NUPOC STUDY GUIDE

NAVY RECRUITING COMMAND JANUARY 2015

Congratulations on pursuing an exciting career in the Naval Nuclear Propulsion Program.

This study guide is designed to help you succeed on your phone technical interview and your final interview in Washington, DC. It contains the most commonly asked topics in Washington, DC. It is by no means all encompassing; Naval Reactors may ask any question at the interview. HOWEVER, it does contain the concepts that you must know at a minimum in order to be successful in DC.

This study guide is laid out in two portions: Study Guide Topics and example problems in each topic. Corresponding example problems are listed in parentheses next to each topic in the study guide. You should review each topic listed and then attempt the corresponding example problems.

The topics are listed in order of how common they are asked historically in the DC interviews. To maximize your efficiency, complete the study guide in the order listed. AT A MINIMUM, complete the calculus and physics sections PRIOR to your technical phone interview in order to be adequately prepared. The entire study guide should be completed prior to the DC interview.

Luck favors the prepared, Commander Timothy Yanik NUPOC Director

Study Guide Topics Calculus

Integration (1-7) o U-substitution o Integration by parts o Definite/indefinite integrals o Disc method integration

Derivatives (8) o Sum Rule o Product Rule o Quotient Rule o Chain Rule

Critical Points (9-11) o Finding a maximum or minimum of a function o Inflection points o 2nd Derivative Test

Related Rates (12) o Utilizing the Chain Rule

Find the limit of a function (2)

Logarithms and Exponential equations (2) o Graph ln(x) and ex

Physics

Kinematic Problems (15, 16, 19) o Calculate time and distance o Derive the kinematic equations

Relationship between distance, velocity, and acceleration

Collisions and conservation laws (14, 18, 20, 21) o Inelastic vs elastic collision o Conservation of momentum o Conservation of energy

Potential Energy Kinetic Energy

Centripetal Force (17)

Springs (17) o Hooke’s Law o Spring energy (stored energy)

Friction (13, 56) o Kinetic friction o Static friction

Angular Velocity and Momentum (22)

Torque (23-25) o Shear and moment diagrams o Torsion

Electrical Engineering

Current, resistance, ohm’s law (26)

Capacitance, RC circuits (27, 28, 30)

Power (26)

Heat generated in resistors (29)

Kirchoff’s Law (31) o Definition o Apply Kirchoff’s Law to calculate current and voltage in a circuit

RL circuits (32)

RLC circuits (33) Chemistry

pH (34-38) o Basic definition of pH o Type of scale o Define acid, base, and neutral o Calculate various pH levels

Ideal Gas Law (39, 40) o Calculate pressure, volume, and temperature o Define the constants in the equation o Temperature (Absolute scale) o Charles’ Law o Boyle’s Law

Fluids and Buoyancy

Bernoulli’s Principle (41, 42, 45)

Buoyant Force (43, 44, 46, 47) o Calculate buoyant forces o Identify environmental factors that affect the buoyant force

Thermodynamics

Carnot Cycle (48)

Rankine Cycle (49)

Laws of Thermodynamics (50)

Define enthalpy, entropy (51) Materials and Civil Engineering

Stress/Strain Curves (52) o Define elastic limit and yield point

Statics and Dynamics

Force balance (53, 54)

Tension (55)

Pulley Systems (57, 58)

Calculus

1. Find the area of A and B using Calculus. Derive the formulas for the volumes of C and D using Calculus.

A. Triangle B. Circle C. Pyramid D. Cone

2. Rotate the function y = 1/x around the x axis from x = 1 to x = infinity and find the volume.

3. Use calculus to find the volume of a plastic solo cup.

4. Find the area between the curves y = x and y = x2 from x = 0 to x = 3.

5. Draw the following curves and find the area between them:

a. y = x3 and y = x2 b. y = x2 and y = x

6. Using Calculus, determine the area between two concentric circles of radii 1 and 2

respectively.

7. Integrate the following: A. ∫ (x sinx) dx B. ∫ x (x2 – 4) ½ dx C. ∫ e4 – 3/x dx

X2 D. ∫ (e-x + 3x2) dx E. ∫ (x sin2x + x3) dx F. ∫sec(u)tan(u) du G. ∫ xex dx H. ∫(y+3)(y+1) dy

R π/2 π/2

I. ∫ ∫ ∫ r sin(Ө)dɸ dӨ dr 0 0 0

J. ∫ (2x + 1) dx

8. Take the derivative with respect to x of the following: A. cos4x sinx B. ae-bx

cx2

C. 5x4 D. x(x2 – 4)1/2

E. sin(x), cos(x), tan(x), cot(x), sec(x), csc(x) F. ln(x) and 10x G. x + x3 + sin(x)cos(x) + sin(x) H. x5 + cos(x)(ex) + sin(x2/3) I. x1/2 + x2sin2x

9. You are going to build a rectangular fence alongside a wall so that the wall forms one side of the enclosure. If you have 80 feet of fencing material, what is the largest area you can enclose?

10. Given the figure below, determine the value of x so that when the corners are removed

and the flaps folded up, the five-sided box formed will have the maximum volume.

11. In the figure below, you can walk 3 mph through the woods. You can walk 5 mph on the trail. What is the quickest that you can get from point A to point B?

12. Air is being pumped into a spherical balloon at a rate of 5 cm3/min. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 20 cm.

Physics 13. What must the angle Ө be in order for the block of mass M to start sliding? µ = 0.8

14. Find the final velocity of M for both an elastic collision and an inelastic collision.

15. Given the following diagram, calculate the distance traveled by the ball being thrown off the

monument.

16. Derive the Kinematic Equations using integration.

17. What height h must the car start at to make it around the loop without falling? Find the

displacement x of the spring when the car impacts the spring.

18. A wooden block with a mass of 1000 grams is suspended by a rope from a tree. You shoot a

bullet with a mass of 10 grams and a velocity of 1000 m/s. The bullet imbeds in the block

causing it to swing upwards. How high in the vertical direction will the block swing?

19. A baseball initially at a height of 5 feet is hit at an angle of 30 degrees to the horizontal at an

initial velocity of 150 feet/sec. Will the baseball clear a fence at a height of 15 feet at a distance

of 400 feet?

20. A block of mass M1 is attached by string to a support. The block is raised to a height h and

released. It then strikes a block of mass M2 on a frictionless surface. Find the velocity of the

block M2, assuming a totally elastic collision.

21. What is the difference between an elastic collision and an inelastic collision? In which cases can

you use Conservation of Energy? Conservation of Momentum?

22. A uniform sphere of mass 5 kg and a radius of 0.2 m spins about an axis passing through its

center with period t = 0.7 s. What is the angular momentum of the sphere?

23. Given an I beam, what types of forces are acting at the point of load on this beam? How do you find these forces?

24. Draw the shear and moment diagrams for this beam.

25. Draw the shear and moment diagrams for this uniformly loaded beam.

Electrical Engineering 26. Find the total current and voltage drop across R1 for the following circuits. Calculate equivalent

resistance and power of the circuit.

R2 R1

R2 R1

27. Graph voltage and current versus time after the switch is closed in the circuit below.

28. What is capacitance and inductance?

29.The switch closes at t = 0 for 20 seconds. Calculate the temperature rise in the 1 kg of water. V = 12V, R = 10Ω

30. Be able to solve for voltage as a function of time for an RC circuit. 31. Determine the values of the current flowing through each of the resistors.

V

t = 0

C

V +

R

32. In the circuit below, the switch has been open for a long time, and closes at t = 0. For t < 0, there is no current in the inductor. For the circuit, IS = 1 A. Find values for R and L so that the transient time constant is 1 ms and that after one time constant, the inductor voltage is 12 V.

33. A series RLC circuit containing a resistance of 12Ω, an inductance of 0.15H and a capacitor of

100uF are connected in series across a 100V, 50Hz supply. Calculate the total circuit impedance, the circuit’s current, and the power factor.

Chemistry 34. What is pH?

35. Determine the final pH and temperature when these two solutions are mixed together in a 3-

liter container.

Solution A: 2 liters, pH = 3, Temp = 80F Solution B: 1 liter, pH = 5, Temp = 40F

36. Why is pH important in materials selection?

37. State the mathematical expression for the pH factor of a solution. What is the pH of pure

water? What happens to pH if the hydrogen ion concentration increases?

38. What is an acid? What is a buffer solution?

39. What is the Ideal Gas Law?

40. A tank of N2 is at 2000 psig and 200K. If the temperature of the tank rises to 400K, what is the new pressure in the tank?

Fluids and Buoyancy

41. If the flow rate is increased by a factor of three, how does the pressure change at both points?

42. What is force F?

43. A ball of diameter 10 cm and mass 10 grams is dropped in a container of water. The cross-sectional area of the container is 100 cm2. What is the change in the height of the water column?

44. What happens to the water level with respect to the shore when the sailor throws the lead

anchor overboard?

45. How far will the water shoot out?

46. Describe how the following will affect the buoyant force acting on a submarine. a. An increase in depth b. An increase in salinity c. A decrease in water temperature

47. You are building a raft out of two by fours. How many two by fours do you need in your raft in

order for you to float? Make assumptions and calculate a buoyant force.

Thermodynamics 48. Draw and explain a typical Carnot cycle.

49. Draw and explain a typical Rankine cycle. Include a discussion of enthalpy and entropy changes.

50. List and discuss the laws of thermodynamics.

51. What is enthalpy? How is it measured? How is it used to calculate entropy?

Materials and Civil Engineering

52. Draw and explain a stress-strain curve for steel. Where is the elastic limit? The yield point? What are stress and strain? How would work be defined on the stress-strain curve?

Statics/Dynamics

53. Find R1 and R2 (Reactions).

54. How far does the man have to walk down the beam in order to tip the beam off fulcrum A?

55. Find the tensions in the two ropes. b) Now describe the forces on the block.

56. A sliding block slows from 16 m/sec to 8 m/sec in two seconds. If it weighs 500 kg, what is the coefficient of sliding friction?

57. What is the velocity of the 50 lb block? (Massless, frictionless pulley)

58. How much would the 1 kg mass raise the 50 kg mass in the figure below?