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Introduction to Mechanics and Applied Trigonometry in Rigid Body Analysis

Welcome to Engineering 8 with Instructor Tom Rebold! This week, we will cover key concepts in mechanics, including basic quantities like length, time, mass, and force. Prepare for a math review and explore the fundamentals of rigid body mechanics grounded in Newton’s laws. Additionally, learn how to tackle applied trigonometry problems using essential tools like the Pythagorean theorem, the law of cosines, and the law of sines. Engage with examples involving angles of elevation and the relationship between sides in triangles.

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Introduction to Mechanics and Applied Trigonometry in Rigid Body Analysis

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  1. Welcome to ENGR 8 Instructor: Tom Rebold

  2. This Week's Agenda • Syllabus • Introduction • Math Review • Force Vectors

  3. What is "Mechanics"?

  4. Basic Quantities • Length: position, size, distance • Time: sequence of events (Dynamics) • Mass: quantity of matter • Force: contact, qravity

  5. 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

  6. Newton's laws are the basis of Rigid Body Mechanics

  7. Units

  8. SI units have prefixes • Giga (G) • Mega (M) • Kilo (K) • milli (m) • micro (u) • nano (n)

  9. 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)

  10. How to Solve an Applied Trigonometry Problem? • Step 1Draw 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

  11. 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)

  12. Defining sin, cos, tan • also, a = c cos(q) , b = c sin(q) q = arccos(a/ c) = arcsin(b/c) = arctan(b/a)

  13. 22.02 m B 28.34 m Example • 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. • The angle of elevation of the sun is 37.85°. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Rev.S08

  14. Example 2 • 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. • The angle of elevation of the sun is 37.85°. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Rev.S08

  15. 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

  16. Find x

  17. Law of Sines • Use when you know an angle and the opposite side and want to find another angle or side:

  18. Find b and unknown side

  19. End of the Lecture Let Learning Continue

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