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

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  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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Vectors AP Physics B Summer Course 20122012年AP物理B暑假班 M Sittig Scalars
  • Examples:
  • 3 years old
  • 10 kg
  • 0.33 J
  • 3.0 × 108 m/s
  • 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:
  • Vector Basics
  • Examples:
  • 70 km/hr, South
  • 9.8 m/s2at 145°
  • 6 meters down
  • 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:
  • 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…
  • Adding and Subtracting Vectors
  • What is the maximum magnitude of the sum of these vectors?
  • The minimum?
  • Adding and Subtracting Vectors
  • Geometrically: Vectors as arrows, lined up head-to-tail. Resultant from start to finish.
  • 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
  • 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 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
  • Adding and Subtracting Vectors
  • Add these two vectors using components. Give the magnitude and direction of the resultant.
  • 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
  • Adding and Subtracting Vectors
  • Subtracting = Adding the negative vector
  • 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 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.
  • 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?
  • Practice Problem
  • Determine the magnitude and direction of the sum of these four vectors:
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