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2/2 The magnitude of the force F is 400 lb. Express F as a vector in terms of the unit vectors i and j. Identify both the scalar and vector components of F. y, ft F = 400 lb -x, ft 30° A (3,-1) PROBLEM 2/2

2/2 The magnitude of the force F is 400 lb. Express F as a vector in terms of the unit vectors i and j. Identify both the scalar and vector components of F. y, ft F = 400 lb -x, ft 30° A (3,-1) PROBLEM 2/2

College Physics
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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**Problem 2/2: Vector Components of a Force** **Problem Statement:** The magnitude of the force **F** is 400 lb. Express **F** as a vector in terms of the unit vectors **i** and **j**. Identify both the scalar and vector components of **F**. **Figure Explanation:** In this problem, we are provided with a diagram illustrating the force **F** acting on point A (3, -1). The force vector **F** has a magnitude of 400 lb and is directed at an angle of 30 degrees above the negative x-axis (to the left). Here's a more detailed breakdown of the diagram: 1. **Axes:** - The horizontal axis represents the x-axis (measured in feet), with positive direction to the right and negative direction to the left. - The vertical axis represents the y-axis (measured in feet), with positive direction upwards and negative direction downwards. 2. **Point A:** - Point A is located at coordinates (3, -1) on the Cartesian plane. 3. **Force Vector F:** - A red arrow represents the force **F**, which has a magnitude of 400 lb. - The arrow is directed from the origin, representing the location where the force is applied, towards the direction 30 degrees above the negative x-axis. **Objective:** The goal is to express the force **F** in vector form using the unit vectors **i** (along the x-axis) and **j** (along the y-axis), and to determine both the scalar and vector components of **F**. **Solution:** 1. **Magnitude of the Force:** Given: |**F**| = 400 lb 2. **Direction Components:** - The angle θ = 30 degrees (above the negative x-axis). Using trigonometric functions to resolve **F** into its x and y components: - The x-component of **F**: \( F_x = F \cdot \cos(180^\circ - \theta) = 400 \cdot \cos(150^\circ) \). - The y-component of **F**: \( F_y = F \cdot \sin(180^\circ - \theta) = 400 \cdot \sin(150^\circ) \). To solve these: - \( \cos(150^\circ) = -
Transcribed Image Text:**Problem 2/2: Vector Components of a Force** **Problem Statement:** The magnitude of the force **F** is 400 lb. Express **F** as a vector in terms of the unit vectors **i** and **j**. Identify both the scalar and vector components of **F**. **Figure Explanation:** In this problem, we are provided with a diagram illustrating the force **F** acting on point A (3, -1). The force vector **F** has a magnitude of 400 lb and is directed at an angle of 30 degrees above the negative x-axis (to the left). Here's a more detailed breakdown of the diagram: 1. **Axes:** - The horizontal axis represents the x-axis (measured in feet), with positive direction to the right and negative direction to the left. - The vertical axis represents the y-axis (measured in feet), with positive direction upwards and negative direction downwards. 2. **Point A:** - Point A is located at coordinates (3, -1) on the Cartesian plane. 3. **Force Vector F:** - A red arrow represents the force **F**, which has a magnitude of 400 lb. - The arrow is directed from the origin, representing the location where the force is applied, towards the direction 30 degrees above the negative x-axis. **Objective:** The goal is to express the force **F** in vector form using the unit vectors **i** (along the x-axis) and **j** (along the y-axis), and to determine both the scalar and vector components of **F**. **Solution:** 1. **Magnitude of the Force:** Given: |**F**| = 400 lb 2. **Direction Components:** - The angle θ = 30 degrees (above the negative x-axis). Using trigonometric functions to resolve **F** into its x and y components: - The x-component of **F**: \( F_x = F \cdot \cos(180^\circ - \theta) = 400 \cdot \cos(150^\circ) \). - The y-component of **F**: \( F_y = F \cdot \sin(180^\circ - \theta) = 400 \cdot \sin(150^\circ) \). To solve these: - \( \cos(150^\circ) = -
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