TEST REVIEW Engineering Practicum Test #1 is Next Week!!! Monday, Tuesday.

TEST REVIEWEngineering Practicum

Test #1 is Next Week!!!Monday, Tuesday

Science vs. Engineering

Science:1. Systematically obtaining knowledge by observation and

experience2. Use the Scientific Method3. Empirical / Objective

Engineering:1. Application of math and science by which matter and

energy are made useful to people2. Designing and implementing solutions that fulfill an

objective, need, or desire – based on knowledge3. Subjective solutions based on objective knowledge

Fields of Engineering

Source: http://en.wikipedia.org/wiki/Fields_of_engineering

Major Fields:1. Aerospace2. Bioengineering 3. Biomedical4. Chemical5. Civil / Structural 6. Electrical7. Electronic 8. Industrial9. Material10. Mechanical11. Nuclear

LETTERING

• Engineer’s communication tool• All capital letters• BETWEEN GUIDELINES• Legible and Consistent

LEGIBLE AND CONSISTENT

LEGIBLE AND INCONSISTENT

LEGIBLE AND CONSISTENT

• 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):

• While the national policy response must be multi-faceted, ensuring an adequate supply of talented scientists and engineers is one key step.

The Facts

1) 11/9 2) 8/9/953) Outsourcing and Y2K 4) Offshoring

/89

• U.S. ranks 29th of 109 countries in the percentage of 24 year olds with a math or science degree.

More Facts

Percentage of First Degree University Students Receiving Degrees in Math/Science

1. Anyone know?

2. We need:MetricsStatistics

3. Johns Hopkins Engineering Innovation Course:

Section D: 3 of 22 Failed (13.6%)

Poly Students: 8 of 8 Failed (100%)

How Do Poly Students Compare?

Trigonometry and Vectors

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:

x2 + y2 = r2

Trigonometry

A

B

C

y

x

r

HYPOTENUSE

Trigonometry and Vectors

NO CALCULATORS – SKETCH – SIMPLIFY ANSWERS

1. Solve for the unknown hypotenuse of the following triangles:

Trigonometry – Pyth. Thm. Problems

4

3?a)

1

1?b)

1?c)

3222 ba c

22 bac 169

5c

22 bac 22 11

2c

22 bac 22 1)3(

2c 13

Align equal signs when possible

Trigonometry and VectorsCommon triangles in Geometry and

Trigonometry

11

1

2

45o

45o

2

3

30o

60o

You must memorize these triangles

2 3

Trigonometry and Vectors

Trigonometric FunctionsNO CALCULATORS – SKETCH – SIMPLIFY ANSWERS

4. Calculate sine, cosine, and tangent for the following angles:a. 30o

b. 60o

c. 45o

12

3

30o

60osin 30 =

12

cos 30 = √3 2

tan 30 = 1 √3

Trigonometry and Vectors

Trigonometric FunctionsNO CALCULATORS – SKETCH – SIMPLIFY ANSWERS

4. Calculate sine, cosine, and tangent for the following angles:a. 30o

b. 60o

c. 45o

12

3

30o

60o

cos 60 = 12

sin 60 = √3 2

tan 60 = √3

Trigonometry and Vectors

Trigonometric FunctionsNO CALCULATORS – SKETCH – SIMPLIFY ANSWERS

4. Calculate sine, cosine, and tangent for the following angles:a. 30o

b. 60o

c. 45o

tan 45 = 1

sin 45 = 1 √2

cos 45 = 1 √2

1

1

2

45o

45o

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

Word ProblemsWord Problems

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?

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?

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?

200m

30o

Variables assigned

x

r

tan 30o = x / 200m

x = (200m)tan 30o

x = (200m) * ( / 3)

x = 115.5m

cos 30o = 200m / r

r*cos 30o = 200m

r = 200m / cos 30o

r = 231m

3

Equal signs aligned

X:

r:

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 / 25 ft

2.5 = y / 25 ft

62.5 ft = y

10’ 25’

25’

y

Systems of EquationsSystems 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. Graphing2. Algebra:

1. Substitution2. Elimination

1. Addition-or-Subtraction2. Multiplication in the Addition-or-Subtraction Method

Classwork:

Systems of Equations – Word ProblemsSystems of Equations – Word Problems

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

Der

ived

Bas

e

Characteristic DimensionSI

(MKS) English

Length L m foot

Mass M kg slug

Time T s s

Area L2 m2 ft2

Volume L3 L gal

Velocity LT-1 m/s ft/s

Acceleration LT-2 m/s2 ft/s2

Force MLT-2 N lb

Energy/Work ML2T-2 J ft-lb

Power ML2T-3 W ft-lb/s or hp

Pressure ML-1T-2 Pa psi

Viscosity ML-1T-1 Pa*s lb*slug/ft

Dimensional Analysis

Fundamental Rules:2. All terms in an equation must reduce to identical

primitive (base) dimensions.

221 attvdd oo

22T

T

LT

T

LLL

Dimensional Homogeneity

Homogeneous Equation

Dimensional Analysis Uses:2. Deduce expressions for physical phenomena.

Example: What is the period of oscillation for a pendulum?

We predict that the period T will be a function of m, L, and g:

(time to complete full cycle)