10T 18T 16T

Principles of Engineering - Classwork

Directions: Select the letter of the response that best completes the item or answers the question and carefully bubble it in on the answer sheet.

Guidelines: Show all formula.

1. The wheel of a bicycle makes one full revolution. The radius of the wheel is 10". Assuming no sliding or slip between the wheel and the road, the distance traveled by the bicycle is ________ inches.

a. 628b. 62.8

c. 314d. 31.4

2. A ramp is used to raise an object 3' from the ground. The lengths of the sides of the ramp are shown in the figure below. The mechanical advantage of the ramp is _____.

a. 1.044b. 3.33c. 3.48d. 0.958

10.44'

3'

10'

3. What is the effort needed to push a 75 pound weight up the ramp?a. 21.00 lbsb. 261.00 lbs

c. 261.55 lbs.d. 21.55 lbs

4. A wheelbarrow is an example of what class of lever?a. Class 1.b. Class 2.

c. Class 3.d. Class 4.

5.Skills that are critical for a good engineer include ____________.a. sketchingb. oral communicationc. technical writingd. all of the above

6.The purpose of the middle gear in the diagram below is to ____________.a. allow the drive and driven gear to rotate in the same direction. b. allow the drive and driven gear to rotate in opposite directions.c. increase the output RPM's of the driven gear.d. increase the output torque of the driven gear.

Drive Gear60 RPMClockwise

7.The middle gear will turn counter clockwise at what rate if the drive gear is moving at 60 RPM?a. 333.33 RPMb. 108.00 RPM

c. 108.33 RPMd. 33.33 RPM

8.What is the overall gear ratio for the gear train?a. 5:8b. 8:9

c. 8:5d. 9:5

9.If 15 lb-ft of torque is applied at the drive gear, what is the output at the driven gear?a. 9.375 lb-ftb. 24 lb-ft

c. 160 lb-ftd. .625 lb-ft

10. Heat is the transfer of energy from one place to another. It naturally occurs by one of three methods. Which one is not a natural heat transfer method?

a. Conductionb. Convection

c. Radiationd. Refrigeration

11. Two resistors with 15 ohms of resistance eachare connected in series to a 1.5-volt battery. The current running through the system will be ___________.

a. 0.50 amps.b. 0.05 amps.

c. 1.0 amps.d. 0.20 amps.

12. An angle, whose sin is equal to 5/13, measures___________.a. 67.40

b. 30.00c. 22.60

d. 65.00

13. What is the weight (resistance) you could lift using a first-class lever if you apply 20 lbs of effort? The effort arm is 10 feet and the resistance arm is 5 feet.

a. 10 lbsb. 20 lbs

c. 30 lbsd. 40 lbs

14. Find the mechanical advantage of a wheel and axle system if the wheel has a radius of 1.5 feet and the axle has a radius of 6 inchesif the force is put on the axle.

a. .25b. .33

c. 2.0d. 3.0

15.Vehicles have an engine that uses a small axle (effort) to turn a much larger wheel against the ground (load). In this scenario, which of the following best describes the mechanical advantage?

a. A value equal to 0b. A value between 0 and 1c. A value equal to 1d. A value greater than 1

2

16.Determine the mechanical advantage of the pulley system shown in the diagram to the right.

a. 3b. 6c. 7d. 8

17. Given the configuration to the right, how many pounds of effort force would a user have to exert on the rope to lift this 60 lb. weight?

a. 15b. 20c. 30d. 60

18. A pulley with 3 supporting strands would require 30 lbs to lift how much weight in pounds?a. 10b. 33

c. 90d. 270

19. The fixed point of rotation on a lever is a(n):a. fulcrumb. center point

c. wedged. pivot

20. In a second class lever, the distance from the effort to the fulcrum is ________the distance from the resistance to the fulcrum.a. Greater thanb. Greater than or less than

c. Less thand. Less than or equal to

21. The diagram at right represents a: a. bar graphb. pie chartc. line graphd. histogram

3

22. Study the gear train at right. If the 20-toothed gear rotates 6 times, how many times will the 40-toothed gear rotate?

a. 3 timesb. 6 timesc. 9 timesd. 12 times

23. A force of 50 lbs is applied to a 1-foot diameter wheel. The wheel is turning a .25 inch diameter axle. How much mechanical advantage does the wheel provide?

a. 4b. 12.5

c. 24d. 48

24. If friction is included in a simple machine, the amount of effort required to move a load will be _____________ what is calculated using the formulas for simple machines.

a. less thanb. less than or equal toc. greater thand. greater or less than

25. Radiation is the chief method of energy transfera. from the sun to an earth satelliteb. from a gas flame to the top layer of water in a teakettle.c. from a soldering iron to metals being solderedd. from the bottom of a glass of water to an ice cube floating in it.

26. Of the processes below, the one in which practically all the heat transfer is by conduction is:a. from the sun to an earth satelliteb. from a gas flame to the top layer of water in a teakettle.c. from a stovetop to a pot of water above it d. from the bottom of a glass of water to an ice cube floating in it.

27. Plastic handles are often used on kitchen utensils becausea. the plastic is a good radiatorb. the plastic is a good insulatorc. the plastic is a good conductord. the plastic softens gradually with excessive heat

N=20

N=40

4

28. Identify which of these circuits is a series circuit (there may be more than one shown!):

29. Given the lengths of the sides of the following triangle, what is the value of angle θ?a. 30°b. 36.9°c. 53.1°d. 60°

30. Given the lengths of the sides of the triangle above, what is the value of y?a. 18b. 14

c. 10d. 12

31. In a series circuit, increasing the resistance while keeping current the same will cause the voltage to:

a. Stay the sameb. Increase

c. Decreased. Go to zero

32. What is the mechanical advantage of a 3/8” diameter screw with 20 threads per inch if a 1.5” diameter screwdriver is used to install the screw?

a. 94b. 47c. .118d. 24

16

20

y

5

40TDriver Driven

10T

20T

5T

A

B

C D

33. Study the circuit above. Which of the following electrical properties is being measured by the multimeter?

a. Resistanceb. Voltage

c. Currentd. RPMs

34. If electrical wires are connected to ports 1 and 2 on the switch above, then the switch will be wired normally-_____________.

a. Commonb. Closed

c. Opend. Neutral

35. A compound gear train above consists of 4 gears with teeth as marked. A is the driver gear and gears B and C share the same shaft. If gear A rotates once, how many times will gear D rotate?

a. 1/16b. 4

c. 1/4d. 1/2

6

FORCE

F = 20. lb

¯2 in.

3 i n .

4 in.

36. A circuit has an applied voltage of 120 volts and a current of 250 mA. What is the resistance in the circuit?

a. 30 kΩb. 2.1 Ω

c. 480 Ωd. .48Ω

37. The moment of the wrench below would be __________.a. 40 lb-inb. 80 lb-in

c. 60 lb-ind. 120 lb-in

38. The moment of inertia of the beam above would be __________.a. 1.6 in4

b. 20.8 in4c. 46.8 in4

d. 249.6 in4

39. If the modulus of elasticity of the beam is 1.5x106 psi and a 200 lb weight is placed at the center, 4 ft from each end, how much would the beam deflect?

a. .118 in b. 6.84x10-5 in

c. 1.54 ind. .57 in

7

40. The x-component of the vector above would be __________.a. -48.2 lbs b. -57.6 lbs

c. 48.2lbsd. 57.6 lbs

41. The y-component of the vector above would be __________.a. -48.2 lbs b. -57.6 lbs

c. 48.2lbsd. 57.6 lbs

42. If another force of 10 lbs in the positive x-direction were added to the vector above, what would be the x-component of the resultant force?

a. -58.2 lbs b. -47.6.2 lbs

c. -38.2 lbsd. -67.6 lbs

43. The total resistance in the circuit above would be ___________.a. 986 Ωb. 6080 Ω

c. 594 Ωd. 5940 Ω

44. The current across R1 would be ___________.a. .003 mAb. 3.33 mA

c. 3 Ad. 3.33 A

45. The total current IT would be ___________.a. 9 Ab. .015 mA

c. 9 mAd. 15.15 mA

46. The voltage across R2 would be ___________.a. 2.65 Vb. 9 V

c. 5.6 Vd. 3 V

8

(0,0)

2 in

1 in

47. The centroid of the triangle to the right is closest to__________ as measured from (0,0).a. (.33, .33)b. (.66, .33)

c. (.33, .66)d. (.66, .66)

48. To increase the insulating qualities of a house, a homeowner should:a. Increase the R-valueb. Increase the U-valuec. Increase radiationd. Increase conduction

49. The law stating that heat energy always goes toward entropy, or moves from hot to cold and from order to disorder, is known as:

a. 1st law of thermodynamicsb. 2nd law of thermodynamicsc. Newton’s first lawd. Newton’s second law

50.If given the following information, draw a free body diagram of joint A and

calculate the forces for members AD and AB. Indicate whether the member is in tension or compression.

a) AD Tension , AB Compressionb) AB Tension, AD Compressionc) AD Tension, AB Tensiond) AD Compression, AB Compression

BONUS – What are the forces at AB and AD.

1200 lbf

750 lbf

150 lbf

RCy=960 lbf ↑R Ay=1140 lbf ↑

R Ax=0 lbf →

45o

9

51. A see-saw at the park is in static equilibrium with two children. The child on the left provides

35lbs of resistance force and the child on the right provides 70lb effort force. The lever’s

effort force (child on the right) is located 4 ft from the fulcrum.

a. What is the actual mechanical advantage of the system?

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

52. An industrial water shutoff valve is designed to operate with 14 lb of effort force. The valve

will encounter 144 lb of resistance force applied to a 3 ½ in. diameter axle.

a. What is the required actual mechanical advantage of the system?

b. What is the required wheel diameter to overcome the resistance force?

53. A worker on a zip line crew lifts participants weighing approximately 240 lb several times

during a day from the ground 42 feet below. A block and tackle system with 30 lb of effort

force is designed to lift the materials.

a. What is the required actual mechanical advantage?

b. How many supporting strands will be needed in the pulley system?

54. A civil engineer must design a skateboard ramp for a new skate park. The height from the

ground to the top of the drop in is 12 ft. For safety reasons, the slope must be 1:6 or less.

a. Using the safety requirements, what is the allowable minimum length of the ramp

base?

b. Using the known height and calculated base length, what is the length of the slope of

the ramp?

55. A 7/16 nut driver with a 6 inch diameter handle is used to install a ¼ 18 UNC bolt into a

robotic arm.

a. Determine the circumference where the effort is applied.

b. Determine the pitch of the screw.

c. What is the mechanical advantage gained in the system?

d. How much force can be overcome if 12 lb of force is exerted?

56. A simple gear train is composed of three gears. Gear A is the driver and has 22 teeth, gear B

has 15 teeth, and gear C has 84 teeth.

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

b. If gear A rotates at 60 rpm, how fast is gear C rotating?

c. If the output of torque at gear C is 125 ft·lb, what is the input torque at gear A?

10

57. Three students set up a mechanical winch with FischerTechniks parts and lift a 225 g weight

25 cm in 8 seconds. The students use a multimeter to measure 8.0 volts in the system and the

winch needs 165mA to lift the weight.

a. How many Newtons did it take to lift the weight?

b. How many meters did the weight travel?

c. How much work (J) was done by the system?

d. Calculate the output power of the system.

e. Calculate the input power of the system.

58. A 3kg piece of aluminum metal at 112°C is placed in 6 liters (=6 kg) of water at 22°C. The

specific heat of water is 4148 J/kg°C and the specific heat of aluminum is 900 J/kg°C.

Determine the final temperature (Tf).

a. List all known values.

b. List all unknown values.

c. Select equations.

d. Apply known values.

e. Solve.

59. A 3/16 in. thick acrylic testing box with dimensions of 12 in. x 6 in. is covered with an

unknown ¾ in. insulation material. Determine the thermal conductivity for the insulating

material if a 65W bulb is used to heat the box. The bulb maintains the inside temperature at

32ºC higher than the outside temperature. (1in = 0.0254m)

a. List all known values.

b. List all unknown values.

c. Select equations.

d. Apply known values.

e. Solve.

60. Calculate the cross-sectional area, Moment of Inertia, and beam deflection, given a load of

265 lbf, Modulus of Elasticity of 1,700,000 psi, and a span of 12 ft.

a. Determine the cross-sectional area for this orientation (1.5 x 5.75) (in.2)

b. Determine the Moment of Inertia (in.4)

c. Determine the Beam Deflection (in.)

11

61. Using the equilibrium formula ∑ M =0about point E, calculate the reaction force at joints E

and D. Note: Joint E is a pin and Joint D is a roller. Clue: Calculate reaction force at roller

first, followed by reaction forces at pin. Determine if the truss is Statically Determinate.

62. If given the following information, Determine the reaction Forces at Point A and Point C.

Determine if the truss is Statically Determinate.

A 2.5 in. by 5 in. rectangular steel bar is used as a diagonal tension member in a bridge truss. The

diagonal member is 30 ft long, and its modulus of elasticity is 30,000,000 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

c. The elongation of the member

45o

12

63. The center of a rod must be machined on a lathe to a smaller diameter for use as a specimen in

a tension test. The rod material is expected to break at a normal stress of 65,800 psi. If the

tension testing machine can apply no more than 850lb of force to the specimen, what is the

maximum rod diameter that should be used for the specimen?

64. A pneumatic system is producing 215 lb/in.2 of gauge pressure. A cylinder is needed to press

an adhesive label onto a product. It has been determined that 16 lb of force is optimal to

complete this task.

a. What is the required area of the pneumatic cylinder?

b. What is the required diameter of the pneumatic cylinder?

65. A hydraulic lift system utilizes (four) 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 3150 lb/in.2. 

a. What is the area of each piston?

b. How much is each piston capable of lifting?

c. How much is the system capable of lifting?

66. The gauge pressure of a pneumatic cylinder reads 61 lb/in.2 when the volume is 12 in.3. The

cylinder is compressed until the gauge reads 12 lb/in.2.  Assume standard atmospheric pressure

(14.7 psi).

a. What is the absolute pressure before and after the cylinder gas is compressed?

b. What is the volume in the cylinder after the gas is compressed?

67. The air temperature in a 55 in.3 container with a free sliding piston is initially measured at 62

°F. The temperature is raised to 132°F. 

a. What are the absolute temperature readings initially and after the temperature is

raised?

b. What is the new volume of the container?

68. A 86 ft3 compressor tank container has a gauge pressure of 130 lb/in.2 and a temperature of 89

°F. The temperature after some time decreases to 44 °F.  

a. What are the absolute temperature readings initially and after the temperature

decreases?

b. What is the absolute pressure of the system before the temperature decreases?

c. What is the final pressure in the tank?  Assume standard atmospheric pressure (14.7

psi)

13

69. A flow meter is attached in a hydraulic line that measures 79 gal/min. The line has an inside

diameter of 2.75 in.  (1gal = 231 in3/gal)

a. What is the flow rate measured as in.3 /min at the meter?

b. What is the area of inside diameter of the line?

c. What is the flow velocity where the fluid passes the meter?

70. An experiment is performed 22 times, in which each trial has probability of success 43%.

What is the probability of getting exactly 12 successes?

71. What is the probability that I will get at least 1 Heads and 1 Tails 8 times if I flip 3 coins 22

Times?

72. Consider the following two data sets A and B.

A = {9,12,11,7,7,13}

B = {1,1,10,19,22,19}

a. Calculate the Mean of each data set.

b. What is the Median of each data set.

c. What is the Mode of each data set.

d. Calculate the Standard Deviation of each data set.

e. Which set has the largest standard deviation?

73. LCD screen components for a large cell phone manufacturing company are outsourced to

three different vendors. Vendor A, B, and C supply 46%, 30%, and 24% of the required LCD

screen components. Quality control experts have determined that 10% of vendor A, 15% of

vendor B, and 5% of vendor C components are defective. If a cell phone was chosen at

random and the LCD screen was determined to be defective, what is the probability that the

LCD screen was produced by vendor C?

74. A projectile is any moving object upon which the only active force is ___________.

75. Neglecting air resistance, the horizontal component velocity of a projectile that moves along

the path of a parabolic curve will ________________.

76. List all of the Analog Sensors Used with the Vex Material.

77. List all of the Digital Sensors Used with the Vex Materials.

78. Explain What a While Loop is and how it works

79. Explain what and If…Then statement is and how it works.

80. How do Motors work and what are their values?

81. What is something that is not a motor but used as a motor? (Hint: Vex Part)

14