2. ME 221Lecture 41 ME 221 Statics Lecture #4 Sections 2.4 – 2.5

3. ME 221Lecture 42 Homework Problems Due Today: –1.1, 1.3, 1.4, 1.6, 1.7 –2.1, 2.2, 2.11, 2.15, 2.21 Due Wednesday, September 9: –Chapt 2: 22, 23, 25, 27, 29, 32, 37, 45, 47 & 50 –On 2.50: Solve with hand calculations first Then use MathCAD, MatLab, Excel, etc. to solve Quiz #1 – Friday, 9/5

4. ME 221Lecture 43 TA Hours Help Sessions – ME Help Room – 1522EB - Cubicle #2 TA’s: – Jimmy Issa, Nanda Methil-Sudhakaran & Steve Rundell Mondays & Wednesdays – 10:15am to 5:00pm Tuesdays & Thursdays – 8:00am to 5:00pm Fridays – 8:00am to 11:00am Grader – Jagadish Gattu 2415EB – Weds: 10:00am to 12:00am

5. ME 221Lecture 44 Last Lecture Vector Components Scalar Multiplication of Vectors Perpendicular Vectors Example 2.3

6. ME 221Lecture 45 3-D Vectors; Base Vectors Rectangular Cartesian coordinates (3-D) Unit base vectors (2-D and 3-D) Arbitrary unit vectors Example problem Vector component manipulation

7. ME 221Lecture 46 3-D Rectangular Coordinates Coordinate axes are defined by Oxyz x y z O Coordinates can be rotated any way we like, but... Coordinate axes must be a right-handed coordinate system.

8. ME 221Lecture 47 x y z O A = Writing 3-D Components Component vectors add to give the vector: x y z O A = AxAx A x + AyAy A y + AzAz AzAz Also,

9. ME 221Lecture 48 3-D Direction Cosines The angle between the vector and coordinate axis measured in the plane of the two x y z O A xx yy zz Where: x 2 + y 2 + z 2 =1

10. ME 221Lecture 49 Unit Base Vectors Associate with each coordinate, x, y, and z, a unit vector (“hat”). All component calculations use the unit base vectors as grouping vectors. x y z O Now write vector as follows: where A x = |A x | A y = |A y | A z = |A z |

11. ME 221Lecture 410 Vector Equality in Components Two vectors are equal if they have equal components when referred to the same reference frame. That is: if A x = B x, A y = B y, A z = B z

12. ME 221Lecture 411 Additional Vector Operations To add vectors, simply group base vectors A scalar times vector A simply scales all the components

13. ME 221Lecture 412 General Unit Vectors Any vector divided by its magnitude forms a unit vector in the direction of the vector. –Again we use “hats” to designate unit vector x y z O b

14. ME 221Lecture 413 Position Vectors in Space Points A and B in space are referred to in terms of their position vectors. x y z O rArA rBrB r B/A Relative position defined by the difference

15. ME 221Lecture 414 Vectors in Matrix Form When using MathCAD or setting up a system of equations, we will write vectors in a matrix form:

16. ME 221Lecture 415 Summary Write vector components in terms of base vectors Know how to generate a 3-D unit vector from any given vector

17. ME 221Lecture 416 Example Problem