Book cover for Physics

Physics

Alan Giambattista, Betty McCarthy Richardson, Robert C. Richardson

ISBN #9780073404530

2nd Edition

2,795 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This section emphasizes the role of vectors in describing motion in a plane. It covers methods of representing vector quantities both graphically and algebraically by breaking them into components. Key ideas include the independent treatment of horizontal and vertical components in projectile motion, the correct use of trigonometry to resolve vectors, and the concept of relative velocity which underscores that motion must be measured with respect to a chosen reference frame. Mastering these concepts is essential for solving complex problems in mechanics.

Learning Objectives

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Key Concepts

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Example Problems

Example 1

Displacement vector $\overrightarrow{\mathbf{A}}$ is directed to the west and has magnitude $2.56 \mathrm{km} .$ A second displacement vector is also directed to the west and has magnitude $7.44 \mathrm{km}$ (a) What are the magnitude and direction of $\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}} ?$ (b) What are the magnitude and direction of $\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}} ?$ (c) What are the magnitude and direction of $\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{A}} ?$

Example 2

Vector $\overrightarrow{\mathbf{A}}$ is directed along the positive $x$ -axis and has magnitude 1.73 units. Vector $\overrightarrow{\mathbf{B}}$ is directed along the negative $x$ -axis and has magnitude 1.00 unit. (a) What are the magnitude and direction of $\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}} ?$ (b) What are the magnitude and direction of $\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}} ?$ (c) What are the magnitude and direction of $\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{A}} ?$

Example 3

Two vectors have magnitudes 3.0 and $4.0 .$ How are the directions of the two vectors related if (a) the sum has magnitude $7.0,$ or $(\mathrm{b})$ if the sum has magnitude $5.0 ?$ (c) What relationship between the directions gives the smallest magnitude sum and what is this magnitude?

Example 4

A runner is practicing on a circular track that is $300 \mathrm{m}$ in circumference. From the point farthest to the west on the track, he starts off running due north and follows the track as it curves around toward the east. (a) If he runs halfway around the track and stops at the farthest eastern point of the track, what is the distance he traveled? (b) What is his displacement?

Example 5

Two displacement vectors each have magnitude $20 \mathrm{km}$ One is directed $60^{\circ}$ above the $+x$ -axis; the other is directed $60^{\circ}$ below the $+x$ -axis. What is the vector sum of these two displacements? Use graph paper to find your answer.
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Step-by-Step Explanations

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Common Mistakes

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