by conservative forces. In addition, an external force acts on each particle. They complete round trips, ending at the points where they started. Which of the following must have the same values at the beginning and end of this trip? A. the total kinetic energy of the two-particle system B. the potential energy of the two-particle system C. the mechanical energy of the two-particle system D. the total linear momentum of the two-particle system E. none of the above ans: B 102 Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 6. Two objects interact with each other and with no other objects. Initially object A has a speed of 5 m/s and object B has a speed of 10 m/s. In the course of their motion they return to their initial positions. Then A has a speed of 4 m/s and B has a speed of 7 m/s. We can conclude: A. the potential energy changed from the beginning to the end of the trip B. mechanical energy was increased by nonconservative forces C. mechanical energy was decreased by nonconservative forces D. mechanical energy was increased by conservative forces E. mechanical energy was decreased by conservative forces ans: C 7. A good example of kinetic energy is provided by: A. a wound clock spring B. the raised weights of a grandfather's clock C. a tornado D. a gallon of gasoline E. an automobile storage battery ans: C 8. No A. B. C. D. E. kinetic energy is possessed by: a shooting star a rotating propeller on a moving airplane a pendulum at the bottom of its swing an elevator standing at the fifth floor a cyclone ans: D 9. The wound spring of a clock possesses: A. kinetic but no potential energy B. potential but no kinetic energy C. both potential and kinetic energy in equal amounts D. neither potential nor kinetic energy E. both potential and kinetic energy, but more kinetic energy than potential energy ans: B 10. A body at rest in a system is capable of doing work if: A. the potential energy of the system is positive B. the potential energy of the system is negative C. it is free to move in such a way as to decrease its kinetic energy D. it is free to move in such a way as to decrease the potential energy of the system E. it is free to move in such a way as to increase the potential energy of the system ans: D Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 103 11. Which one of the following five quantities CANNOT be used as a unit of potential energy? A. wattsecond B. gramcm/s2 C. joule D. kgm2 /s2 E. ftlb ans: B 12. Suppose that the fundamental dimensions are taken to be: force (F), velocity (V) and time (T). The dimensions of potential energy are then: A. F/T B. FVT C. FV/T D. F/T2 E. FV2 /T2 ans: B 13. The graphs below show the magnitude of the force on a particle as the particle moves along the positive x axis from the origin to x = x1 . The force is parallel to the x axis and is conservative. The maximum magnitude F1 has the same value for all graphs. Rank the situations according to the change in the potential energy associated with the force, least (or most negative) to greatest (or most positive). F F1 ........ .. ...... ...... ..... .. ...... .... x1 x F ...................... F1 ...................... . . . . . . . . . . . . . x1 x F x1 ... ...... x ...... .... ...... ...... .. F1 .... 3 1 A. B. C. D. E. 1, 2, 3 1, 3, 2 2, 3, 1 3, 2, 1 2, 1, 3 ans: E 2 104 Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 14. A golf ball is struck by a golf club and falls on a green three meters above the tee. The potential energy of the Earth-ball system is greatest: A. just before the ball is struck B. just after the ball is struck C. just after the ball lands on the green D. when the ball comes to rest on the green E. when the ball reaches the highest point in its flight ans: E 15. A ball is held at a height H above a floor. It is then released and falls to the floor. If air resistance can be ignored, which of the five graphs below correctly gives the mechanical energy E of the Earth-ball system as a function of the altitude y of the ball? y . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. .. .. .. .. .. .. .. .. .. .. .. H 0 E . .. . .. .... . .. . .. ... . .. ... .. ... ... . y H C E ..... . ....... ..... ... ... ... .. .. .. .. .. .. . y H A E E .. .... ... .... ... ... ... ... ... .... ... ... . y H B E ans: E .. .. . .. ... ... ... ..... ......... ... y H D ...................... ..................... H E y 16. A 6.0-kg block is released from rest 80 m above the ground. When it has fallen 60 m its kinetic energy is approximately: A. 4800 J B. 3500 J C. 1200 J D. 120 J E. 60 J ans: B Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 105 17. A 2-kg block is thrown upward from a point 20 m above Earth's surface. At what height above Earth's surface will the gravitational potential energy of the Earth-block system have increased by 500 J? A. 5 m B. 25 m C. 46 m D. 70 m E. 270 m ans: C 18. An I. II. III. IV. V. A. B. C. D. E. elevator is rising at constant speed. Consider the following statements: the upward cable force is constant the kinetic energy of the elevator is constant the gravitational potential energy of the Earth-elevator system is constant the acceleration of the elevator is zero the mechanical energy of the Earth-elevator system is constant all five are true only II and V are true only IV and V are true only I, II, and III are true only I, II, and IV are true ans: E 19. A projectile of mass 0.50 kg is fired with an initial speed of 10 m/s at an angle of 60 above the horizontal. The potential energy of the projectile-Earth system (relative potential energy when the projectile is at ground level) is: A. 25 J B. 18.75 J C. 12.5 J D. 6.25 J E. none of these ans: B 20. For a block of mass m to slide without friction up the rise of height h shown, it must have a minimum initial kinetic energy of: v . ................................. .................................. . ..... . .... .. . ... ... . . ... .. . . .. .. . .. . . .. . . .. . .. . .. . . ... ... ... . .. . . ..... ..... .. . .. .................... .................... . ... .... .............................................................................. ............................................................................. m h A. B. C. D. E. gh mgh gh/2 mgh/2 2mgh ans: B 106 Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 21. A 2.2-kg block starts from rest on a rough inclined plane that makes an angle of 25 with the horizontal. The coefficient of kinetic friction is 0.25. As the block goes 2.0 m down the plane, the mechanical energy of the Earth-block system changes by: A. 0 B. -9.8 J C. 9.8 J D. -18 J E. 18 J ans: B 22. A simple pendulum consists of a 2.0-kg mass attached to a string. It is released from rest at X as shown. Its speed at the lowest point Y is about: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... .... .... .... .... ..... ..... ....... ... ....... ... ............................. ... ......... .................. .. .... ... .... .... .... .... .... .... ... .... X . . . . . . . . ... . ... ........ ....... .. .. . . . . . . . . ..... . ... . . .. . . 1.85 m . . . . . . ... .... . . . . . . . . . Y A. B. C. D. E. 0.90 m/s 3.6 m/s 3.6 m/s 6.0 m/s 36 m/s ans: D 23. The long pendulum shown is drawn aside until the ball has risen 0.50 m. It is then given an initial speed of 3.0 m/s. The speed of the ball at its lowest position is: . . . . . . . . . . . . . . . . . . . . . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... .... .... .... .... ..... ..... ....... ....... ........................... ........................... .... ... .... .... .... .... .... .... ... .... . . . . ... . . ... .... .... ... .. . . . ... ...... ...... ... ... . . . . . . . . .... . .... . . .. . . 0.5 m . . . .. .. .... . .. . . . . . . . . . A. B. C. D. E. zero 0.89 m/s 3.1 m/s 3.7 m/s 4.3 m/s ans: E Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 107 24. A particle moves along the x axis under the influence of a stationary object. The net force on 3 the particle is given by F = (8 N/m )x3 . If the potential energy is taken to be zero for x = 0 then the potential energy is given by: 4 A. (2 J/m )x4 B. (-2 J/m4 )x4 C. (24 J/m2 x2 2 D. (-24 J/m )x2 4 E. 5 J - (2 J/m )x4 ans: B 25. A 0.20-kg particle moves along the x axis under the influence of a stationary object. The potential energy is given by U (x) = (8.0 J/m )x2 + (2.0 J/m )x4 , where x is in coordinate of the particle. If the particle has a speed of 5.0 m/s when it is at x = 1.0 m, its speed when it is at the origin is: A. 0 B. 2.5 m/s C. 5.7 m/s D. 7.9 m/s E. 11 m/s ans: E 26. Which of the five graphs correctly shows the potential energy of a spring as a function of its elongation x? U ...................... ..................... U .. ... .... .. .... .. .... . .. ... . .. ... . . B U ........... .. .... . ... .. .. . . .. .. . D U. .. .. .. ... ... .... ... ... ..... ......... .. E U . .. . .. .. .. ... . .. ... ...... ...... . .. C 2 4 x A x x x x ans: C 108 Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 27. A force of 10 N holds an ideal spring with a 20-N/m spring constant in compression. The potential energy stored in the spring is: A. 0.5 J B. 2.5 J C. 5 J D. 10 J E. 200 J ans: B 28. An ideal spring is used to fire a 15.0-g pellet horizontally. The spring has a spring constant of 20 N/m and is initially compressed by 7.0 cm. The kinetic energy of the pellet as it leaves the spring is: A. zero B. 2.5 10-2 J C. 4.9 10-2 J D. 9.8 10-2 J E. 1.4 J ans: C 29. A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface. The total mechanical energy is 0.12 J. The greatest extension of the spring from its equilibrium length is: A. 1.5 10-3 m B. 3.0 10-3 m C. 0.039 m D. 0.054 m E. 18 m ans: D 30. A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface. The total mechanical energy is 0.12 J. The greatest speed of the block is: A. 0.15 m/s B. 0.24 m/s C. 0.49 m/s D. 0.69 m/s E. 1.46 m/s ans: D 31. A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface. When the spring is 4.0 cm longer than its equilibrium length, the speed of the block is 0.50 m/s. The greatest speed of the block is: A. 0.23 m/s B. 0.32 m/s C. 0.55 m/s D. 0.71 m/s E. 0.93 m/s ans: D Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 109 32. A 0.5-kg block slides along a horizontal frictionless surface at 2 m/s. It is brought to rest by compressing a very long spring of spring constant 800 N/m. The maximum spring compression is: A. 0 B. 3 cm C. 5 cm D. 80 cm E. 80 m ans: C 33. A block of mass m is initially moving to the right on a horizontal frictionless surface at a speed v. It then compresses a spring of spring constant k. At the instant when the kinetic energy of the block is equal to the potential energy of the spring, the spring is compressed a distance of: A. v m/2k B. (1/2)mv2 C. (1/4)mv2 D. mv2 /4k E. (1/4) mv/k ans: A 34. A 700-N man jumps out of a window into a fire net 10 m below. The net stretches 2 m before bringing the man to rest and tossing him back into the air. The maximum potential energy of the net, compared to its unstretched potential energy, is: A. 300 J B. 710 J C. 850 J D. 7000 J E. 8400 J ans: E 35. A toy cork gun contains a spring whose spring constant is 10.0 N/m. The spring is compressed 5.00 cm and then used to propel a 6.00-g cork. The cork, however, sticks to the spring for 1.00 cm beyond its unstretched length before separation occurs. The muzzle velocity of this cork is: .... .... .. .... .... .... ... ... .... . .... ... . ..... .... .. .... . . .... ... .... .. . . . . .... ..... .. ... . ............................................................................... ... ......... ................................................................... .. ........ ... .. .. . .. . . .. ......................... . . . . .. . . ............... . ............ ............ .......................... ................................. .. .. .. .................... .. ................ . . .... .. .. ... . . . ... .............. ....... ........ ... ........ . ... .. ...... .. .. .. .. .. .. .. . . .. . ............... ...... ... . .. .. .. . . .. . .. . . .. . . . .. . . . .. .. .. .. .. .. .. .. .. .. .. . . ...... . .. . . . . .. .. . . .. . . .. .. . . . . . .. . . . . .. . ... .. . . .. . . . .. .. . . . . . . .. .... .... .. . .. .. .. .. .. .. .. .. .. .. .. . . . .. ..... .. ............ .. ... .................. .. . ... .... . . . . . . . . . . . . ............... .. . . .. . ........................................................................................................... . ............... ........... .... .......... .. ............................................................ . . . .. . . . . . . . . . . .. . . . . . .. .. . . . . . . . . . . .. .. .. .. .. . .. .. .. .. . ........ ....... .... .... ....... . . ............ ........... . .... ..... . . . ..... . ..... . ...... . ...... . ..... . . ....... . . .... . ... . .. ... . spring cork . . ... .. .. . . . .. . . . . . . . . .. . .. .. A. B. C. D. E. 1.02 m/s 1.41 m/s 2.00 m/s 2.04 m/s 4.00 ans: m/s C 110 Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 36. A small object of mass m, on the end of a light cord, is held horizontally at a distance r from a fixed support as shown. The object is then released. What is the tension force of the cord when the object is at the lowest point of its swing? . . . . . . . . . . . . . . . . . . . . . . . .. . .. . . .. .. .. .. ... .. ... ... .... .... ..... . .... ... ..... ... . .... . ... ... ... ...... .. ................... ...... ...... r ... ......................... m . . A. B. C. D. E. mg/2 mg 2mg 3mg mgr ans: D 37. The string in the figure is 50 cm long. When the ball is released from rest, it swings along the dotted arc. How fast is it going at the lowest point in its swing? . . . . . . . . . . .. .. .. ..... .... .... ... .. 50 cm... ........................ ... . .. . . ... .... ... ... .... .... ... ... . . .. .. . .. .... ... ... A. B. C. D. E. 2.0 m/s 2.2 m/s 3.1 m/s 4.4 m/s 6.0 m/s ans: C 38. A block is released from rest at point P and slides along the frictionless track shown. At point Q, its speed is: P ........................... ..... ... | ... | ... Q ... ............ ... h1 | ........ ............ .. ...... ..... ................. | ..... h2 | . . . . . . . . . . . . . . . . . . . | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ground level A. B. C. D. E. 2g h1 - h2 2g(h1 - h2 ) (h1 - h2 )/2g 2g(h1 - h2 ) (h1 - h2 )2 /2g ans: D Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 111 39. A small object of mass m starts from rest at the position shown and slides along the frictionless loop-the-loop track of radius R. What is the smallest value of y such that the object will slide without losing contact with the track? ... . ..... . . . .. ..... .. ...... . . ... . .. . ... ... . .... . ...... ... ...... . .. . .. ...... ... ...... .. .. . ...... ..... ... ... ... ... ... ... ... ... ..... ..... ..... . ... ... . ..... ........ .. ..... ... . .. ... ... ... ... ... .... . ... . ... .. . . .. . .. ... .. ... ... . . . .. ... . ... .. .. . ... . . . ... . .. ... .. ... . .. .. .. . . . ... .. . ... . . .. . ... . . .. .. .. . . . .. ....... ...... . ... . . . . .. . . . ... .. ... . ... . .... .... . .... ... .. . . . .... .... .. . .. .... ..... .. .. .. ..... .. ..... .. ...... ... ....... ..... . ............... .. .. ... ............................................................................ ..................................................................... . .... . .. . .. .. .. .. m y R A. B. C. D. E. R/4 R/2 R 2R zero ans: B 40. A small object slides along the frictionless loop-the-loop with a diameter of 3 m. What minimum speed must it have at the top of the loop? ... ..... .. ..... .. ...... ... .. .. ... ... . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .............. ................ ... .... ... ... ... ... ... ... ... .. ... ... .. ... ... .. .. .. .. ... ... . ... . . .. ... . ... . .... .. . ... . . ... . . . .. .. . .. . . . ....... ....... . . . .. . . .. . .. . ... . ... ... . .... . .... .... .. . . .. .. . . .... .... .. .. . .... .... .. . .. ..... ..... .. .. .. ... ...... ...... ... .............. ... ........... .. . .. ....................................................................... . ... ............ .................................................. . .. . ... . .... .... | 3m | A. B. C. D. E. 1.9 m/s 3.8 m/s 5.4 m/s 15 m/s 29 m/s ans: B 41. A rectangular block is moving along a frictionless path when it encounters the circular loop as shown. The block passes points 1, 2, 3, 4, 1 before returning to the horizontal track. At point 3: ..... .................... . . ........ .......... . .... ... ... . .... . ... ... ... . .. ... .. ..... ... . . ..... ... .. ... .. .. .. .. .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. . . .. .. . .. . .. ...... ...... .. . .. . .. .. ... .. .... ...... ... ...... .... . .... .. .. .. . ... .... . . . .... . ...................................................................................................................... ..................................................................................... ... ............................ .. . . ... . .... ... .... . .... . ... 3 1 2 1 A. B. C. D. E. its mechanical energy is a minimum the forces on it are balanced it is not accelerating its speed is a minimum it experiences a net upward force ans: D Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 112 42. A ball of mass m, at one end of a string of length L, rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. The speed of the ball at the bottom of the circle is: ................. .................. ... .... ... ...... ... ... ... ... .. .. .. .. .. .. .. . .. . . . . . . . . . . . . . . . . . . . . . . . .. . . .... . ... . . . . . . . . . . .. . .. . . .. .. .. .. ... . ... .. . .. . ... ........ ....... . . ... ................. ................ A. B. C. D. E. 2gL 3gL 4gL 5gL 7gL ans: D .. .... L ..... ... . . m 43. A particle is released from rest at the point x = a and moves along the x axis subject to the potential energy function U (x) shown. The particle: U ... .. ... .. ... .. ... ... .. ... .. ... .. ... .. ... ... .... ... .... .. .. . .... .. ... ... .... .. ..... ... ..... .... ..... ....... .......... ......... x a A. B. C. D. E. moves to moves to moves to moves to moves to ans: B b c d e a point to the left of x = e, stops, and remains at rest a point to x = e, then moves to the left infinity at varying speed x = b, where it remains at rest x = e and then to x = d, where it remains at rest 44. The potential energy of a particle moving along the x axis is given by U (x) = (8.0 J/m )x2 + (2.0 J/m )x4 . If the total mechanical energy is 9.0 J, the limits of motion are: A. -0.96 m; +0.96 m B. -2.2 m; +2.2 m C. -1.6 m; +1.6 m D. -0.96 m; +2.2 m E. -0.96 m; +1.6 m ans: A 2 4 Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 113 45. The potential energy of a 0.20-kg particle moving along the x axis is given by U (x) = (8.0 J/m )x2 + (2.0 J/m )x4 . When the particle is at x = 1.0 m it is traveling in the positive x direction with a speed of 5.0 m/s. It next stops momentarily to turn around at x = A. 0 B. -1.1 m C. 1.1 m D. -2.3 m E. 2.3 m ans: C 46. Given a potential energy function U (x), the corresponding force F is in the positive x direction if: A. U is positive B. U is negative C. U is an increasing function of x D. U is a decreasing function of x E. it is impossible to obtain the direction of F from U ans: D 47. As a particle moves along the x axis it is acted upon by a conservative force. The potential energy is shown below as a function of the coordinate x of the particle. Rank the labeled regions according to the magnitude of the force, least to greatest. . . . U (x) . . . .................... ............. .... . ... . . ... . .. . ... . . ... . ... . . .. . ... . ... . .................. ........... A A. B. C. D. E. AB, BC, CD AB, CD, BC BC, CD, AB BC, AB, CD CD, BC, AB ans: D B C D x 2 4 114 Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 48. The first graph shows the potential energy U (x) for a particle moving on the x axis. Which of the other five graphs correctly gives the force F exerted on the particle? U .. parabola . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. ... .. .. .. ... .... .... ... ..... ... x F .. F .. .. .. .. .. .. .. .. .. .. .. .. .. x .. .. .. .. .. .. .. .. .. .. . . C F .. .. . .. .. ... .. .. ... .. .... ..... ......... . ..... x F . . . . .. .. .. . .. . . . ... x .......... .. .. . .. .. .. . . . A .. .... . . ... . ..... ..... ...... x ... ... ... .. . .. . . .. B F. .. .. .. .. .. .. .. .. .. .. .. .. .. x .. .. .. .. .. .. .. .. .. .. .. . D E ans: D Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 115 49. The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis. The points of stable equilibrium are: U .. .. .. . .. ............. .. .. .. .... .. ... .. ... . .. . .. .. ..... .. ...... ........ .. ................... . .. .. ... . .. .. .. .. . ... . .. ... ... .. .. . .. .... .. .. .. .. x a b A. B. C. D. E. only a only b only c only d b and d ans: B c d e 50. The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis. The points of unstable equilibrium are: U .. .. ... . .. ............. .. .. ... ... .. .. .. ... ... . .. .. .. .. .............. ... .. ..................... . .. ... .. .. .. .. . ... .. .. ... ... . . .. .. .. . .... .. .. .. . x a b A. B. C. D. E. only a only b only c only d b and d ans: D c d e 116 Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 51. The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis. Of the labeled points, the points of neutral equilibrium are: U .. .. .. . .. ............. .. .. .. .... .. ... .. ... . .. . .. .. ..... .. ...... ........ .. ................... . .. .. ... . .. .. .. .. . ... . .. ... ... .. .. . .. .... .. .. .. .. x a b A. B. C. D. E. only a only b only c only d b and d ans: C c d e 52. The potential energy of a body of mass m is given by U = -mgx + 1 kx2 . The corresponding 2 force is: A. -mgx2 /2 + kx3 /6 B. mgx2 /2 - kx3 /6 C. -mg + kx/2 D. -mg + kx E. mg - kx ans: E 53. The potential energy of a 0.20-kg particle moving along the x axis is given by U (x) = (8.0 J/m )x2 + (2.0 J/m )x4 . When the particle is at x = 1.0 m the magnitude of its acceleration is: A. 0 B. -8 m/s2 2 C. 8 m/s 2 D. -40 m/s 2 E. 40 m/s ans: D 2 4 Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 117 54. The potential energy for the interaction between the two atoms in a diatomic molecule is U = A/x12 - B/x6 , where A and B are constants and x is the interatomic distance. The magnitude of the force of one atom on the other is: . .. . .. ................................................. F ---- x ----- ----- ---- F . . ......................... ........................ .. .. .... ... A. B. C. D. E. 12A/|x|13 - 6B/|x|7 -13A/|x|13 + 7B/|x|7 -11A/|x|11 + 5B/|x|5 72A/|x|12 - 72B/|x|6 A/|x|13 - B/|x|7 ans: A 55. The thermal energy of a system consisting of a thrown ball, Earth, and the air is most closely associated with: A. the gravitational interaction of Earth and the ball B. the kinetic energy of the ball as a whole C. motions of the individual particles within the ball D. motions of individual particles within the ball and the air E. the kinetic energy of Earth as a whole ans: D 56. Three identical blocks move either on a horizontal surface, up a plane, or down a plane, as shown below. They start with different speeds and continue to move until brought to rest by friction. They all move the same distance. Rank the three situations according to the initial speeds, least to greatest. . .. .. ....... ...... .... .. .... ... . .. ... .... .. ......... ........ . . .... .... .. .. . .. ... .. ..... ... .. . ... . .. .... . .... .... .. .......... . .. .... . . . ........ . . . .... .... . ... . . . ....... . .... .......... . .... . .. .. .... .. .. . .... . . ..... . . . .. .. ..... ... . .. . . .... . . . .. ..... .. . .. .. . .... . . . . ... . . .. . ... . . .. ........ . ........ . . . .. .......... .. ........ . . .. .... .... ..... . . . .. . .... . . .... . .. . .. . .... . . . .... .... . ......... . . ... ...... . . ...... . . .. .. . . . .... . .. . .. v .. . . .............. .............. .. . .. ... ... . v v . . . . . . . . . . . . . . . . . . . . . . . . . .. .. .. .. . . . . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . . . . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . . . . . . . .. .... .. .... ... ... .... .. .. . .... . .... .. ... .. .... ... .... . .. . .. .... . .... .... .. .......... . .... . . .... . ........ .. . .... . . . . ... . . . ....... . .... .......... . .... . .. .. .... .. .. .... . . .... ... . .. .. .... . . . ..... .... . .. ... . . ..... . . . .. . .... . . . .. . ... . . ..... . . ........ . . ...... ... ........ . .... .. . ... ... . .. ............ . ..... .. ... ..... . . .. ...... ...... . . .. . . .... .... . . .... . . ..... . .. . .. . .... . . . .... .... . ......... . . .. ... ..... . . ........ . .. . . . .... . .. . .. (1) A. B. C. D. E. The same for all cases 1, 2, 3 1, then 2 and 3 tie 3, 1, 2 2, 1, 3 ans: D (2) (3) 118 Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 57. Objects A and B interact with each other via both conservative and nonconservative forces. Let KA and KB be the kinetic energies, U be the potential energy, and Eint be the thermal energy. If no external agent does work on the objects then: A. KA + U is conserved B. KA + U + Eint is conserved C. KA + KB + Eint is conserved D. KA + KB + U is conserved E. KA + KB + U + Eint is conserved ans: E 58. A block slides across a rough horizontal table top. The work done by friction changes: A. only the kinetic energy B. only the potential energy C. only the internal energy D. only the kinetic and potential energies E. only the kinetic and internal energies ans: E 59. A 25-g ball is released from rest 80 m above the surface of Earth. During the fall the total internal energy of the ball and air increases by 15 J. Just before it hits the surface its speed is A. 19 m/s B. 36 m/s C. 40 m/s D. 45 m/s E. 53 m/s ans: A 60. A 5-kg projectile is fired over level ground with a velocity of 200 m/s at an angle of 25 above the horizontal. Just before it hits the ground its speed is 150 m/s. Over the entire trip the change in the internal energy of the projectile and air is: A. +19, 000 J B. -19, 000 J C. +44, 000 J D. -44, 000 J E. 0 ans: C 61. A 0.75-kg block slides on a rough horizontal table top. Just before it hits a horizontal ideal spring its speed is 3.5 m/s. It compresses the spring 5.7 cm before coming to rest. If the spring constant is 1200 N/m, the internal energy of the block and the table top must have: A. not changed B. decreased by 1.9 J C. decreased by 2.6 J D. increased by 1.9 J E. increased by 2.6 J ans: C Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 119
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SUNY Buffalo - PHYSICS - 108
Chapter 9:CENTER OF MASS AND LINEAR MOMENTUM1. Which one of the following statements is true? A. the center of mass of an object must lie within the object B. all the mass of an object is actually concentrated at its center of mass C. the center
SUNY Buffalo - PHYSICS - 108
SUNY Buffalo - PHYSICS - 108
Chapter 12:EQUILIBRIUM AND ELASTICITY1. A net torque applied to a rigid object always tends to produce: A. linear acceleration B. rotational equilibrium C. angular acceleration D. rotational inertia E. none of these ans: C 2. The conditions that
SUNY Buffalo - PHYSICS - 108
Chapter 13:GRAVITATION1. In the formula F = Gm1 m2 /r2 , the quantity G: A. depends on the local value of g B. is used only when Earth is one of the two masses C. is greatest at the surface of Earth D. is a universal constant of nature E. is rela
SUNY Buffalo - PHYSICS - 108
Chapter 15:OSCILLATIONS1. In simple harmonic motion, the restoring force must be proportional to the: A. amplitude B. frequency C. velocity D. displacement E. displacement squared ans: D 2. An A. B. C. D. E. oscillatory motion must be simple harm
SUNY Buffalo - PHYSICS - 108
Chapter 16:WAVES I1. For a transverse wave on a string the string displacement is described by y(x, t) = f (x - at), where f is a given function and a is a positive constant. Which of the following does NOT necessarily follow from this statement
SUNY Buffalo - PHYSICS - 108
Chapter 17:1. The speed of a sound wave is determined by: A. its amplitude B. its intensity C. its pitch D. number of harmonics present E. the transmitting medium ans: EWAVES II2. Take the speed of sound to be 340 m/s. A thunder clap is heard a
SUNY Buffalo - PHYSICS - 108
Chapter 19: TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS1. If two objects are in thermal equilibrium with each other: A. they cannot be moving B. they cannot be undergoing an elastic collision C. they cannot have different pressures D. the
SUNY Buffalo - PHYSICS - 108
Chapter 19:THE KINETIC THEORY OF GASES1. Evidence that a gas consists mostly of empty space is the fact that: A. the density of a gas becomes much greater when it is liquefied B. gases exert pressure on the walls of their containers C. gases are
SUNY Buffalo - PHYSICS - 108
Chapter 22:1. An A. B. C. D. E.ELECTRIC FIELDSelectric field is most directly related to: the momentum of a test charge the kinetic energy of a test charge the potential energy of a test charge the force acting on a test charge the charge carrie
SUNY Buffalo - PHYSICS - 108
Chapter 23:GAUSS' LAW1. A total charge of 6.3 10-8 C is distributed uniformly throughout a 2.7-cm radius sphere. The volume charge density is: A. 3.7 10-7 C/m3 3 B. 6.9 10-6 C/m 2 C. 6.9 10-6 C/m 3 D. 2.5 10-4 C/m E. 7.6 10-4 C/m3 ans: E 2.
SUNY Buffalo - PHYSICS - 108
Chapter 24:ELECTRIC POTENTIAL1. An electron moves from point i to point f , in the direction of a uniform electric field. During this displacement: E. . . . .. . . . . . . . i f system system system system systemA. the work done by the fie
SUNY Buffalo - PHYSICS - 108
Chapter 25:1. The units of capacitance are equivalent to: A. J/C B. V/C C. J2 /C D. C/J E. C2 /J ans: E 2. A farad is the same as a: A. J/V B. V/J C. C/V D. V/C E. N/C ans: CCAPACITANCE3. A capacitor C &quot;has a charge Q&quot;. The actual charges on its
SUNY Buffalo - PHYSICS - 108
Chapter 26:CURRENT AND RESISTANCE1. A car battery is rated at 80 A h. An ampere-hour is a unit of: A. power B. energy C. current D. charge E. force ans: D 2. Current has units: A. kilowatthour B. coulomb/second C. coulomb D. volt E. ohm ans: B 3
SUNY Buffalo - PHYSICS - 108
Chapter 30:INDUCTION AND INDUCTANCE1. The normal to a certain 1-m2 area makes an angle of 60 with a uniform magnetic field. The magnetic flux through this area is the same as the flux through a second area that is perpendicular to the field if th
SUNY Buffalo - PHYSICS - 108
Chapter 31:ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT1. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period of the resulting oscillations, the
SUNY Buffalo - PHYSICS - 108
Chapter 32:MAXWELL'S EQUATIONS; MAGNETISM AND MATTER1. Gauss' law for magnetism: A. can be used to find B due to given currents provided there is enough symmetry B. is false because there are no magnetic poles C. can be used with open surfaces be
SUNY Buffalo - PHYSICS - 108
Chapter 33:ELECTROMAGNETIC WAVES1. Select the correct statement: A. ultraviolet light has a longer wavelength than infrared B. blue light has a higher frequency than x rays C. radio waves have higher frequency than gamma rays D. gamma rays have h
SUNY Buffalo - PHYSICS - 108
Chapter 34:IMAGES1. A virtual image is one: A. toward which light rays converge but do not pass through B. from which light rays diverge but do not pass through C. from which light rays diverge as they pass through D. toward which light rays conv
SUNY Buffalo - PHYSICS - 108
Chapter 35:1. A &quot;wave front&quot; is a surface of constant: A. phase B. frequency C. wavelength D. amplitude E. speed ans: AINTERFERENCE2. Huygens' construction can be used only: A. for light B. for an electromagnetic wave C. if one of the media is v
SUNY Buffalo - PHYSICS - 108
Chapter 36:DIFFRACTION1. Sound differs from light in that sound: A. is not subject to diffraction B. is a torsional wave rather than a longitudinal wave C. does not require energy for its origin D. is a longitudinal wave rather than a transverse
SUNY Buffalo - PHYSICS - 108
Chapter 37:SPECIAL THEORY OF RELATIVITY1. A basic postulate of Einstein's theory of relativity is: A. moving clocks run more slowly than when they are at rest B. moving rods are shorter than when they are at rest C. light has both wave and partic
SUNY Buffalo - PHYSICS - 108
Chapter 38:PHOTONS AND MATTER WAVES1. The units of the Planck constant h are those of: A. energy B. power C. momentum D. angular momentum E. frequency ans: D 2. If h is the Planck constant, then is: h A. 2h B. 2h C. h/2 D. h/2 E. 2h/ ans: D 3. T
SUNY Buffalo - PHYSICS - 108
Chapter 39:1. If a A. B. C. D. E.MORE ABOUT MATTER WAVESwave function for a particle moving along the x axis is normalized, then: |2 dt = 1 |2 dx = 1 /x = 1 /t = 1 |2 = 1 ans: B2. The energy of a particle in a one-dimensional trap with zero p
SUNY Buffalo - PHYSICS - 108
Chapter 40:ALL ABOUT ATOMS1. The magnitude of the orbital angular momentum of an electron in an atom is what multiple of ? ( is a positive integer.) h A. 1 B. 1/2 ( + 1) C. D. 2 + 1 E. 2 ans: C 2. The magnetic quantum number m is most closely as
SUNY Buffalo - PHYSICS - 108
Chapter 41:CONDUCTION OF ELECTRICITY IN SOLIDS1. In a pure metal the collisions that are characterized by the mean free time in the expression for the resistivity are chiefly between: A. electrons and other electrons B. electrons with energy abo
SUNY Buffalo - PHYSICS - 108
Chapter 42:NUCLEAR PHYSICS1. The smallest particle of any chemical element that can exist by itself and yet retain the qualities that distinguish it as that element is: A. an electron B. a proton C. a neutron D. an atom E. a molecule ans: D 2. Of
SUNY Buffalo - PHYSICS - 108
Chapter 43:ENERGY FROM THE NUCLEUS1. If the nucleus of a lead atom were broken into two identical nuclei, the total mass of the resultant nuclei would be: A. the same as before B. greater than before C. less than before D. converted into radiatio
SUNY Buffalo - PHYSICS - 108
Chapter 44:QUARKS, LEPTONS, AND THE BIG BANG1. Which of the following particles is stable? A. Neutron B. Proton C. Pion D. Muon E. Kaon ans: B 2. The stability of the proton is predicted by the laws of conservation of energy and conservation of:
SUNY Buffalo - PHYSICS - 108
FINAL EXAMPhysics 108 Fall 2003 Print your FIRST name: _ Print your LAST name: _ Sign your name: _ Person number: _ Circle your lecture Instructor Cerne Petrou T,Th 12:30-1:45 pm M,W,F 2:00-2:50 pm December 17, 2003 3:30 p.m. - 6:30 p.m.Instructio
SUNY Buffalo - PHYSICS - 108
SUNY Buffalo - PHYSICS - 108
WPUNJ - COMM - 101
Social Context and Culture: Linking Use and Digital Libraries Elfreda A. Chatman University of North Carolina at Chapel Hill A. Introduction In this article Elfreda Chatman has conducted research which has focused on the information needs and seeking
SUNY Buffalo - PHYSICS - 108
SUNY Buffalo - PHYSICS - 108
MIDTERM IIPhysics 108 Fall 2003 Saturday, October 11, 2003 10: a.m. - noon Print your FIRST name:_ Print your LAST name: _ Sign your name:__ Person number:_ Circle your lecture Instructor Cerne Petrou T,Th 12:20-1:45 pm M,W,F 2:00-2:50 pmInstructi
SUNY Buffalo - PHYSICS - 108
MIDTERM IIIPhysics 108 Fall 2003 Friday, October 31, 2003 6:00-8:00 pm Print your FIRST name:_ Print your LAST name: _ Sign your name:_ Person number:_ Circle your lecture Instructor Cerne Petrou T,Th 12:20-1:45 pm M,W,F 2:00-2:50 pmInstructions
SUNY Buffalo - PHYSICS - 108
MIDTERM IPhysics 108 Fall 2003 Friday, September 19, 2003 6:00 8:00 p.m.Print your FIRST name:_ Print your LAST name: _ Sign your name:__ Person number:_ Circle your lecture Instructor Cerne PetrouT,Th 12:20-1:45 pm M,W,F 2:00-2:50 pmInstruct
SUNY Buffalo - PHYSICS - 108
Chapter 25Capacitors and DielectricsIn this chapter we will describe devices called &quot;capacitors&quot;. These have the ability to: 1. Store charge and 2. Store energy Capacitors are found in practically all electronic circuits In addition we will exami
SUNY Buffalo - PHYSICS - 108
Chapter 26Currents in materialsIn this chapter we will study the following topics : 1. The notion of electric current ( I ) 2. The motion of charges in current carrying conductors 3. The notion of resistance 4. The relation between the voltage V
SUNY Buffalo - PHYSICS - 108
Chapter 32 Inductance and Circuit OscillationsIn this chapter we will study the properties of inductors (also known as &quot;coils&quot;). Inductors, together with capacitors and resistors are the passive elements of electric and electronic circuits In partic
SUNY Buffalo - PHYSICS - 108
Chapter 30Faraday's lawUsing Ampere's law in chapter 29 we investigated how an electric current I can generate a magnetic field B. In this chapter we shall study the fourth (and last) of Maxwell's equations known as Faraday's law. Faraday's law t
UCLA - ECON - 171
Eco 171 - Industrial Organization First Midterm Exam InstructionsName: Section:There are 6 short questions and 2 problems. Short questions are worth a total of 40 points and the problems a total of 60 points. Answer in the space provided (no need
UCLA - ECON - 171
UCLA - ECON - 171
Eco 171 - Industrial Organization Second Midterm Exam InstructionsName: Section:There are 6 short questions and 2 problems, each worth 1/3 of the total points. Answer in the space provided (no need to use it all.) If necessary use the back of the
WPUNJ - COMM - 101
More Than Rumors. Understanding the Organizational Grapevine Zaremba, Alan David Spodofora A. Introduction This paper discusses the development, accuracy, resilience, and management of the grapevine. Since grapevines do not develop by managerial desi
UCLA - ECON - 171
UCLA - ECON - 171
Lehigh - PHYSIC - 2
Lehigh University HW-23 SolutionsPhysics 21, Spring 2008April 2, 200823-1. (HRW 33-67) In Fig. 33-65, light enters a 90 triangular prism at point P with incident angle , and then some of it refracts at point Q with an angle of refraction of 90.
WPUNJ - COMM - 101
WPUNJ - COMM - 101
Social Context and Culture: Linking Use and Digital Libraries Elfreda A. Chatman University of North Carolina at Chapel Hill A. Introduction In this article Elfreda Chatman has conducted research which has focused on the information needs and seeking
Lehigh - PHYSIC - 2
Lecture-23 Examples Solutions HW-23-5. (HRW 34-33) In Fig. 34-38, a beam of parallel light rays from a laser is incident on a solid transparent sphere of index of refraction n. (a) If a point image is produced at the back of the sphere, what is the i
Lehigh - PHYSIC - 2
Lecture-23 Geometrical Optics - continued Lensmaker's equationSnell's law givesand1 n 2 4 n 3Parallel linesR2h1 1 sin 1 = ; R1 h h2 ; and 2 R2 f Also from figure, weR1have = 1 - 2 = 3 - =Or,4n- ( 1- 2) =n+n
Virginia Tech - MATH - 3214
WPUNJ - COMM - 101
More Than Rumors. Understanding the Organizational Grapevine Zaremba, Alan David Spodofora A. Introduction This paper discusses the development, accuracy, resilience, and management of the grapevine. Since grapevines do not develop by managerial desi
Virginia Tech - MATH - 2224
Math 2224 CRN 974201Math 2224 Multivariable Calculus CRN 97420Class Meeting Time: Monday, Wendsday, Friday 12:20PM 1:10PM McBryde 307 Instructor: Zlatko Drmac, McBryde 440, phone 2317533, email: zlatko@math.vt.edu Office hours: Monday, Wendsday
Virginia Tech - MATH - 3134
Prufer Code Problems 1. Construct the Prufer Code for the tree.2. Construct trees that are represented by the following Prufer Codes. What conclusions can you draw about isomorphism as related to the codes? (a) [6, 6, 4, 4, 4, 1] (b) [6, 4, 4, 6, 4
Virginia Tech - CS - 2606
CS 2606 Data Structures &amp; OO Devel IIHomework 1: ComplexityYou will submit your solution to this assignment to the Curator System (as HW1). Your solution must be either a plain text file (e.g., NotePad) or a MS Word document; submissions in other
Virginia Tech - CS - 2606
CS 2606 Data Structures &amp; OO Devel IIHomework 3: Secondary StoragePrepare your answers to the following questions either in a plain text file or in a file that can be opened with Microsoft Word. Submit your file to the Curator system (www.cs.vt.e
CofC - ENGLISH - 102
English 102 E. Baker Benjamin DeMott Summary In Benjamin DeMott's response to William Faulkner's &quot;Barn Burning&quot; story, he focuses on Abner Snopes' character. The title of his response is Abner Snopes as a Victim of Class so it is evident that he sees
Mississippi State - FIN - 3123
Solutions to End-of-Chapter ProblemsAccounting-Based Methods A8-1. a. If the computers are depreciated on a straight-line basis, depreciation will be \$5,000 per year for 4 years. Contribution to net income will be: Year 1 2,500 Year 2 4,100 Year 3 4
Mississippi State - FIN - 3123
Chapter 9 Cash Flow and Capital BudgetingAnswers to End-of-Chapter ProblemsTypes of Cash Flows A9-1. Depreciation A/T (\$) 3 7 20 Present Values (\$) a. 3 b. 7 c. 20PV of Depr. Tax Savings A9-2. End of Year Depr. % Depr.\$1,414,802 \$1,226,481 \$752