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Lecture 1
GEN_ENG 205-2: Engineering Analysis 2
Winter Quarter 2018
Prof. James P. Hambleton
Chapter 1: Introduction
1
Acknowledgements
Portions of these lecture notes are taken from those of Prof. Jeff Thomas.
Introduction to Mechanics
Mechanics is essentially the study of forces and their effects. It forms the basis of all
modern engineering, which rests on mathematical modeling.
Statics is the study of objects at rest. Dynamics is the study of objects in motion. Newton’s
laws form the basis for these analyses.
We can use mechanics to predict forces in structures (statics), the trajectory of objects
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(dynamics), and much more.
You can build on the concepts from this course to study fluid flow, deformation of solids,
and so much more…
(^1) Bedford, A., & Fowler, W. (2008). Engineering Mechanics: Statics and Dynamics (5th ed.). Upper Saddle River, NJ:
Pearson Prentice Hall. (^2) Sketch orbit and refer to early works by Greek Philosophers (400 B.C. to A.D. 500), Tycho Brahe, Johannes Kepler, and
Galileo Galilei (late 1500’s to early 1600’s).
Problem Solving
General steps:
- Identify given information and what you must determine.
- Develop a strategy: identify appropriate principles and equations.
- Predict the answer.
- Solve the equations, interpret your results, and compare with your prediction.
Hone your problem solving skills with practice!
Five basic tools in this course:
- Newton’s laws
- Vector algebra (dot product, cross product, etc.)
- Basic geometry and trigonometry
- Free body diagrams
- Simple differential and integral calculus.
Numbers and Units
“Significant digits” refers to the number of meaningful digits. This is typically determined
by the accuracy of a measurement. In the textbook, data and answers are almost always
expressed to 3 significant digits. You must do the same!
Use higher precision for intermediate steps to avoid round-off errors.
Converting and Determining Units
Converting units is straightforward but must be done with care.
Example
5 (converting units)
ft
s
mi 5280ft 1 h 1 mi/h 1 1. h 1 mi 3600 s
Example
6 (determining units)
Given:
2 gR v r
where the units of g , R , and r are [ ] 2
m
s
g = , [ R ] = m, and [ r ] = m
Find:
(a) the units of v
(b) the value of v if R = 6370 km, r = 6670 km, and g = 9.81 m/s
2
(c) to what physical problems does this pertain?
(^5) Emphasize that this is unit conversion , so the rules for significant figures do not apply (otherwise 1 mi/h = 1 ft/s).
(^6) Active learning example.
Solution:
(a)
[ ][ ]
[ ]
2
2 2 2
2
g R
r
m m s m m v m (^) s s
=
(b)
2 m 2 1000 m 9.81 6370 km s 1 km
1000 m 6670 km 1 km
v
^ ^ (^)
m 3 m km 7.73 10 or 7. s s s
= ×
(c) Celestial body (orbiting satellite)
Angles
Watch out for angles!
Examples:
rad 45 deg 45 deg 0.785 rad 180 deg
sin x l l
θ θ = ≈ for small θ
θ must be in radians!
We can use this equation to approximate the weight W of an object at sea level.
2
E
E
Gmm W r
Upon defining (^2)
E
E
Gm g r
= , one finds W = mg.
Acceleration due to gravity varies on Earth’s surface, but we typically assume
11 g = 9.
m/s
2 = 32.2 ft/s
2 .
(^11) Ask students if they recall these numbers. Good example of significant digits.
