Welcome to ENGR 8
Instructor: Tom Rebold
This Week's Agenda
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Syllabus
Introduction
Math Review
Force Vectors
What is "Mechanics"?
Basic Quantities
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Length: position, size, distance
Time: sequence of events (Dynamics)
Mass: quantity of matter
Force: contact, qravity
Idealizations
• Particle: mass but no size
• Rigid Body:
– large number of particles
– fixed with respect to each other
• Concentrated Force:
– effect of a loading acting at a point
Newton's laws are the
basis of Rigid Body Mechanics
Units
SI units have prefixes
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Giga (G)
Mega (M)
Kilo (K)
milli (m)
micro (u)
nano (n)
Rounding
• Answers expressed with 3 significant figures
• Intermediate answers use 4
4.56 * 1.23 + 1.8 = 5.609 + 1.8 = 7.409 = 7.41
• Round
– 1.2345 = 1.23
– 5.678 = 5.69
– 2.345 = 2.34 (even numbers before 5, don't go up)
– 2.335 = 2.34 (odd numbers before 5, go up)
How to Solve an
Applied Trigonometry Problem?
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Step 1
Draw a sketch, and label it with the
given information. Label the quantity to
be found with a variable.
Step 2
Use the sketch to write an equation
relating the given quantities to the
variable.
Step 3
Solve the equation, and check that
your answer makes sense.
Rev.S08
12
Laws of Trig you will Master
• Pythagorean theorem: a2+b2=c2 (right triangles)
• Sum of internal angles = 180 (all triangles)
• Definition of sin, cos, tan, arcsin, arccos, arctan
(right triangles)
• Law of Cosines (all triangles)
• Law of Sines (all triangles)
Defining sin, cos, tan
• also, a = c cos(q) , b = c sin(q)
q = arccos(a/ c) = arcsin(b/c) = arctan(b/a)
Example
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The length of the shadow of a tree 22.02 m tall is
28.34 m. Find the angle of elevation of the sun.
Draw a sketch.
22.02 m
B
28.34 m
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The angle of elevation of the sun is 37.85.
Rev.S08
16
http://faculty.valenciacc.edu/ashaw/
Click link to download other modules.
Example 2
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The length of the shadow of a tree is 100 ft, and the
angle of elevation of the sun is 60 degrees. Find the
height of the tree
Draw a sketch.
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The angle of elevation of the sun is 37.85.
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Rev.S08
17
http://faculty.valenciacc.edu/ashaw/
Click link to download other modules.
Law of Cosines
• Use when you know an angle and two adacent
sides to find the 3rd side
• Use when you know three sides and want to
find an angle
Find x
Law of Sines
• Use when you know an angle and the
opposite side and want to find another angle
or side:
Find b and unknown side