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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 • 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 • • • • • • 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? 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 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 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 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. 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