1. RECITATION

2. EF 151 Recitation Solve Problems Demonstrations Team Projects

3. Recitation: What to bring Textbook Calculator Pencil and Paper Questions

4. Attendance and Grading Policy

5. Today Introduce you to course website and online homework Take pictures and Meyers-Briggs test Practice algebra and trigonometry

6. Online Homework ef.engr.utk.edu Need to be within 1% of correct answer to get credit. Enter three significant figures.

7. On-line Homework Problems On-line HW is graded. You should work out the solution on paper prior to submitting your answers. Working the homework will improve your learning Several quiz questions will often be similar to the homework The best way to learn is to do; watching doesn’t cut it It is your responsibility to learn the material!

8. Problems - Portfolio Keep a portfolio of all your problem solutions Bring the portfolio when you come to help sessions This will enable us to provide better help Students with their portfolios receive priority at help sessions Being able to look at the work you have done will aid in reviewing for quizzes and the final exam

9. Working Together? Work together only if you are truly learning from each other Copying is a violation of the University honor policy It is your job to maintain your integrity, and to learn the material

10. Module 1, Recitation 3 Estimate amount of paint needed to paint supports of Jumbotron. Put in picture of Jumbotron supports

11. Problem Solving Define the problem Identify the critical data of the problem. Do not be misled by data that is extraneous, erroneous, or insignificant. Diagram A diagram or schematic of the system being analyzed is often very helpful, and may be required. Governing equations Determine what type of problem is being solved. Recognize when certain equations apply and when they do not apply. The governing equations should be written out in symbolic form before substituting in numerical quantities. Calculations Carry out your calculations only after you have completed the first three steps. Check to make sure units are consistent. Solution check Make sure you solved the problem that was posed. If possible, use an independent method or equation to check your result. Check to see that your solution is physically reasonable. Make sure both the magnitude and sign of the answer makes sense.

12. Problem Philosophy Documentation -- must be NEAT. Clearly state all relevant assumptions. Provide diagrams where needed. List fundamental relationships in symbolic terms (e.g., V = 4  r 3 ) Always provide units with your answers. Ensure that your answer makes sense.

13. Module 1, Recitation 4 Review of vector properties

14. Vectors - Components Generalize from previous slide x y q Mag x comp = y comp =  always measured: Origin is always located: at tail of vector counterclockwise from positive x-direction Mag(cos  ) Mag(sin  )

15. Vectors - Components x y θ Be careful with signs. Remember tangent is sine/cosine.

16. Angle Determination x + y + x - y + x - y - x + y - x y θ x y θ x y θ x y θ

17. Vector addition Ways to add vectors: Graphically Trigonometrically Using components Tail Head Vector sum is vector from tail of first vector to head of last vector (start to end).

18. Vectors - Forces Determine the resultant (vector sum) of the forces acting on the bolt. 60 lb 40 lb 20º 45º VectorMag.  x-comp.y-comp. 160 lb135°-42.4 lb42.4 lb 240 lb20°37.6 lb13.7 lb Sum56.3 lb94.9°-4.8 lb56.1 lb

19. Module 1, Recitation 5 Vector component questions

20. If two vectors are given such that A + B = 0, what can you say about the magnitude and direction of vectors A and B ? 1) same magnitude, but can be in any direction 2) same magnitude, but must be in the same direction 3) different magnitudes, but must be in the same direction 4) same magnitude, but must be in opposite directions 5) different magnitudes, but must be in opposite directions ConcepTest Vectors I

21. If two vectors are given such that A + B = 0, what can you say about the magnitude and direction of vectors A and B ? 1) same magnitude, but can be in any direction 2) same magnitude, but must be in the same direction 3) different magnitudes, but must be in the same direction 4) same magnitude, but must be in opposite directions 5) different magnitudes, but must be in opposite directions The magnitudes must be the same, but one vector must be pointing in the opposite direction of the other, in order for the sum to come out to zero. You can prove this with the tip-to-tail method. ConcepTest Vectors I

22. Given that A + B = C, and that lAl 2 + lBl 2 = lCl 2, how are vectors A and B oriented with respect to each other? 1) they are perpendicular to each other 2) they are parallel and in the same direction 3) they are parallel but in the opposite direction 4) they are at 45° to each other 5) they can be at any angle to each other ConcepTest Vectors II

23. Given that A + B = C, and that lAl 2 + lBl 2 = lCl 2, how are vectors A and B oriented with respect to each other? 1) they are perpendicular to each other 2) they are parallel and in the same direction 3) they are parallel but in the opposite direction 4) they are at 45° to each other 5) they can be at any angle to each other Note that the magnitudes of the vectors satisfy the Pythagorean Theorem. This suggests that they form a right triangle, with vector C as the hypotenuse. Thus, A and B are the legs of the right triangle and are therefore perpendicular. ConcepTest Vectors II

24. Given that A + B = C, and that lAl + lBl = lCl, how are vectors A and B oriented with respect to each other? 1) they are perpendicular to each other 2) they are parallel and in the same direction 3) they are parallel but in the opposite direction 4) they are at 45° to each other 5) they can be at any angle to each other ConcepTest Vectors III

25. Given that A + B = C, and that lAl + lBl = lCl, how are vectors A and B oriented with respect to each other? 1) they are perpendicular to each other 2) they are parallel and in the same direction 3) they are parallel but in the opposite direction 4) they are at 45° to each other 5) they can be at any angle to each other The only time vector magnitudes will simply add together is when the direction does not have to be taken into account (i.e., the direction is the same for both vectors). In that case, there is no angle between them to worry about, so vectors A and B must be pointing in the same direction. ConcepTest Vectors III

26. If each component of a vector is doubled, what happens to the angle of that vector? 1) it doubles 2) it increases, but by less than double 3) it does not change 4) it is reduced by half 5) it decreases, but not as much as half ConcepTest Vector Components I

27. If each component of a vector is doubled, what happens to the angle of that vector? 1) it doubles 2) it increases, but by less than double 3) it does not change 4) it is reduced by half 5) it decreases, but not as much as half The magnitude of the vector clearly doubles if each of its components is doubled. But the angle of the vector is given by tan  = 2y/2x, which is the same as tan  = y/x (the original angle). Follow-up: If you double one component and not the other, how would the angle change? ConcepTest Vector Components I

28. A certain vector has x and y components that are equal in magnitude. Which of the following is a possible angle for this vector, in a standard x-y coordinate system? 1) 30° 2) 180° 3) 90° 4) 60° 5) 45° ConcepTest Vector Components II

29. A certain vector has x and y components that are equal in magnitude. Which of the following is a possible angle for this vector, in a standard x-y coordinate system? 1) 30° 2) 180° 3) 90° 4) 60° 5) 45° The angle of the vector is given by tan  = y/x. Thus, tan  = 1 in this case if x and y are equal, which means that the angle must be 45°. ConcepTest Vector Components II

30. ConcepTest Vector Addition You are adding vectors of length 20 and 40 units. What is the only possible resultant magnitude that you can obtain out of the following choices? 1) 0 2) 18 3) 37 4) 64 5) 100

31. ConcepTest Vector Addition You are adding vectors of length 20 and 40 units. What is the only possible resultant magnitude that you can obtain out of the following choices? 1) 0 2) 18 3) 37 4) 64 5) 100 minimum opposite20 unitsmaximum aligned 60 units The minimum resultant occurs when the vectors are opposite, giving 20 units. The maximum resultant occurs when the vectors are aligned, giving 60 units. Anything in between is also possible, for angles between 0° and 180°.