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2) Workmen are trying to free an SUV stuck in the mud. y B (350 N) To extricate the vehicle, they use four horizontal ropes 30° 530 producing the force vectors shown. a) Find the x- and y- components of the each of the four pulls. b) Use the components to find the magnititude and direction D (400 N)' X with respect to +x axis of the resultants of the four pulls. 250 C (450 N) A (600 N)

2) Workmen are trying to free an SUV stuck in the mud. y B (350 N) To extricate the vehicle, they use four horizontal ropes 30° 530 producing the force vectors shown. a) Find the x- and y- components of the each of the four pulls. b) Use the components to find the magnititude and direction D (400 N)' X with respect to +x axis of the resultants of the four pulls. 250 C (450 N) A (600 N)

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: SUV Extrication with Force Vectors** Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they use four horizontal ropes producing the force vectors shown. **Tasks:** a) Find the x- and y-components of each of the four pulls. b) Use the components to find the magnitude and direction with respect to the +x axis of the resultant of the four pulls. **Diagram Explanation:** - The diagram shows an SUV with four ropes attached, each applying a force at different angles. - **Vector A**: 600 N directed directly downward along the -y axis. - **Vector B**: 350 N at a 30° angle above the +x axis. - **Vector C**: 450 N at a 25° angle below the -x axis. - **Vector D**: 400 N at a 53° angle above the -x axis. **Coordinate System:** - Horizontal axis: x-axis. - Vertical axis: y-axis. ##### Steps to Solve the Problem: 1. **Determine the Components**: - For each vector, resolve it into x (horizontal) and y (vertical) components using trigonometric functions: - \( F_{x} = F \cdot \cos(\theta) \) - \( F_{y} = F \cdot \sin(\theta) \) 2. **Calculate Components for Each Vector**: - **Vector A**: - \( A_x = 600 \cdot \cos(270°) = 0 \) (since it's vertical) - \( A_y = 600 \cdot \sin(270°) = -600 \, \text{N} \) - **Vector B**: - \( B_x = 350 \cdot \cos(30°) \) - \( B_y = 350 \cdot \sin(30°) \) - **Vector C**: - \( C_x = 450 \cdot \cos(205°) \) - \( C_y = 450 \cdot \sin(205°) \) - **Vector D**: - \( D_x = 400 \cdot \cos(127°) \) - \( D_y = 400 \cdot \sin(127°) \) 3
Transcribed Image Text:**Problem 2: SUV Extrication with Force Vectors** Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they use four horizontal ropes producing the force vectors shown. **Tasks:** a) Find the x- and y-components of each of the four pulls. b) Use the components to find the magnitude and direction with respect to the +x axis of the resultant of the four pulls. **Diagram Explanation:** - The diagram shows an SUV with four ropes attached, each applying a force at different angles. - **Vector A**: 600 N directed directly downward along the -y axis. - **Vector B**: 350 N at a 30° angle above the +x axis. - **Vector C**: 450 N at a 25° angle below the -x axis. - **Vector D**: 400 N at a 53° angle above the -x axis. **Coordinate System:** - Horizontal axis: x-axis. - Vertical axis: y-axis. ##### Steps to Solve the Problem: 1. **Determine the Components**: - For each vector, resolve it into x (horizontal) and y (vertical) components using trigonometric functions: - \( F_{x} = F \cdot \cos(\theta) \) - \( F_{y} = F \cdot \sin(\theta) \) 2. **Calculate Components for Each Vector**: - **Vector A**: - \( A_x = 600 \cdot \cos(270°) = 0 \) (since it's vertical) - \( A_y = 600 \cdot \sin(270°) = -600 \, \text{N} \) - **Vector B**: - \( B_x = 350 \cdot \cos(30°) \) - \( B_y = 350 \cdot \sin(30°) \) - **Vector C**: - \( C_x = 450 \cdot \cos(205°) \) - \( C_y = 450 \cdot \sin(205°) \) - **Vector D**: - \( D_x = 400 \cdot \cos(127°) \) - \( D_y = 400 \cdot \sin(127°) \) 3
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