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CHAPTER 1
INTRODUCTION TOSTATICS
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OBJECTIVES1. DESCRIBE THE FUNCTION AND USAGE OF STATICS
2. DEMONSTRATE KNOWLEDGE OF BASIC GEOMETRY
3. SOLVE FOR UNKNOWN ANGLES USING TRIGONOMETRY4. SOLVE FOR UNKNOWN ANGLES USING PYTHAGOREAN THEOREM
5. SOLVE FOR UNKNOWN ANGLES USING SIMILAR TRIANGLES THEOREM
6. DISTINGUISH SIGNIFICANT DIGITS IN A NUMBER
7. DEMONSTRATE ABILITY TO ROUND NUMBERS
8. DEMONSTRATE ABILITY TO PERFORM UNIT CONVERSIONS
9. CALCULATE FORCE AND WEIGHT
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the study of force, deformation and motion,
and the relations between them.
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STATICS the science of determining the forces and force systems acting on RIGID
bodies
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The Skywalk
Hualapai IndianReservation outside
of Las Vegas
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160 FT LONG, 72 FT HIGHSUSPENDED 90 FT IN THE AIR
WEIGHING IN AT 600 TONS(1,200,000 POUNDS)
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STATICS MATH ERROR
CHICAGO 2003
12 PEOPLE KILLED
30 PEOPLE SERIOUSLY HURTwww.youtube.com/watch?v=4OOg7vL3rNY&feature=related
http://www.youtube.com/watch?v=4OOg7vL3rNY&feature=relatedhttp://www.youtube.com/watch?v=4OOg7vL3rNY&feature=related8/4/2019 CHAPTER 1 Introduction to Statics
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I. ANGLES AND LINES
1. A straight line has 180 degrees on each side
2. If 2 lines (or more ) lines are parallel to the same line, they
are perpendicular to each other.
3. Intersecting lines create 2 pairs of opposite and equal
angles
4. Intersecting lines create a common vertex for 4 angles, the
sum of which is 360
g 1 =g 3
g 2 = g 4
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4. When 2 lines intersected by a third line:
- equal pairs of alternate interior angles are formed
- equal pairs of alternate exterior angles are formed
- equal pairs of interior and exterior corresponding angles are formed
< 3 = < 6
< 4 = < 5
< 1 = < 8
< 2 = < 7
< 1 = < 5< 2 = < 6
< 3 = < 7
< 4 = < 8
II. TRIANGLES
6. Right Triangle
-Contains one 90 degree angle
-the sum of remaining 2 angles = 90 degrees
5. Are three sided figures containing 3 angles that add up to 180 degrees.
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-contains two sides of equal length
-angles opposite the equal sides are also equal-the altitude divide the triangle into two congruent triangles
7. Isosceles Triangle
8. Equilateral Triangle
-Contains three equal sides
-The three angles are equal and measure 60 degrees
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9. Similar Triangles
Angle-Angle rule If 2 angles of 1 triangle are equal to 2 angles
of another triangle they are similar
6 = 9
2 S
350 350280 280
6 92 S
Side Angle Side rule If the angle of one triangle is the same as the angle of
Another triangle AND the sides containing these angles have the same ratio, the
Triangles are similar.
350
35
4 6
10
2S
5
4 = 6
2 S
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common applications
ALL OF THESE TRIANGLESARE SIMILAR!
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ONLY WORKS FOR RIGHT TRIANGLES
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3-4-5 TRIANGLES
52
=32
+42
Any triangle that has these
proportions must be a right triangle
by Pythagorean Theorem
6-8-109-12-15
12-16-20
15-20-25
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SIN
OPPOSITE
HYPOTENUSE COS
ADJACENT
HYPOTENUSE
TAN
OPPOSITE
ADJACENT
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OR
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LAW OF SINES
LAW OF COSINES
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sin corresponds to x axis
cos corresponds to y axis
If x is positive, cosine is positive.
If x is negative, cosine is negative.
If y is positive, sine is positive.If y is negative, sine is negative.
THEREFORE
Angle sin cos0o 0 1
90o 1 0
180o 0 -1
270o -1 0
OTHER USEFUL TRIG TRIVIA
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Systems of Linear Equations
y= 3x 2y= x 6STEP 1
Solve one equation to isolate one variable by itself, in this case the Y is already
done for us.y=3x-2
STEP 2
Substitute into the second equation, so that there will only be 1 type of
variable in it
3x 2 = x 6STEP 3
Solve for the unknownx = 1
STEP 4
Substitute that value back into the first equation to solve for the other
unknown variable y=3(1) 2 = 1
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OUTPUT CANNOT BE MORE ACCURATE THAN INPUT
58
7= 8.285714286
1)ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant.
2)ALL zeroes between non-zero numbers are ALWAYS significant.
3) ALL zeroes which are SIMULTANEOUSLY to the right of the decimal
point AND at the end of the number are ALWAYS significant.
4) ALL zeroes which are to the left of a written decimal point and are in
a number >= 10 are ALWAYS significant.
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MATHEMATICS OF MEASUREMENT
ADDITION/SUBTRACTION
10ft + 5ft = 15ft
units are handled mathematically just like variables!
18in -10in =8 in
only like units may be added or subtracted
30 in + 5 ft - 3m
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MULTIPLICATION
TO MULTIPLY 3ft x 3ft = ?
multiply 3 x 3
multiply 1ft x 1ft
= 9 ft2
6in x 3in x 2in = 6 x 3 x 2
in x in x in = 36 in3
what about the like units rule?
1ft x 5 lb = 5 ft-lb
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DIVISION
10 ft 2 ft =
1. 10 2 = 5
2. ft ft = 1=ft
ft= 5
25 ft2 5 ft 1. 25 5 = 5
2. ft2 ft = ftft
ftft
ft
ft=
=
2
= 5ft
200 miles 3.5 hrs = 55 miles/hr
50 lb .25 in2 = 200 lb/in2
and, once again, unlike units?
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UNITY FRACTIONS
1 yd = 3 ft
ftyd3
1
yd
ft
1
3or
15 yd X
yd
ft
1
3
15 ft X
ft
yd
3
1
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2
2
2
2
37.1144
1
197 ftin
ft
in =
1 ft2 = 144 in2
1 ft3 = 1078 in3
1ft
1ft
=
12 in
12 in
1 ft(12 in)
1
ft(12
in)
1ft(12
in)
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UNITS OF FORCE
POUND (LB)KILOPOUND (KIP) = 1,000 LB
NEWTON (N)
KILONEWTON (Kn) = 1,000 N
FORCEAND WEIGHTARE USED INTERCHANGEABLY
F= ma
W = mg
F=force
m=mass
a=acceleration
W=weight
m=mass
g=acceleration due to gravity
(32.2 ft/sec2 or 9.81 m/sec2
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SI PREFIXES
1,000,000,000 bytes = 1,000,000 kilobytes = 1,000 megabytes = 1 gigabyte
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