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

9. Units

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

11. 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)

12. 12 Rev.S08 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 2Use the sketch to write an equation relating the given quantities to the variable. Step 3Solve the equation, and check that your answer makes sense.

13. Laws of Trig you will Master Pythagorean theorem: a 2 +b 2 =c 2 (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)

15. Defining sin, cos, tan also, a = c cos(  ), b = c sin(  )  = arccos(a/ c) = arcsin(b/c) = arctan(b/a)

16. 16 Rev.S08 Example http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. 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 . 22.02 m 28.34 m B

17. 17 Rev.S08 Example 2 http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. 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 .

18. Law of Cosines Use when you know an angle and two adacent sides to find the 3 rd side Use when you know three sides and want to find an angle

19. Find x

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

21. Find b and unknown side