Principles of Engineering
Final Examination
Parts A, B & C
ANSWER KEY
Spring 2009
PRACTICE EXAM
For Teacher Use ONLY
®
Project Lead The Way
Copyright 2006 - Page 1 of 16
** IMPORTANT **
Please read the document “POE Exam Directions – Spring 2006”
before you administer and grade your students’ exams.
All three parts of the POE End-Of-Course exam (A, B & C) require a
conversion to obtain a student’s score out of 50 points.
Each student’s raw (unconverted) scores for Parts A & B or Parts A &
C must be entered into the Excel score conversion chart (POE
Conversion Chart – Spring 2006.xls) in order to obtain the student’s
calculated score.
The spreadsheet is designed to convert the student’s raw score for
each part of the exam, and to calculate the student’s final test score
for either the high school or college credit portion of the exam.
A sample conversion chart for each part of the exam has been
included below. These are for information purposes only. Please
download and use the spreadsheet to obtain your students’ final
exam scores and do not convert and add your students’ scores by
hand.
Part A Scoring Conversion Chart
Score
40
39
38
37
36
35
34
33
32
31
Conversion
50
49
48
46
45
44
43
41
40
39
Score
36
35
34
33
32
31
30
29
28
Conversion
50
49
47
46
44
43
42
40
39
Score
30
29
28
27
26
25
24
23
22
21
Conversion
38
36
35
34
33
31
30
29
28
26
Score
20
19
18
17
16
15
14
13
12
11
Conversion
25
24
23
21
20
19
18
16
15
14
Score
10
9
8
7
6
5
4
3
2
1
Conversion
13
11
10
9
8
6
5
4
3
1
Part B and C Scoring Conversion Chart
Score
27
26
25
24
23
22
21
20
19
Conversion
38
36
35
33
32
31
29
28
26
Score
18
17
16
15
14
13
12
11
10
Conversion
25
24
22
21
19
18
17
15
14
Score
9
8
7
6
5
4
3
2
1
Conversion
13
11
10
8
7
6
4
3
1
®
Project Lead The Way
Copyright 2006 - Page 2 of 16
Part A – Multiple Choice Questions
Question
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
35
36
37
38
39
40
Answer
B
D
D
C
A
A
B
A
A
C
D
C
A
B
D
D
B
A
C
C
B
C
A
D
A
A
C
D
A
B
B
C
B
D
C
D
B
D
C
B
POE Assessment Concepts
1.1 – Engineers as Problem Solvers
1.3 – Careers in Engineering
2.1 – Sketching
2.1 – Sketching
2.3 – Data Representation & Presentation
3.1 – Design Process
4.1 – Mechanisms
4.1 – Mechanisms
4.1 – Mechanisms
4.1 – Mechanisms
4.1 – Mechanisms
4.1 – Mechanisms
4.2 – Thermodynamics
4.3 – Fluid Systems
4.3 – Fluid Systems
4.4 – Electrical Systems
4.4 – Electrical Systems
4.5 – Control Systems
4.5 – Control Systems
4.5 – Control Systems
4.5 – Control Systems
5.1 – Statics
5.1 – Statics
5.1 – Statics
5.1 – Statics
5.2 – Strength of Materials
6.1 – Categories of Materials
6.2 – Properties of Materials
6.3 – Manufacturing Processes
6.3 – Manufacturing Processes
6.4 – Quality Control
6.4 – Quality Control
6.5 – Material Testing
6.5 – Material Testing
7.1 – Reliability
7.2 – Case Study
8.1 – Linear Motion
8.2 – Trajectory Motion
8.2 – Trajectory Motion
8.2 – Trajectory Motion
Answer Breakdown: A-10; B-10; C-10; D-10
®
Project Lead The Way
Copyright 2006 - Page 3 of 16
Part B – High School Performance Exam
1 point for correctly
labeling RAX
Figure 1
Figure 2
1. Study the truss in Figures 1 and its (incomplete) free body diagram in Figure
2, and answer the following questions.
[Unit 5.1 Statics]
a. Calculate the length of truss member BC. (answer precision = 0.0)
[3 points]
BC =
AB2 + AC2
1 point for stating
the formula
=
(60 in)2 + (50 in)2
=
3600 in2 + 2500 in2
=
6100 in2
BC = 78.1 in
1 point for the
correct answer with
correct units
1 point for showing
substitutions
b. Calculate the magnitude and direction of the missing reaction force that
occurs at joint A. Then, draw and label that reaction force on Figure 2.
(answer precision = 0.0) [4 points]
ΣFX = 0 = RBX + RAX
ΣMB = 0
0 = 83.3 lbs + RAX
RAX = -83.3 lbs
The sum of the moments around node B could also be
used to determine the missing reaction force at joint A.
Alternative Method
1 point for stating
the formula
1 point for showing
substitutions
Negative value means the
reaction force is acting to
the left. See label in
Figure 2.
1 point for the correct
answer with correct units
®
Project Lead The Way
Copyright 2006 - Page 4 of 16
[Unit 8.2 Trajectory Motion]
Figure 3
2. The actual performance of a POE student’s ballistic device was recorded and
plotted for comparison against its calculated ideal performance. Study the
graph in Figure 3 and use it to answer the following questions.
a. What two initial trajectory angles could be used to shoot the projectile an
ideal distance of 6 feet? [2 points]
angle 1: ____10°_____
angle 2: ____80°_____
b. What would the actual initial velocity be if it were calculated using the
results of a 30° firing angle? Use 32.15 ft/sec2 for acceleration due to
gravity. (answer precision = 0.00) [3 points]
VI =
gX_
sin(2θ)
1 point for stating
the formula
=
32.15 ft/sec2 x 12 ft
sin(2 x 30°)
=
385.8 ft2/sec2
sin60°
=
385.8 ft2/sec2
0.87
=
443.4 ft2/sec2
1 point for showing
substitutions
Formatted: Bullets and Numbering
VI = 21.06 ft/sec
1 point for the correct
answer with correct units
®
Project Lead The Way
Copyright 2006 - Page 5 of 16
3. A tensile test sample had an original cross-sectional area of 0.2 in2 and an
original test length of 2 in. It was pulled apart in a tensile test machine, and
the resulting Force-Displacement diagram is shown in Figure 4. Use this
diagram to answer the following questions. [Unit 6.2 Properties of Materials]
a. At point “A” on the diagram, the test sample had reached its
_____yield_____ point. [1 point]
b. At point “B” on the diagram, the test sample had reached its
____ultimate___ force point. [1 point]
c. If the change in force identified on the diagram is 100,000 lbs, and the
change in displacement is 0.1 in, what is the modulus of elasticity for this
material? [3 points]
∆F • Lo
E = ∆δ
• Ao
1 point for stating
the formula
100,000 lbs • 2 in
E = 0.1 in • 0.2 in2
E = 10,000,000 psi
200,000 in•lbs
E=
0.02 in3
E = 10 x 106 psi
1 point for showing
substitutions
…or…
1 point for the correct
answer with correct units
Figure 4
®
Project Lead The Way
Copyright 2006 - Page 6 of 16
4. The closed-loop program shown below is designed to control a light using a
digital switch. Study the program description and decide which of the icons
from the answer bank (A through F) must be used to complete the flowchart
program. Write the letter of the correct icon in the proper empty box. No icon
will be used more than once, and some may not be used at all. [4 points]
Program Description:
[Unit 4.5 Control Systems]
When the program starts, lamp (M1) is turned ON, and the computer checks
to see if the switch (I1, wired normally open) is being pressed. The program
will loop back until the switch is pressed. When the switch is pressed, the
value of variable A will be incremented by 1. The computer will then wait 0.2
seconds before checking the value of variable A to see if it is greater than or
equal to 13. If the value of variable A is less than or equal to 12, the program
will loop back to the beginning. If variable A is greater than or equal to 13, the
lamp will turn OFF and the program will end.
E
A
C
F
®
Project Lead The Way
Copyright 2006 - Page 7 of 16
5.
The image below identifies a 9-step design process in which four of the steps
have been omitted. Write the answer letter for the correct process step from
the answer bank in the proper location within the graphic. [4 points]
[Unit 3.1 Design Process]
C
D
A
B
Answer Bank
Answer
Process Step
A
Model and Prototype
B
Choose a Solution
C
Redesign and Improve
D
Investigate and Research
®
Project Lead The Way
Copyright 2006 - Page 8 of 16
6. Study the technical drawing below, and sketch the missing center line and
hidden lines in the orthographic views. Assume the circle represents a thru
hole. [6 points]
[Unit 2.1 Sketching]
2 points for the two
missing hidden lines,
and 1 point for the
missing center line in
the top view
2 points for the two
missing hidden lines in
the left-side view
1 point for the missing
hidden line in the front
view
1 point will be subtracted for each line that is incorrectly sketched (i.e. an
object line appears where a hidden line should be), incorrectly located
(i.e. a hidden line appears where none should exist), or completely
missing.
®
Project Lead The Way
Copyright 2006 - Page 9 of 16
[Unit 4.1 Mechanisms]
Figure 5
7a. What class of lever is shown in Figure 5? Justify your answer. [2 points]
Figure 5 shows a second class lever. Second class levers always have
the load located between the effort and the fulcrum.
1 point for stating the
correct class of lever
1 point for stating a
valid justification
7b. How much effort force is needed to balance the 100 lb load? [3 points]
LE x E = LR x R
8 ft x E = 4 ft x 100 lbs
8 ft x E = 400 ft•lbs
400 ft•lbs ÷ 8 ft = E
1 point for stating
the formula
ΣM = 0 = (LE x E) + (LR x R)
Alternative Method
1 point for showing
substitutions
E = 50 lbs
1 point for the correct
answer with correct units
0 = -(8 ft x E) + (4 ft x 100 lbs)
0 = -(8 ft x E) + 400 ft•lbs
-400 ft•lbs = -(8 ft x E)
-400 ft•lbs ÷ -8 ft = E
®
Project Lead The Way
Copyright 2006 - Page 10 of 16
Part C – College Credit Performance Exam
[Unit 5.1 Statics]
Figure 1
Figure 2
1. Study the truss in Figure 1 and its free body diagram in Figure 2, and answer
the following questions.
a. Draw a point free body diagram for joint C and label all of the given
information for that node (assume all member forces are tension).
[2 points]
A 1-point response may consist of:
C
FAC
FAC, FBC and/or F1 arrows
30°
improperly labeled (or not labeled
at all); FAC and/or FBC arrows
F1
FBC
pointing toward node C (assuming
100 lbs
compression)
b. Calculate the length of truss member BC. (answer precision = 0.000)
[3 points]
BC = cosine θACB x AC
BC = 3.464 ft
BC = cosine 30° x 4 ft
BC = 0.866 x 4 ft
1 point for stating
the formula
1 point for showing
substitutions
1 point for the correct
answer with correct units
c. Using joint C, determine the magnitude and type of force (tension or
compression) that is being carried by truss member BC. (answer precision
= 0.0) [4 points]
ΣFCY = 0 = F1 + FBCY
0 = -100 lbs + -(FBCsinθACB)
0 = -100 lbs + -(FBCsin30°)
0 = -100 lbs + -(FBC • 0.5)
100 lbs = -FBC • 0.5
100 lbs ÷ -0.5 = FBC
FBC = -200 lbs
Negative sign shows
initial assumption of
tensile force was
incorrect. Member BC is
experiencing
compression
1 point for stating
the formula
1 point for showing
substitutions
1 point for the correct
answer with correct units,
and 1 point for correctly
identifying compression
®
Project Lead The Way
Copyright 2006 - Page 11 of 16
Take-off angle = 35°
Take-off speed = 36.99 ft/sec
[Unit 8.2 Trajectory Motion]
Figure 3
2. Study Figure 3 and answer the following questions.
a. What was the motorcyclist’s initial horizontal velocity? (answer precision =
0.00) [3 points]
VIX = VI cosine θ
VIX = 36.99 ft/sec cosine 35°
VIX = 30.33 ft/sec
VIX = 36.99 ft/sec • 0.82
1 point for stating
the formula
1 point for showing
substitutions
1 point for the correct
answer with correct units
b. What was the horizontal distance between the take-off and landing points?
Assume that both points exist on the same horizontal plane. Use 32.15
ft/sec2 for acceleration due to gravity. (answer precision = 0.00) [3 points]
X =
VI2 sin(2θ)
g
1 point for stating
the formula
X =
(36.99 ft/sec)2 sin(2 • 35°)
32.15 ft/sec2
X =
1368.26 ft2/sec2 sin 70°
32.15 ft/sec2
X =
1368.26 ft • 0.94
32.15
X =
1286.16 ft
32.15
1 point for showing
substitutions
X = 40.00 ft
1 point for the correct
answer with correct units
®
Project Lead The Way
Copyright 2006 - Page 12 of 16
3. A test sample, having a cross-sectional area of 0.2 in2 and a 2 inch test
length, was pulled apart in a tensile test machine. Figure 4 shows the
resulting Stress-Strain diagram. Use the information in the diagram to answer
the following questions.
[Unit 6.2 Properties of Materials]
a. Calculate the force that the sample experienced at the proportional limit.
(answer precision = 0.0) [3 points]
Fp.l. = AO x σp.l.
Fp.l. = 0.2 in2 x 40,000 psi
1 point for stating
the formula
1 point for showing
substitutions
Fp.l. = 8,000 lbs
1 point for the correct
answer with correct units
b. Starting at the origin and ending at the proportional limit, calculate the
modulus of elasticity for this material. [3 points]
E = σp.l.
E = 0.005 in/in
E = 8,000,000 psi
E = ∆F • Lo
∆δ • Ao
8,000 lbs • 2 in
E = 0.01 in • 0.2 in2
E = 8 x 106 psi
v p.l.
Alternative Method
1 point for stating
the formula
40,000 psi
E=
…or…
16,000 in•lbs
0.002 in3
1 point for showing
substitutions
1 point for the correct
answer with correct units
Figure 4
®
Project Lead The Way
Copyright 2006 - Page 13 of 16
4. The closed-loop program shown below is designed to control a light and
shuttle motor. Study the program description and decide which of the icons
from the answer bank (A through I) must be used to complete the flowchart
program. Write the letter of the correct icon in the proper empty box. No icon
will be used more than once, and some may not be used at all. [5 points]
[Unit 4.5 Control Systems]
Program Description:
When the program starts, the computer waits for a start switch (I1, wired
normally-open) to be pressed. When the start switch is pressed a lamp (M2)
is turned ON, and a shuttle (M1) moves toward limit switch #1 (I2, wired
normally-closed). When limit switch #1 is contacted the shuttle stops and
reverses direction toward limit switch #2 (I3, wired normally-open). When limit
switch #2 is contacted, the shuttle stops, and the value of variable A will be
incremented by 1. The computer will then check the value of variable A to see
if it is equal to 4. If the value of variable A is less than 4, the program will loop
back and the shuttle will complete another back-and-forth cycle between the
two limit switches. After 4 cycles, the lamp will turn OFF and the program will
end.
C
B
E
D
H
®
Project Lead The Way
Copyright 2006 - Page 14 of 16
5. Each of the following four statements represents a step in a design process.
There are nine design process steps listed in the answer bank. Identify which
of the steps from the answer bank is being represented by each statement by
writing the step number on the line provided. [4 points]
[Unit 3.1 Design Process]
a. A team of Principles of Engineering students spent half of a class period
debating which one of their initial sketches would be worth pursuing.
Identify the step in the design process: _____5_____
b. A team of Principles of Engineering students downloads their control
program to the computer interface device on their marble-sorting machine.
The machine proceeds to sort marbles with 30% overall accuracy.
Identify the step in the design process: _____8_____
c. A team of Principles of Engineering students modifies a section of their
marble-sorting machine that is not working correctly.
Identify the step in the design process: _____9_____
d. A team of Principles of Engineering students uses the internet to gather
information about how a phototransistor functions as a digital switch.
Identify the step in the design process: _____3_____
Answer Bank
Step #
Design Process Step Description
1
Identify the Problem
2
Define the Criteria
3
Research and Investigate
4
Generate Alternative Solutions
5
Choose a Solution
6
Refine and Develop the Solution
7
Model and Prototype the Solution
8
Test and Evaluate the Solution
9
Redesign and Improve the Solution
®
Project Lead The Way
Copyright 2006 - Page 15 of 16
6. Study the technical drawing below. The front, back, right- and left-side faces
are identical in appearance. As shown in the top view of the orthographic
drawing, the flat-bottomed, blind hole has been machined to the same depth
in all instances. Complete the front view of the orthographic drawing by
sketching the missing object line and hidden lines. [6 points]
[Unit 2.1 Sketching]
5 points for the five missing hidden
lines, and 1 point for the missing
object line in the front view
1 point will be subtracted for each line that is incorrectly sketched (i.e. an
object line appears where a hidden line should be), incorrectly located
(i.e. a hidden line appears where none should exist), or completely
missing.
®
Project Lead The Way
Copyright 2006 - Page 16 of 16