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Question 3 Road map : We obtain the velocity fastest By Taking the derivative of a(t)

Question 3 Road map : We obtain the velocity fastest By Taking the derivative of a(t) By Integrating a(t) By integrating the accel as function of displacement By computing the time to bottom, then computing the velocity. Question 3 Road map : We obtain the velocity fastest

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Question 3 Road map : We obtain the velocity fastest By Taking the derivative of a(t)

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  1. Question 3Road map: We obtain the velocity fastest • By Taking the derivative of a(t) • By Integrating a(t) • By integrating the accel as function of displacement • By computing the time to bottom, then computing the velocity.

  2. Question 3Road map: We obtain the velocity fastest • By Taking the derivative of a(t) • By Integrating a(t) • By integrating the accel as function of displacement • By computing the time to bottom, then computing the velocity.

  3. Chapter 12-5 Curvilinear Motion X-Y Coordinates

  4. Here is the solution in Mathcad

  5. Example: Hit target at Position (360’, -80’)

  6. Example: Hit target at Position (360, -80)

  7. 12.7 Normal and Tangential Coordinates ut : unit tangent to the path un : unit normal to the path

  8. Normal and Tangential Coordinates Velocity Page 53

  9. Normal and Tangential Coordinates ‘e’ denotes unit vector (‘u’ in Hibbeler)

  10. ‘e’ denotes unit vector (‘u’ in Hibbeler)

  11. 12.8 Polar coordinates

  12. Polar coordinates ‘e’ denotes unit vector (‘u’ in Hibbeler)

  13. Polar coordinates ‘e’ denotes unit vector (‘u’ in Hibbeler)

  14. 12.8 Polar coordinates In a polar coordinate system, the velocity vector can be written as v = vrur + vθuθ = rur + rquq. The term q is called A) transverse velocity. B) radial velocity. C) angular velocity. D) angular acceleration . . .

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  18. 12.10 Relative (Constrained) Motion vA is given as shown. Find vB Approach: Use rel. Velocity: vB = vA +vB/A (transl. + rot.)

  19. Vectors and Geometry r(t) y q q(t) x

  20. Given: vectors A and B as shown. The RESULT vector is: • (A) RESULT = A - B • (B) RESULT = A + B • (C) None of the above

  21. Given: vectors A and B as shown. The RESULT vector is: • (A) RESULT = A - B • (B) RESULT = A + B • (C) None of the above

  22. 12.10 Relative (Constrained) Motion V_truck = 60 V_car = 65 Make a sketch: A V_rel v_Truck B • The rel. velocity is: • V_Car/Truck = v_Car -vTruck

  23. 12.10 Relative (Constrained) Motion Make a sketch: A V_river v_boat B • The velocity is: • V_total = v+boat – v_river • V_total = v+boat + v_river

  24. 12.10 Relative (Constrained) Motion Make a sketch: A V_river v_boat B • The velocity is: • V_total = v+boat – v_river • V_total = v+boat + v_river

  25. Rel. Velocity example: Solution

  26. Example Vector equation: Sailboat tacking at 50 deg. against Northern Wind (blue vector) We solve Graphically (Vector Addition)

  27. Example Vector equation: Sailboat tacking at 50 deg. against Northern Wind An observer on land (fixed Cartesian Reference) sees Vwind and vBoat . Land

  28. 12.10 Relative (Constrained) Motion Plane Vector Addition is two-dimensional. vA vB vB/A

  29. Example cont’d: Sailboat tacking against Northern Wind 2. Vector equation (1 scalar eqn. each in i- and j-direction). Solve using the given data (Vector Lengths and orientations) and Trigonometry 500 150 i

  30. Chapter 12.10 Relative Motion

  31. Vector Addition

  32. Differentiating gives:

  33. Exam 1 • We will focus on Conceptual Solutions. Numbers are secondary. • Train the General Method • Topics: All covered sections of Chapter 12 • Practice: Train yourself to solve all Problems in Chapter 12

  34. Exam 1 Preparation: Start now! Cramming won’t work. Questions: Discuss with your peers. Ask me. The exam will MEASURE your knowledge and give you objective feedback.

  35. Exam 1 Preparation: Practice: Step 1: Describe Problem Mathematically Step2: Calculus and Algebraic Equation Solving

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