Principles of Engineering – Midterm Exam Instructions: Respond to all questions below by circling the correct answer, or by writing your answer in the blank space. Use a dark pen/pencil and write neatly and legibly. When you are done, scan-in your work and submit as an email attachment.

To get full credit, be sure to answer all essay-type questions completely. When a problem requires it, show all calculations and use the correct units in your answer.

Engineering formulas and reference tables are provided at the back of the test. Look these over before you begin.

You may also refer to the PowerPoint lecture slides on the class website.

Scoring: there are 141 total points possible. Your test grade will be reported as a percentage as follows: (total points earned ÷ 141) x 100%. Partial grading: to receive partial credit for a problem, show all your work! Show the formula(s) used, substitute the correct values, solve for the answer, and show the correct units.

Part 1: Machines and Mechanisms

1. (5 pts) Which of the following engineering achievements occurred first? What specific era or time frame did it occur in? You will need to do some internet research.

a. Development of the catapult. b. Development of methods to create fire at will. c. Development of stone bridges that incorporated wood stringers. d. Development of the water wheel.

2. (5 pts) The gear train depicted consists of a 40-tooth

gear (input), 20-tooth gear (idler), and 30-tooth gear (output). If the input gear rotates 10 times, how many times will the output gear rotate?

a. 7.5 times b. 13.3 times c. 15 times d. 20 times

3. (3 pts) In a third class lever, the distance from the

effort to the fulcrum is ____________ the distance from the load/resistance to the fulcrum.

a. Less than b. Less than or equal to c. Greater than d. Greater than or equal to

4. (5 pts) The wheels on a bicycle have a 10-inch radius. If the bike must travel exactly 2000 inches, how many revolutions are required? Assume that no sliding or slipping occurs between the wheel and the road.

a. 31.8 b. 62.8 c. 314 d. 31.4

5. (3 pts) When used to pry open a can of paint (see figure), a

screwdriver functions as a __________. a. Wheel and axle b. Screw c. Inclined plane d. Lever

6. (5 pts) The wheels on a mousetrap-powered vehicle have a diameter of 8.15 inches. If the

mousetrap-powered vehicle must travel exactly 12 feet, how many revolutions of the wheel are required? Assume that no sliding or slipping occurs between the wheel and the road.

a. .563 b. .469 c. 5.63 d. 4.69

7. (3 pts) The stapler shown is an example of what class of lever? a. 1st class b. 2nd class c. 3rd class d. 4th class

8. (5 pts) Refer to the belt driven system shown. Pulley B, which

has a diameter of 16 inches, is being driven by Pulley A, which has a diameter of 4 inches. If Pulley A is spinning at 60 RPMs, then Pulley B is spinning at __________ RPMs.

a. 240 b. 15 c. 4 d. 64

9. (3 pts) What class of lever is shown in the figure? Justify your answer.

10. (5 pts) Referencing the above lever, how much effort force is needed to balance 20.8 pounds of resistance?

11. (5 pts) If pulley ‘a’ rotates in a clockwise direction, what direction does pulley ‘f’ rotate? Refer to figure below.

a. Clockwise b. Counter clockwise

Part 2: DC Circuits

12. (5 pts) If a motor requires 6 Volts and has 80 Ohms of resistance, what is the amperage value?

a. 65 b. 0.75 c. 480 d. 0.075

13. (10 pts) In the circuit shown, a 22-Ω lamp and a 4.5-Ω lamp are connected in series and placed across a potential difference of 45-V.

a. What is the equivalent resistance of the circuit?

b. What is the current in the circuit?

c. What is the voltage drop across each lamp?

d. What is the power dissipated in each lamp?

14. (10 pts) In the circuit shown with 3 resistors, the voltmeter reads 70.0 V. a. Which resistor is the hottest? b. Which resistor is the coolest? c. What will the ammeter read? d. What is the power supplied by the

battery?

Part 3: The Design Process

15. (15 pts) A team of engineering students is trying to develop an alternative-energy car to enter in a national competition. For each of the statements below, identify which of the steps in the “Design Process” rubric below is being represented. Write the step number on the line provided.

a. The team of students conducts trial runs to determine the ability of the vehicle to accelerate under different wind conditions. _________

b. The students scour magazine articles and the internet to look for ideas. ___________ c. The students build their first vehicle. _____________ d. The team of students modifies the steering system of their design after the steering

mechanism fails after a hard day of trial runs. ____________ e. A team meeting is called to discuss other types of steering mechanisms that might work.

__________ f. A different steering mechanism is chosen and then run through several trials to see if it will

do the job. ___________ g. At first, a lead-acid type battery system is utilized. This setup is found to be too heavy for

the vehicle. ___________ h. After evaluating several other battery types, the team decides to utilize a combination of

solar panels and Lithium batteries. ________

Step # “The Design Process”

1. Define the problem 2. Research what’s already out there 3. Generate alternatives 4. Choose the best one to pursue 5. Develop the idea further 6. Build a prototype 7. Test and evaluate 8. Redesign and improve 9. Report on your results, and then seek funding for production

16. (10 pts) List at least 3 improvements you could make to this machine, using modern materials and methods. Explain how these would improve the device (there are probably 10 engineering improvements). Spend a couple days thinking about it. First, you will have to figure out what the machine does….

17. (10 pts) List and explain at least 3 problems a person would have in deploying and using this machine in medieval warfare (there are probably 10 problems with it). Spend some time thinking about it.

Part 4: Energy and Power

18. (5 pts) Why does a wind turbine need gears? (see figure) What purpose(s) do they serve? Give a complete answer. We discussed this at length in class.

19. (10 pts) The picture shows a type of solar power plant called a “Power Tower”, in which thousands of mirrors reflect the sunlight onto a 300-ft tall tower. The top of the tower gets very hot and actually starts to glow. The concentrated sunlight is used to heat a liquid substance, which is pumped down to the ground and powers a steam turbine, which in turn is used to generate lots and lots of electricity. The now-cooled liquid is continuously pumped back up to the top of the tower for re-heating. Question: In your own words, what are two advantages, and what are two disadvantages, of solar power? (I mean solar power in general). This will take some internet research. Explain so a 7th grade person can understand.

a. Advantage:

b. Advantage:

c. Disadvantage:

d. Disadvantage:

Part 5: Structural Design

20. (10 pts) Engineered structures sometimes fail, and property damage and large-scale human suffering can result.

a. When designing a structure such as a highway bridge, what is meant by the terms “live load” and “dead load”? Explain so a 7th grade person can understand. Definitions:

b. Give at least two examples of each (DL and LL). Assume we are talking about a bridge. Examples:

21. (3 pts) Which of the following is a vector quantity? a. Distance b. Mass c. Density d. Velocity

22. (3 pts) As shown in the hook figure, a _____________ force has the

same effect on a body as two or more forces acting concurrently on that body.

a. compressive b. tensile c. resultant d. reaction

23. (3 pts) Moment of inertia is a cross-sectional property that gives the engineer an indication of the

stiffness of a particular shape. Its value can be used to: a. Calculate the amount of deflection that occurs in structural beams. b. Calculate the weight of a structural beam. c. Locate the centroidal axis of a structural shape. d. Describe the linear relationship between stress and strain.

DC Circuits formulas we covered in class

Ohm’s Law: V = I x R (volts = amps x resistance)

Watt’s Law: P = V x I (watts = volts x amps)

Power “heat loss” equation: P = I2 x R (watts = amps2 x resistance)

P = power (watts)

V = potential (volts)

I = current intensity (amps)

R = resistance (ohms)

Kirchhoff’s Voltage Law: The sum of all voltage drops in a series circuit equals the total applied voltage

Kirchhoff’s Current Law: The total current in a parallel circuit equals the sum of the individual branch currents

POE Exam Reference Tables

Circular Shapes

Formulas Variables C = circumference

C = πD π = pi A = πr2 D = diameter

A = area r = radius

Electrical Systems

Formulas Variables E = voltage

E = IR I = current R = resistance

Mechanisms

Formulas Variables MA = Mechanical Advantage

MA = R ÷ E R = resistance force Lever MA = LE ÷ LR E = effort force Wheel and Axle MA = LE ÷ LR LE = distance to effort Pulley MA = Total number of strands

supporting the load LR = distance to resistance

Inclined Plane or Wedge MA = L ÷ H L = slope length Screw MA = C ÷ Pitch H = slope height or width thickness Pitch = 1 ÷ TPI C = circumference

Pitch = screw pitch TPI = threads per inch

Statics Static Equilibrium

Formulas Variables M = moment about a point

M = F×D F = force D = perpendicular distance

Formulas Variables S = sum

SFX=0=X(right) – X(left) F = force

SFY=0=Y(up) – Y(down) M = moment about a point

SM=0=CCW - CW CCW = counter-clockwise CW = Clockwise

Properties of Materials

Formulas Variables δ = total deformation

σ = P ÷ A σ = stress ∈ = δ ÷ L ∈ = strain

δ = PL ÷ AE E = modulus of elasticity, Young’s Modulus E = σ ÷ ∈ P = axial force

E = (P1-P2)L0 /( δ 1-δ2)A A = area

Right Triangle Ratios

Gear Ratios

Formulas Variables GR = gear ratio Nin = number of teeth on driver gear Nout = number of teeth on driven gear

GR = Input Rate / Output Rate Din = driver gear diameter, in SR = Win / Wout Dout = driven gear diameter, in Win / Wout = Dout / Din Win = driver gear speed, rpm Tin / Tout = Din / Dout Wout = driven gear speed, rpm

Tin = torque of driver gear, ft lbs. Tout = torque of driven gear, ft lbs. SR = speed ratio

Kinematics

Formulas Variables sin θ= opposite / hypotenuse θ = angle cos θ= adjacent / hypotenuse tan θ= opposite / adjacent

Formulas Variables vi = initial velocity θ = angle g = gravity

Vi2 sin(2θ)

x= g

x = range