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Welcome to ENGR 8

Welcome to ENGR 8. Instructor: Tom Rebold. This Week's Agenda. Syllabus Introduction Math Review Force Vectors. What is "Mechanics"?. Basic Quantities. Length: position, size, distance Time: sequence of events (Dynamics) Mass: quantity of matter Force: contact, qravity. Idealizations.

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Welcome to ENGR 8

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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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