Physics I -- Final Exam Spring 2003

Name _______________________________________________________________________

Final Exam

Physics I

Spring 2007

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 of every page,and section number below.

Section #

QuestionsValueScore

Part A80

B-120

B-220

B-320

C-120

C-220

C-320

Total200

_____ 1 M/R 8-10 (Bedrosian)

_____ 2 M/R 10-12 (Wilke)

_____ 4 M/R 12-2 (Yamaguchi)

_____ 5 M/R 2-4 (Yamaguchi)

_____ 7 M/R 4-6 (Wilke)

_____ 9 T/F 10-12 (Wetzel)

_____ 10 T/F 10-12 (Washington)

_____ 11 T/F 12-2 (Eah)

_____ 12 T/F 2-4 (Eah)

_____ 14 M/R 12-2 (Zhang)

_____ 15 M/R 2-4 (Bedrosian)

You may not unstaple this exam.

Only work written on the same page as the question will be graded.

Cheating on this exam will result in an F in the course.

On this exam, please neglect any relativistic and/or quantum mechanical effects. If you dont know what those are, dont 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 graphing and numerical questions (Parts B and C), show all work to receive credit.IMPORTANT REMINDER FOR PARTS B AND C: You are allowed to use only the formulas given with the exam and standard math (trigonometry, algebra, etc.). If you want to use a formula not on the list, you must derive it using the formulas on the list and standard math.

Part A-1 80 Points Total (20 at 4 Points Each)

IMPORTANT: There is only ONE correct answer for each question in Part A.

Questions 1-3 refer to the following situation: Two cars, A and B, have a drag race in the X direction. Both cars experience the same net force as a function of time as shown in the graph below. Both start from rest at t = 0. The mass of car A is greater than the mass of car B.

______ 1.Which car has greater speed at t = 20 seconds?

A. Car A.B. Car B.C. Both have the same speed at t = 20 seconds.______ 2.Which car has greater magnitude of momentum at t = 20 seconds?

A. Car A.B. Car B.C. Both have the same magnitude of momentum at t = 20 seconds.______ 3.Which car has greater kinetic energy at t = 20 seconds?

A. Car A.B. Car B.C. Both have the same kinetic energy at t = 20 seconds.Questions 4-7 refer to the following situation: Two particles A and B, with masses mA and mB respectively, have initial velocities that take them into a region in which they interact, as shown by the dotted square. After the interaction, they emerge from the region with different final velocities. Assume that the particles exert forces on each other only within the dotted square.

The system consists of particles A and B. Assume that mA > mB.

______ 4.What condition is necessary and sufficient* for the linear momentum of the system to be conserved?A. The net external force is zero.B. Only conservative external forces act on the system.C. The interaction forces between the two particles are conservative forces.D. The objects remain separate during the interaction and do not stick together.______ 5.Assume that no external forces act on the system. Which statement below can be correctly concluded about the magnitude of impulse on particle A, JA, compared to the magnitude of impulse on particle B, JB, during the interaction?A. JA > JBB. JA < JBC. JA = JBD. There is insufficient information to determine the correct relationship.______ 6.Assume that the linear momentum of the system is conserved. What condition below is necessary for the interaction to be considered an elastic collision?A. The collision is one-dimensional.B. Only conservative external forces act on the system.C. The initial kinetic energy of the system equals the final kinetic energy of the system.D. The center of mass of the system does not move.______ 7.Assume the center of mass of the system moves with a constant velocity. Which statement below is a correct conclusion about the system?

A. The linear momentum of the system is conserved.B. Only conservative external forces act on the system.C. The interaction force between the particles is zero.D. The interaction of the particles is an elastic collision.For questions 8 and 9, consider angles in the range [0,180].______ 8.Consider an object at a specific instant of time that is moving with velocity and acceleration . At this instant, it is slowing down. What can one correctly conclude about the angle between and ?

A. The angle between and is greater than 90.B. The angle between and is equal to 90.C. The angle between and is less than 90.D. There is not enough information to conclude any of A-C above.______ 9.Consider an object at another specific instant of time that is moving with velocity and acceleration . At this instant (not the same as question 8 above), it is moving at a constant speed and changing direction. What can one correctly conclude about the angle between and ?

A. The angle between and is greater than 90.B. The angle between and is equal to 90.C. The angle between and is less than 90.D. There is not enough information to conclude any of A-C above._______10.The net force acting on the object in Question 8 is doing

A. Positive work.B. Negative work.C. Zero work._______11.The net force acting on the object in Question 9 is doing

E. Positive work.F. Negative work.G. Zero work._______12.The figure below shows an electron at an instant of time moving in the +X direction in a region where the electric field (E) points in the +Y direction.What is the direction of the electric force on the electron?

A. +X.B. X.C. +Y.D. Y.E. +Z.F. Z._______13.The figure below shows an electron at an instant of time moving in the +X direction in a region where the magnetic field (B) points in the +Y direction.What is the direction of the magnetic force on the electron?

A. +X.B. X.C. +Y.D. Y.E. +Z.F. Z._______14.The figure below shows the respective paths taken by two particles, A and B, in a region containing a constant, uniform magnetic field directed into the plane of motion (into the page). There are no other forces acting on A and B.We know that both particles have charge +e.However, we do not know the mass of either particle.What can we correctly conclude about particles A and B?

A. The mass of A > the mass of B.B. The speed of A > the speed of B.C. The magnitude of linear momentum of A >the magnitude of linear momentum of B.D. The kinetic energy of A >the kinetic energy of B.Questions 15-20 refer to the figure shown below and the directions given as A-I. At the instant shown, the fan is rotating at 2 rad/s (clockwise as seen from the front). It is slowing down with a constant angular acceleration of +4 rad/s2.The questions refer to directions of six vector quantities at the instant shown in the figure.Take the center of rotation as the origin of the coordinate system.

A).

B).

C).

D).

E).

F)(.

G)Out of the page.

H)Into the page.

I)Direction is undefined because the quantity is zero or insufficient information was given.

_______15.What is the direction of the angular velocity vector of the fan?_______16.What is the direction of the angular momentum vector of the fan?_______17.What is the direction of the angular acceleration vector of the fan?_______18.What is the direction of the net torque vector acting on the fan?_______19.What is the direction of linear velocity at point X on the tip of the fan blade? Note: Linear velocity is motion measured in m/s._______20.What is the direction of linear acceleration at point X on the tip of the fan blade? Note: Linear acceleration is the acceleration we refer to in .Part B Graphing 60 Points Total (3 at 20 Points Each)

IMPORTANT REMINDER FOR PARTS B AND C: You are allowed to use only the formulas attached to the exam and standard math (trigonometry, algebra, etc.). If you want to use a formula not on the list, you must derive it using the formulas on the list and standard math.Show all work on Parts B and C, particularly what formulas and/or principles you used.

B-1 One-Dimensional Motion (20 Points)

An object moves in one dimension (x) according to the velocity graph shown below. It begins at x = 0 at t = 0. Plot displacement (x) and acceleration (a) versus time for the object.

Make sure to show the following features.

1. Shapes of the curves.

2. Maximum/minimum points.

B-2 Mass on a Spring (20 Points)

A mass on a vertical spring begins its motion at rest at y = 0 cm. It reaches a maximum height of y = 10 cm. The two forces acting on the mass are gravity and the spring force. The graph of the total potential energy (PE) of the system versus position is given below.Graph the kinetic energy of the mass and the total (net) force on the mass versus y.Be sure to include:

1. Shape of the curve(s).

2. Minimum and maximum points.

3. Clearly labeled scales on the axes.

Show all work, including what equations and/or principles of physics you are using.

B-3 Helium Nucleus in Electric and Magnetic Fields (20 Points)

In the figure below, Regions A and B are squares with side lengths = 10.0 cm.

A helium nucleus (charge = +2e and mass = 6.64 ( 1027 kg) enters into Region A at the tip of the arrow as shown, halfway along a side, with a velocity of 7.00 ( 10+5 m/s in the +X direction. There is a uniform electric field of 1.00 ( 10+5 N/C in the +X direction and no magnetic field in Region A. In Region B, the electric field is zero and the magnetic field is uniform with the value 0.500 T in the Z direction (into the page).

Plot the path of the helium nucleus as it travels through region A, then into region B, through region B, and finally exiting region B.

Show all work. Your plot should clearly show the shape of the path through each region (straight line, parabola, circle, etc.) and exactly where the particle exits each region.

Part C Problems Three Problems 60 Points Total

IMPORTANT REMINDER FOR PARTS B AND C: You are allowed to use only the formulas attached to the exam and standard math (trigonometry, algebra, etc.). If you want to use a formula not on the list, you must derive it using the formulas on the list and standard math.Show all work on Parts B and C, particularly what formulas and/or principles you used.C-1 The Pirate Ship in a Harbor (20 Points)

A pirate ship in a harbor at sea level fired its cannon and hit the top of a hill 310 meters above sea level. The cannon ball was in the air for 10.0 seconds. The elevation angle of the cannon was 30 above horizontal. What was the horizontal distance from the pirate ship to the top of the hill (distance d as shown in the figure below)? Use g = 9.8 m/s2 and ignore air resistance.

Horizontal Distance to Top of Hill: _________________________ units _______

C-2 Calculating Torque (20 Points)

A particle at location (3.0,4.0) m is moving in the +X direction at 2.0 m/s at the instant shown. Gravity is the only force acting on the particle (in the Y direction). Use g = 9.8 m/s2.The +Y direction is up. The +Z direction is out of the page and the particle is at Z = 0.

Find the X, Y, and Z components of the torque acting on the particle about the origin at the instant shown.

Torque X Component: _________________________________________________ units _________

Torque Y Component: _________________________________________________ units _________

Torque Z Component: _________________________________________________ units _________

C-3 Electric Field and Electric Potential (20 Points)

Find the electric field and electric potential at the origin of the (X,Y) coordinate system due to the three point charges as shown in the figure below. ("X marks the spot.") The point charges are located at the corners of a square 0.10 m on a side. The origin is the lower left corner.Note: 1.0 nC = 1.0 109 C.Assume that the electric potential is defined to be zero at infinity.

Electric Field X Component:

_________________________________ units ________

Electric Field Y Component:

_________________________________ units ________

Electric Potential:

_________________________________ units ________

Formula Sheet for Homework and Exams Page 1 of 2

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35a.

35b.

36.

37.

38.

39.

40.

41.

42.

43.

44x.

44y.

44z.

45a.

45b.

Formula Sheet for Homework and Exams Page 2 of 2

46a.

46b.

47a.

47b.

48a.

48b.

49.

50.

51.

52.

53x.

53y.

53z.

54.

55.

56.

Useful Constants

(You can use the approximate values on exams.)

Universal Gravitation Constant

Electrostatic Force Constant

Magnetic Constant

Speed of Light in Vacuum

Charge of a Proton

Electron-Volt Conversion Constant

Mass of a Proton

Mass of an Electron

EMBED Zoner.Draw.Document

EMBED PBrush

EMBED Zoner.Draw.Document

EMBED Zoner.Draw.Document

EMBED Zoner.Draw.Document

EMBED Zoner.Draw.Document

EMBED Zoner.Draw.Document

* "Necessary" means if the condition is not true, momentum is never conserved. "Sufficient" means if the condition is true, momentum is always conserved.

15

_1137570404.bin

_1151424646.unknown

_1177168138.unknown

_1239365930.bin

_1239605186.bin

_1239614330.bin

_1239366046.bin

_1216816695.bin

_1234862234.unknown

_1239365746.bin

_1217154307.unknown

_1177168340.unknown

_1203233439.unknown

_1166859212.unknown

_1177099068.unknown

_1177165757.unknown

_1177165779.unknown

_1177099266.unknown

_1177098584.unknown

_1166724430.unknown

_1166859019.unknown

_1166859139.unknown

_1166725606.unknown

_1164292198.unknown

_1164292704.bin

_1164292128.unknown

_1157260684.unknown

_1151424550.unknown

_1151424625.unknown

_1151424636.unknown

_1151424613.unknown

_1151424530.unknown

_1151424541.unknown

_1151424516.unknown

_1095249496.unknown

_1095253503.unknown

_1095432267.unknown

_1099908596.unknown

_1110737652.unknown

_1112081144.unknown

_1112082157.unknown

_1112082158.unknown

_1112082154.unknown

_1112082155.unknown

_1112081152.unknown

_1112080781.unknown

_1112081036.unknown

_1112080766.unknown

_1110737540.unknown

_1110737595.unknown

_1110737617.unknown

_1110737553.unknown

_1099908634.unknown

_1099908699.unknown

_1099908614.unknown

_1098022335.unknown

_1098551733.unknown

_1098551757.unknown

_1098551705.unknown

_1095971047.unknown

_1098019506.unknown

_1098022334.unknown

_1098019203.unknown

_1095768394.unknown

_1095253707.unknown

_1095254791.unknown

_1095255011.unknown

_1095255551.unknown

_1095255560.unknown

_1095255442.unknown

_1095254851.unknown

_1095254299.unknown

_1095253636.unknown

_1095253678.unknown

_1095253536.unknown

_1095250456.unknown

_1095253066.unknown

_1095253223.unknown

_1095252187.unknown

_1095252291.unknown

_1095252456.unknown

_1095250596.unknown

_1095249942.unknown

_1095250327.unknown

_1095249716.unknown

_1095247474.unknown

_1095248813.unknown

_1095248932.unknown

_1095249091.unknown

_1095248874.unknown

_1095247713.unknown

_1095248302.unknown

_1095248438.unknown

_1095247849.unknown

_1095247533.unknown

_1095246595.unknown

_1095246803.unknown

_1095247236.unknown

_1095246708.unknown

_1095246516.unknown

_1095246532.unknown

_1095246434.unknown