Transcript TEST REVIEW_DrSmith

TEST REVIEW
Engineering Practicum
Test #1 is Next Week!!!
Monday, Tuesday
Science
vs.
Engineering
Science:
1. Systematically obtaining knowledge by observation and
experience
2. Use the Scientific Method
3. Empirical / Objective
Engineering:
1. Application of math and science by which matter and
energy are made useful to people
2. Designing and implementing solutions that fulfill an
objective, need, or desire – based on knowledge
3. Subjective solutions based on objective knowledge
Fields of Engineering
Major Fields:
1. Aerospace
2. Bioengineering
3. Biomedical
4. Chemical
5. Civil / Structural
6. Electrical
7. Electronic
8. Industrial
9. Material
10. Mechanical
11. Nuclear
Source: http://en.wikipedia.org/wiki/Fields_of_engineering
LETTERING
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Engineer’s communication tool
All capital letters
BETWEEN GUIDELINES
Legible and Consistent
LEGIBLE AND CONSISTENT
LEGIBLE AND CONSISTENT
LEGIBLE AND INCONSISTENT
The Facts
• A growing number of nations seek to gain global market
share in technology-based economic activities.
• What’s made global competitiveness possible in the first
place?
– The Flatteners (4 of 10):
2) 8/9/95
1) 11/9/89
3) Outsourcing and Y2K
4) Offshoring
• While the national policy response must be multifaceted, ensuring an adequate supply of talented
scientists and engineers is one key step.
More Facts
• U.S. ranks 29th of 109 countries in the percentage of 24
year olds with a math or science degree.
Percentage of First Degree University Students Receiving Degrees in Math/Science
How Do Poly Students Compare?
1. Anyone know?
2. We need:
Metrics
Statistics
3. Johns Hopkins Engineering Innovation Course:
Section D:
3 of 22 Failed
(13.6%)
Poly Students:
8 of 8 Failed
(100%)
Trigonometry and Vectors
Trigonometry
State the Pythagorean Theorem in words:
“The sum of the squares of the two sides of a right triangle is
equal to the square of the hypotenuse.”
Pythagorean Theorem:
B
x2 + y2 = r2
r
A
y
x
C
Trigonometry and Vectors
Trigonometry – Pyth. Thm. Problems
NO CALCULATORS – SKETCH
– SIMPLIFY ANSWERS
1. Solve for the unknown hypotenuse of the following triangles:
a)
b)
?
3
4
?
c)
1
?
1
3
1
c2  a 2  b2
2
2
2
2
c a b
c a b
c  a 2  b2 Align equal
signs
possible
2
2
2 when
2
 ( 3)  1
 1 1
 9  16
 3 1
c

2
c5
c2
Trigonometry and Vectors
Common triangles in Geometry and
Trigonometry
You must memorize these triangles
45o
60o
2
2
1
30o
45o
1
2
1
3
3
Trigonometry and Vectors
Trigonometric Functions
NO CALCULATORS – SKETCH
– SIMPLIFY ANSWERS
4. Calculate sine, cosine, and tangent for the following angles:
a. 30o
1
b. 60o
sin 30 =
o
2
60
c. 45o
2
cos 30 = √3
2
tan 30 = 1
√3
1
30o
3
Trigonometry and Vectors
Trigonometric Functions
NO CALCULATORS – SKETCH
– SIMPLIFY ANSWERS
4. Calculate sine, cosine, and tangent for the following angles:
a. 30o
√3
b. 60o
sin 60 =
o
2
60
c. 45o
2
1
cos 60 =
2
tan 60 = √3
1
30o
3
Trigonometry and Vectors
Trigonometric Functions
NO CALCULATORS – SKETCH
– SIMPLIFY ANSWERS
4. Calculate sine, cosine, and tangent for the following angles:
a. 30o
b. 60o
45o
1
cos 45 =
o
√2
c. 45
2
1
sin 45 =
√2
tan 45 = 1
1
45o
1
Word Problems
Read the entire problem through. Note that not all information given is
relevant.
1.
Write Given, Assign Variables, Sketch and Label Diagram
1. Whenever you write a variable, you must write what that variable
means.
2. What are the quantities? Assign variable(s) to quantities.
3. If possible, write all quantities in terms of the same variable.
2.
Write Formulas / Equations
What are the relationships between quantities?
3.
Substitute and Solve
Communication: All of your work should communicate your thought
process (logic/reasoning).
4.
Check Answer, then Box Answer
DRILL A: A radio antenna tower stands 200 meters tall. A
supporting cable attached to the top of the tower stretches to
the ground and makes a 30o angle with the tower. How far is
it from the base of the tower to the cable on the ground?
How long must the cable be?
DRILL B: During the day, a 25 foot tall telephone pole casts a
10 foot shadow on the ground. At that same time and not far
away, a tree casts a 25 foot shadow. How tall is the tree?
Engineering Problem Solving
1. Write Given, Assign Variables, Sketch and Label Diagram
2. Write Formulas / Equations
3. Substitute and Solve
4. Check Answer, THEN box answer
DRILL A: RADIO TOWER – SOLUTION
A radio antenna tower stands 200 meters tall. A supporting cable
attached to the top of the tower stretches to the ground and makes a
30o angle with the tower. How far is it from the base of the tower to
the cable on the ground? How long must the cable be?
tan 30oassigned
= x / 200m
X:Variables
x = (200m)tan 30o
30o
x = (200m) * ( 3 / 3)
200m
x = 115.5m
r
r:
cos 30o = 200m / r
r*cos 30o = 200m
r = 200m / cos 30o
Equal signs aligned
x
r = 231m
DRILL B: SHADOWS – SOLUTION
During the day, a 25 foot tall telephone pole casts a 10 foot
shadow on the ground. At that same time, a tree casts a 25
foot shadow. How tall is the tree?
This problem can be solved by setting up a ratio.
(POLE) Height / Shadow = (TREE) Height / Shadow
25 ft / 10 ft
y
2.5
=
y / 25 ft
=
y / 25 ft
62.5 ft = y
25’
10’
25’
Systems of Equations
•
Because two equations impose two conditions on the
variables at the same time, they are called a system of
simultaneous equations.
• When you are solving a system of equations, you are
looking for the values that are solutions for all of the
system’s equations.
• Methods of Solving:
1. Graphing
2. Algebra:
1. Substitution
2. Elimination
1. Addition-or-Subtraction
2. Multiplication in the Addition-or-Subtraction Method
Systems of Equations – Word Problems
Classwork:
Algebra A:
The perimeter of a rectangle is 54 centimeters. Two times the
altitude is 3 centimeters more than the base. What is the area
of the rectangle?
Algebra B:
At one point along a trail the angle of elevation from a hiker to
the top of a nearby tree is 30 degrees. After walking 40 feet
closer to the tree, the angle of elevation from the hiker to the
top of the tree is now 60 degrees. Find the height of the tree.
SUMMARY OF THE 7 FUNDAMENTAL SI UNITS:
1. LENGTH
- meter
2. MASS
- kilogram
3. TIME
- second
4. ELECTRIC CURRENT
- ampere
5. THERMODYNAMIC TEMPERATURE - Kelvin
6. AMOUNT OF MATTER
- mole
7. LUMINOUS INTENSITY
- candela
Quality (Dimension)
Quantity – Unit
Base
Derived
Characteristic
Length
Mass
Time
Area
Volume
Velocity
Acceleration
Force
Energy/Work
Power
Pressure
Viscosity
Dimension
L
M
T
L2
L3
LT-1
LT-2
MLT-2
ML2T-2
ML2T-3
ML-1T-2
ML-1T-1
SI
(MKS)
m
kg
s
m2
L
m/s
m/s2
N
J
W
Pa
Pa*s
English
foot
slug
s
ft2
gal
ft/s
ft/s2
lb
ft-lb
ft-lb/s or hp
psi
lb*slug/ft
Dimensional Analysis
Fundamental Rules:
2. All terms in an equation must reduce to identical
primitive (base) dimensions.
d  d o  vot  at
1
2
2
Homogeneous
Equation
L
L 2
L  L T  2 T
T
T
Dimensional
Homogeneity
Dimensional Analysis
Uses:
2. Deduce expressions for physical phenomena.
Example: What is the period of oscillation for a pendulum?
(time to complete full cycle)
We predict that the period T will be a function of m, L,
and g: