LO 4: A force of 6 N acts 60° north of west. What is the effective force along the wel north?

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Vector and Force Analysis

#### Problem 5
**Objective:** 
Calculate the effective components of a force.

- **Problem Statement:** A force of 6 N acts at an angle of 60° north of west. What are the effective force components along the west and along the north?

#### Problem 6
**Objective:**
Analyze and interpret vector components.

- **Problem Statement:** A vector has components (4, -3). Draw the vector and determine the magnitude and direction of the vector.
- **Equation Note:** 
  - You are given a note saying `tan θ = OPP/ADJ = x/y / x/x`.

#### Problem 7
**Objective:**
Component calculation from vectors in diagrams.

**Diagrams and Explanation:**

1. **First Diagram:**
   - Shows a vector with a length of 10 m at a 60° angle above the horizontal line. The components are shown as `x` and `y` with `x` along the horizontal and `y` pointing vertically upward.

2. **Second Diagram:**
   - Shows a vertical vector `y` with a line passing horizontally through a labeled angle 30° from the vector. Unknown components are labeled as `y` and `x`.

3. **Third Diagram:**
   - Displays a vector pointing along the diagonal with a -45° angle. Components `y` and `x` are indicated, with the horizontal component shown as extending towards the right.

**Task:**
- Calculate the `x` and `y` components for the vectors represented in the diagrams, considering the provided angles and magnitudes.

This educational scenario guides students in understanding vector components using diagrams and given problems.
Transcribed Image Text:### Vector and Force Analysis #### Problem 5 **Objective:** Calculate the effective components of a force. - **Problem Statement:** A force of 6 N acts at an angle of 60° north of west. What are the effective force components along the west and along the north? #### Problem 6 **Objective:** Analyze and interpret vector components. - **Problem Statement:** A vector has components (4, -3). Draw the vector and determine the magnitude and direction of the vector. - **Equation Note:** - You are given a note saying `tan θ = OPP/ADJ = x/y / x/x`. #### Problem 7 **Objective:** Component calculation from vectors in diagrams. **Diagrams and Explanation:** 1. **First Diagram:** - Shows a vector with a length of 10 m at a 60° angle above the horizontal line. The components are shown as `x` and `y` with `x` along the horizontal and `y` pointing vertically upward. 2. **Second Diagram:** - Shows a vertical vector `y` with a line passing horizontally through a labeled angle 30° from the vector. Unknown components are labeled as `y` and `x`. 3. **Third Diagram:** - Displays a vector pointing along the diagonal with a -45° angle. Components `y` and `x` are indicated, with the horizontal component shown as extending towards the right. **Task:** - Calculate the `x` and `y` components for the vectors represented in the diagrams, considering the provided angles and magnitudes. This educational scenario guides students in understanding vector components using diagrams and given problems.
Expert Solution
Step 1: Given and Required

5. Given,

               Magnitude of force

                                                F thin space equals space 6 space N space

               Direction of force,

                                               theta space equals space 60 degree space N o r t h space o f space w e s t

We need to find,

       Effective force   a) along the west

                                 b) along the north

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