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Principles of Engineering Name___________________ Directions: Show ALL work (initial equation & solving for) to receive ALL points possible. FINAL EXAM REVIEW Simple Machines- Lever A first class lever, in static equilibrium, has a 150 lb resistance force and 107 effort force. The lever’s effort force is located 6 ft from the fulcrum. 1. Sketch and annotate (Variables & Numbers) the lever system described above 2. What is the AMA of the system? 3. Using static equilibrium calculations, calculate the length from the fulcrum to the resistance force Simple Machines- Inclined Plane A civil engineer must design a wheelchair accessible ramp next to a set of steps leading up to a building. The height from the ground to the top of the stairs is 3 ft. Based on ADA codes the slope must be 1:10 or less. Slope= Rise Run 4. Sketch and annotate (Variables & Numbers) the inclined plane described above.

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Principles of Engineering Name___________________Directions: Show ALL work (initial equation & solving for) to receive ALL points possible. FINAL EXAM REVIEW Simple Machines- LeverA first class lever, in static equilibrium, has a 150 lb resistance force and 107 effort force. The lever’s effort force is located 6 ft from the fulcrum.

1. Sketch and annotate (Variables & Numbers) the lever system described above

2. What is the AMA of the system?

3. Using static equilibrium calculations, calculate the length from the fulcrum to the resistance force

Simple Machines- Inclined PlaneA civil engineer must design a wheelchair accessible ramp next to a set of steps leading up to a building. The height from the ground to the top of the stairs is 3 ft. Based on ADA codes the slope

must be 1:10 or less. Slope=RiseRun

4. Sketch and annotate (Variables & Numbers) the inclined plane described above.

5. Using the ADA code, what is the allowable minimum length of the ramp base”

6. Using the known height and calculated base length, what is the length of the slop of the ramp?

7. What is the IMA of the ramp?

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8. If a person and wheelchair have a combined weight of 185 lbs, how much ideal effort force is required to travel up the ramp?

Simple Machines- GearsA simple gear train is composed of three gears. Gear A is the driver gear and has 10 teeth, gear B has 28 teeth and gear C has 12 teeth.

9. Sketch and annotate (Variables & Numbers) the gear train described above.

10. If the output is at gear C, what is the gear ratio?

11. If gear A rotates at 65 rpm, how fast is gear C rotating?

12. If the output of torque at gear C is 158 ft-lb, what is the input torque at gear A?

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Electrical Circuits13. Calculate the value of RT for each of the circuits shown below

Circuit 1 Circuit 2Picture

Formula

Calculations

Answer WITH UNITS

14. Use Ohm’s Law to calculate the unknown quantity for each. Be sure to use proper Engineering notation and correct units. (4 pts each)

1000 mA = 1A1,000,000 A=1Aμ

1k = 1000Ω ΩCircuit 1 Circuit 2 Circuit 3

Picture

Formula

Calculations

Answer WITH UNITS

950 Ω

1.5kΩ

200Ω

4.8kΩ

7.3kΩ

720Ω

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15. Convert 50 C to Fahrenheit⁰

16. Convert 50 C to Kelvin⁰

Work/Energy/Power17. The electric winch is powered by a 12V battery. The winch lifts 175 Newton weight a total of

9 meters in 13 seconds and draws 25 A.a. Sketch and annotate (Variables & Numbers) the winch described above.

b. Find the efficiency of the electric winch as a percentage and round to the nearest tenth

18. Give two advantages and two disadvantages for the following types of alternative energy.Advantages Disadvantages

Solar Panel 1.

2.

1.

2.

Hydrogen Fuel Cell 1.

2.

1.

2.

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Thermodynamics19. A piece of aluminum block at 90 C is placed in 4 L (= 4 kg) of water at 25 C. Determine the ⁰ ⁰

mass of the block if the final equilibrium temperature T f=31° C.Givens

cwater=4184 Jkg° C

c Al=900 Jkg° C

a. List known value(s)

b. List unknown value(s)

c. Select Equations

d. Substitute and Solve

20. Use the provided R-value chart and illustration below to calculate the R-value of the wall cavity (3pts)

2 X 4 Construction

Wood Bevel Lab Siding

1” Extruded Polystyrene3.5 ‘

Fiberglass Batt5/8 “ Drywall

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R-Value Chart

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Construction Material R-Value½ in. Drywall 0.455/8 in. Drywall 0.56Particle Board – ½ in. 0.63Particle Board – ¾ in. 0.94Fiberboard ½ in. 1.32Extruded Polystyrene 1 in. 4.00Extruded Polystyrene 1 ½ in. 6.00Foil-faced Polyisocyanurate 1 in. 7.202 x 4 4.382 x 6 6.88Hardwood 0.90

Masonry Systems R-ValueBrick 4 in. common 0.80Brick 4 in. face 0.44Concrete Block – Normal wt. 12 in. empty core 1.23Concrete Block – Light wt. 12 in. empty core 2.60 - 2.30Cement Mortar 0.20Sand and Gravel 0.60Stucco 0.20

Roofing R-ValueAsphalt Roll 0.15Asphalt Shingle 0.44Slate 0.05Wood 0.94

Siding R-ValueWood Shingles 0.87Wood Drop 0.79Wood Bevel Lapped 0.80Aluminum/Steel – Hollow 0.61Aluminum/Steel – with 3/8 in. Backer 1.82

Insulation R-Value per in.Fiberglass Batt 3.142 Blankets – Rock Wool 3.0 - 3.8Loose Fill – Cellulose 2.8 - 3.7Loose Fill – Fiberglass 0.7 lb/cu.ft 2.2 - 4.0Loose Fill – Rock Wool 3.1Loose Fill – Vermiculite 2.2Extruded Polystyrene 4.00

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21. Find the x and y coordinates of the centroid of the entire shape.

x= =¿

y= =¿

AREA (A) CENTROID X (X) CENTRIOD Y (Y) Σ AX Σ AYShape 1Shape 2TOTAL

22. Complete the chart below by calculating the cross-sectional area, Moment of Inertia, and beam deflection, given a load of 250 lbf, a Modulus of Elasticity of 2,500,000 psi, and a span of 12 ft. Show all work.

Beam Actual Dimensions (in.)

4.5 x 6.5

Horizontal Orientation

Formula Work Answer

Cross-Sectional Area (in.2)

Moment of Inertia(in.4)

Beam Deflection(in.)

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23. Study the truss in Figure1 and complete the following problems.

a) Calculate the height of the truss. (answer precision = 0.00)

b) The free body diagram of joint A in Figure 2 shows FAC in compression, FAD in tension, RAX, and RAY replaced with a magnitude of 100 lbs. Using the free body diagram in Figure 2, calculate the magnitude of force FAC. (answer precision = 0.00)

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24. The stapler in Figure 3 is an example of what class of lever?

A.1st classB.2nd class C. 3rd classD.4th class

25. If the pulley system, shown in Figure 4, is in static equilibrium and supports a 125 lbs. of weight, what is the effort force?

A.20 lbsB.25 lbsC. 400 lbsD.C. 500 lbs

26. Figure 5 represents a belt driven system. Pulley B, which has a diameter of 24 inches, is being driven by Pulley A, which has a diameter of 8 inches. If Pulley A is spinning at 45 RPMs, then Pulley B is spinning at ______ RPMs.

A. 240C. 4 B. 15D. 64

27. Circular motion that occurs in a heated fluid, as shown in Figure 6, is an example of _________.A. convection.C. radiation.

B. conduction.D. R-value.

28. If a string of lights is wired in ______, all the lights go out when one light fails. A. seriesC. order

B. lineD. parallel

29. If a motor requires 12 Volts and has 80 Ohms of resistance, what is the amperage value?

A. 65 B. 0.75

C. 480 D. 0.15

30. Because brass is a combination of copper and zinc, it would be classified as a(n) ____________.A. alloyC. thermoset

B. elastomerD. oxide

31. Which of the following is the process that breaks unwanted material away from the part?A. TurningC. Milling

B. ShearingD. Rolling

32. A material that is capable of considerable plastic deformation would be referred to as a __________ material.

A. brittleC. tensile

B. polymerD. ductile

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33. a. What class of lever is shown in Figure 6? Justify your answer. ____________________________________________________________________________________________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________b. How much effort force is needed to balance 40 pounds of resistance?

34. A wheel is used to turn a valve stem on a water valve. If the wheel radius is 1.25 foot and the axle radius is 2 inches, what is the mechanical advantage of the wheel and axle?

35. Identify the meaning of number in the middle (refer to the picture on the right).A. Identifies resin contentB. Indicates that the product is made from recycled materialC. Indicates the percentage of the product made from recycled materialD. Indicated the percentage of the product that will be recycled

36. What is the mechanical advantage of a 3/8” diameter screw with 15 threads per inch if a 1.5” diameter screwdriver is used to install the screw?

37. Study pictures and graph below. Explain: A. Fill in the table below

Graph # Material A Material or B Brittle or Ductile12

C. Explain term “necking” and identify material and graph that exhibits necking

38. Is truss shown statically determinate? Justify your answer.

Material A Material B

20 3 ft

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____________________________________________________________________________________________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

39. Following graph represents a tension test of titanium alloy. Label the following points on the graph:

A. Proportional limitB. Point where material breaksC. Material exhibits neckingD. Modulus of ElasticityE. Ultimate Stress

40. A 5 in. by 6 in. rectangular steel bar is used as a member in a bridge truss. The diagonal member is 18 ft long, and its modulus of elasticity is 32,000,000 psi. If the strain in the diagonal member is measured as 0.0015, determine:

A. The axial stress

B. The tension force in the bar

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41.A

brass tensile test sample with an original cross-sectional area of 0.008 in2 and an original test length of 1 inch was pulled apart in a tensile test machine. A stress vs. strain diagram (above) was developed from the test information. Use the diagram to answer the following question.

What is the modulus of elasticity for this material? In your calculations, start at the origin and end at the proportional limit.

42. A hydraulic lift system utilizes two 3 in. diameter cylinders. Workers must determine how much the system is capable of lifting before deciding how much weight can be lifted safely. The system runs at a gauge pressure of 2000 lb/in.2.

a) Sketch and label all known and unknown values.

Sketch

b) How much is the system capable of lifting? Formula Substitute / Solve Final Answer

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43. The air temperature in a 28 in.3 container with a free sliding piston is initially measured at 45 °F. The temperature is raised to 200 °F. What is the new volume of the container?

a) Sketch and label all known and unknown values.Sketch

b) What is the volume in the cylinder after the temperature has been raised? Formula Substitute / Solve Final Answer

44. The owner of the Harborside restaurant is interested in how much people spend at the restaurant. He examines 10 randomly selected receipts for parties of four and writes down the following data.

134, 155, 138, 199, 142, 234, 245, 112, 146, 360

Find out the spending range of 95% of people. Write your answer as a compound inequality. Hint: 95% of people will be within 2 standard deviations.

45. In the old days, there was a probability of 0.75 of success in any attempt to make a telephone call. Calculate the probability of having 3 successes in 10 attempts.

46. What is the theoretical probability of rolling a die four times and getting an odd every time?

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47. What is the realitive frequency of at least two tails occuring based on the data below?

HTH TTH TTT THH HHH THT HHT HHH TTH HTH HTT

48. What is the theoretical probability of choosing a face card or a diamond from a deck of 52 cards?

49. Solve following problem two ways. What is the probability of tossing a coin four times and it landing heads up two times? First, use conventional probability approach that you learned in the middle school:

Second, use Bernoulli Process.

50. Use Bayes’ theorem to solve following problem:Suppose that Andrew moved to the city and now can decide to go to school by one of three modes of transportation, car, bus, or commuter train. Because of high traffic, if he decides to go by car, there is a 40% chance he will be late. If he goes by bus, which has special reserved lanes but is sometimes overcrowded, the probability of being late is only 25%. The commuter train is almost never late, with a probability of only 3%, but is more expensive than the bus. (a) Suppose that Andrew is late one day, and his Principal wishes to estimate the probability that he drove to school that day by car. Since he does not know which mode of transportation Andrew usually uses, he gives a prior probability of 1/3 each of the three possibilities. What is the Principal’s estimate of the probability that Andrew drove to school?

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51. Find the x and y components of the initial velocity of the projectile.Known/Unknown Equations Work Solution (units)

52. Find the range of the projectile using the information in the problem above. Known/Unknown Equations Work Solution (units)

53. How many seconds until the projectile reaches the maximum height?Known/Unknown Equations Work Solution (units)

54. Find the angle needed to launch a projectile 40 ft more.Known/Unknown Equations Work Solution (units)

550

V = 45 ft/sec

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55. Please write a flow chart for the following:

Make the left motor spin as long as the bump switch is being held down. Its direction depends on the sonar. If a person is within 15 cm of the ultrasonic sensor the it will turn three-quarter speed clockwise (positive), if a person is from 15-25 cm away then it will turn full speed counterclockwise (negative) and if a person is over 25 cm away the right motor will turn on half speed for 5 seconds before turning off. If the button is released, the behavior will repeat if it is pressed again.

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56. Please write the code for the program:**Add comments in your program to explain the purpose of each step.**** Do NOT forget to put a “;” after each line****Code as if you are in RobotC****Call the functions correctly, make sure they are spelled and capitalized right**

#pragma config(Sensor, in1, lineFollower, sensorLineFollower) __________________________________#pragma config(Sensor, in2, potentiometer, sensorPotentiometer) ______________________________#pragma config(Sensor, in3, lightSensor, sensorReflection) _______________________________________#pragma config(Sensor, dgtl1, limitSwitch, sensorTouch) ________________________________________#pragma config(Sensor, dgtl2, bumpSwitch, sensorTouch) ________________________________________#pragma config(Sensor, dgtl3, quad, sensorQuadEncoder) _____________________________________#pragma config(Sensor, dgtl5, sonar, sensorSONAR_cm) _______________________________________#pragma config(Sensor, dgtl12, green, sensorLEDtoVCC) ______________________________________#pragma config(Motor, port1, flashlight, tmotorVexFlashlight, openLoop, reversed)#pragma config(Motor, port2, rightMotor, tmotorServoContinuousRotation, openLoop)#pragma config(Motor, port3, leftMotor, tmotorServoContinuousRotation, openLoop)#pragma config(Motor, port9, servoMotor, tmotorServoStandard, openLoop)/* PLTW Pre-Engineering Principles of Engineering_____________________________________________________________ Activity:_________________________________________________________________________________________________ Name:__________________________________________________________________________________________________ Date:____________________________________________________________________________________________________ Class:___________________________________________________________________________________________________ Period:____________________________________________________________________________________ */__________ task main()_________________________________________________________________________________________________{_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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