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ME 221 Statics Lecture #4 Sections 2.4 – 2.5

ME 221 Statics Lecture #4 Sections 2.4 – 2.5. 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

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ME 221 Statics Lecture #4 Sections 2.4 – 2.5

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  1. ME 221 StaticsLecture #4Sections 2.4 – 2.5 Lecture 4

  2. 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 Lecture 4

  3. 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 Lecture 4

  4. Last Lecture • Scalar Multiplication of Vectors • Perpendicular Vectors • Vector Components • Example 2.3 Lecture 4

  5. 3-D Vectors; Base Vectors • Rectangular Cartesian coordinates (3-D) • Unit base vectors (2-D and 3-D) • Arbitrary unit vectors • Vector component manipulation • Example problem Lecture 4

  6. y O x z 3-D Rectangular Coordinates • Coordinate axes are defined by Oxyz Coordinates can be rotated any way we like, but ... • Coordinate axes must be a right-handed coordinate system. Lecture 4

  7. y y A Ay Az O O Ax x x z z A = Ax + Ay + Az Writing 3-D Components • Component vectors add to give the vector: = Also, Lecture 4

  8. y qy A O qx x z qz 3-D Direction Cosines The angle between the vector and coordinate axis measured in the plane of the two Where: lx2+ly2+lz2=1 Lecture 4

  9. y O x z 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. Now write vector as follows: where Ax = |Ax| Ay = |Ay| Az = |Az| Lecture 4

  10. Vector Equality in Components • Two vectors are equal if they have equal components when referred to the same reference frame. That is: if Ax = Bx , Ay = By , Az = Bz Lecture 4

  11. Additional Vector Operations • To add vectors, simply group base vectors • A scalar times vector A simply scales all the components Lecture 4

  12. y b O x z 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 Lecture 4

  13. y rA O x z rB/A rB Position Vectors in Space • Points A and B in space are referred to in terms of their position vectors. • Relative position defined by the difference Lecture 4

  14. Vectors in Matrix Form • When using MathCAD or setting up a system of equations, we will write vectors in a matrix form: Lecture 4

  15. Summary • Write vector components in terms of base vectors • Know how to generate a 3-D unit vector from any given vector Lecture 4

  16. Example Problem Lecture 4

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