AP Physics B Summer Course 2012

2012年 AP物理 B暑假班

M Sittig

Vectors

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/s2 at 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.

v

vx

vy

cos θ = adj / hyp = vx / vvx = v cos θ

sin θ = opp / hyp = vy / vvy = v sin θ

x-component of vector v

y-component of vector v

θ

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?

ca

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 x ̂ + 20 N ŷ and B = -30 N x ̂ + 40 N ŷ as 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: