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AP Physics B Summer Course 2012 2012 年 AP 物理 B 暑假班

Vectors. AP Physics B Summer Course 2012 2012 年 AP 物理 B 暑假班. M Sittig. Scalars. Examples: 3 years old 10 kg 0.33 J 3.0 × 10 8 m/s. Scalars. Scalar: a physical quantity with a magnitude but no direction. Example of scalar quantities: time, mass , speed, energy, work, and distance.

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AP Physics B Summer Course 2012 2012 年 AP 物理 B 暑假班

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  1. Vectors AP Physics B Summer Course 20122012年AP物理B暑假班 M Sittig

  2. Scalars • Examples: • 3 years old • 10 kg • 0.33 J • 3.0 × 108 m/s

  3. Scalars • Scalar: a physical quantity with a magnitude but no direction. • Example of scalar quantities: time, mass, speed, energy, work, and distance. • Example of scalar measurement:

  4. Vector Basics • Examples: • 70 km/hr, South • 9.8 m/s2at 145° • 6 meters down

  5. Vector Basics • Vector: a physical quantity with a magnitude and a direction. • Examples of vector quantities: velocity, acceleration, displacement, force, fields. • Example of scalar measurement:

  6. What is this? • Magnitudes? • Directions? • A=3 m at 60° • B=3 m at 180°-β • Or 3 m at β° above the negative x-axis • C=1.5 m at 270° • Or…

  7. Adding and Subtracting Vectors • What is the maximum magnitude of the sum of these vectors? • The minimum?

  8. Adding and Subtracting Vectors • Geometrically: Vectors as arrows, lined up head-to-tail. Resultant from start to finish.

  9. Adding and Subtracting Vectors • Lewin, Walter. 8.01 Physics I: Classical Mechanics, Fall 1999. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed 22 Feb, 2012). License: Creative Commons BY-NC-SA

  10. Adding and Subtracting Vectors • Components: Break down a vector into component vectors along a set of axes. cosθ = adj / hyp = vx / v vx = v cosθ y-component of vector v vy v sin θ = opp / hyp = vy / v vy = v sin θ θ vx x-component of vector v

  11. Adding and Subtracting Vectors • Lewin, Walter. 8.01 Physics I: Classical Mechanics, Fall 1999. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed 22 Feb, 2012). License: Creative Commons BY-NC-SA

  12. Adding and Subtracting Vectors • Add these two vectors using components. Give the magnitude and direction of the resultant.

  13. Adding and Subtracting Vectors • Lewin, Walter. 8.01 Physics I: Classical Mechanics, Fall 1999. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed 22 Feb, 2012). License: Creative Commons BY-NC-SA

  14. Adding and Subtracting Vectors • Subtracting = Adding the negative vector

  15. Practice Problem In which case is the magnitude of vector A+B largest? In which case is the magnitude of vector A+B smallest? c a

  16. Practice Problem • Two horizontal ropes are attached to a post that is stuck in the ground. The ropes pull the post producing the vector forces A = 70 N x̂ + 20 N ŷ and B = -30 N x̂+ 40 N ŷas shown in the figure. Find the direction and magnitude of the horizontal component of a third force on the post that will make the vector sum of forces on the post equal to zero.

  17. Practice Problem • A Coast Guard ship is located 35 km away from a checkpoint in a direction 42°north of west. A sailboat located in still water 20 km from the same checkpoint in a direction 36°south of east is about to sink. Draw a diagram indicating the position of both ships. In what direction and how far must the Coast Guard ship travel to reach the sailboat?

  18. Practice Problem • Determine the magnitude and direction of the sum of these four vectors:

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