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A sailboat is acted on by a wind force of 340N directed 40° south of east and a current force of 210N directed 35° south of west. Pick an appropriate scale and make a full-size vector diagram. Find the components of the wind & the current. Draw and label these components on the diagram. Show how to use the components you found and the Component Rule for Adding Vectors to find: a. The east component of the resultant force.. b. The north component of the resultant force.

A sailboat is acted on by a wind force of 340N directed 40° south of east and a current force of 210N directed 35° south of west. Pick an appropriate scale and make a full-size vector diagram. Find the components of the wind & the current. Draw and label these components on the diagram. Show how to use the components you found and the Component Rule for Adding Vectors to find: a. The east component of the resultant force.. b. The north component of the resultant force.

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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**Vector Addition and Resultant Forces** **Problem 5:** A sailboat is acted on by two forces: - A wind force of 340N directed 40° south of east. - A current force of 210N directed 35° south of west. Tasks: 1. Pick an appropriate scale and create a full-size vector diagram. 2. Find and label the components of both the wind and the current on your diagram. **Instructions:** - **Components Calculation:** - Use trigonometric functions to resolve each force into its east-west and north-south components. - **Component Rule for Adding Vectors:** - Use the separated components to determine the overall resultant force by adding corresponding components. a. **East Component:** Calculate and write down the east component of the resultant force. b. **North Component:** Calculate and document the north component of the resultant force. **Problem 6:** Use your results from problems 5a and 5b to: - Draw the resultant force vector on your diagram. - Determine and label the magnitude and direction of the resultant force. **Problem 7:** Verify your results for problems 6 and 7 using: - Direct measurement from the diagram. - Mathematical calculations for magnitudes and angles of the components and resultant. **Comparison:** - Clearly show your methods on your diagram. - Compare results from the two methods: direct measurement and mathematical calculation. Be specific in discussing the comparison.
Transcribed Image Text:**Vector Addition and Resultant Forces** **Problem 5:** A sailboat is acted on by two forces: - A wind force of 340N directed 40° south of east. - A current force of 210N directed 35° south of west. Tasks: 1. Pick an appropriate scale and create a full-size vector diagram. 2. Find and label the components of both the wind and the current on your diagram. **Instructions:** - **Components Calculation:** - Use trigonometric functions to resolve each force into its east-west and north-south components. - **Component Rule for Adding Vectors:** - Use the separated components to determine the overall resultant force by adding corresponding components. a. **East Component:** Calculate and write down the east component of the resultant force. b. **North Component:** Calculate and document the north component of the resultant force. **Problem 6:** Use your results from problems 5a and 5b to: - Draw the resultant force vector on your diagram. - Determine and label the magnitude and direction of the resultant force. **Problem 7:** Verify your results for problems 6 and 7 using: - Direct measurement from the diagram. - Mathematical calculations for magnitudes and angles of the components and resultant. **Comparison:** - Clearly show your methods on your diagram. - Compare results from the two methods: direct measurement and mathematical calculation. Be specific in discussing the comparison.
## Transcription of Educational Content on Force Vectors ### Text Explanation **Figure 6: A force \( W \) due to wind and a force \( C \) due to current produce a resultant \( R \) along the diagonal of the force parallelogram.** The components of \( R \) along any axis are the sum of the components of \( W \) and \( C \) along that axis. This demonstrates a critical property of the resultant of two forces: if two forces act together on the same object, the resultant force along any axis is the sum of the components of the two forces along that axis. This is known as the **Component Rule for Adding Vectors.** **Component Equations:** 1. \( R_E = W_E + C_E \) 2. \( R_N = W_N \) In these equations, the components \( W_E, W_N, C_E, \) and \( C_N \) may be positive or negative. --- ### Diagram Explanation The diagram on the left illustrates vectors \( W \) (wind force) and \( C \) (current force) forming a parallelogram, with the resultant vector \( R \) along the diagonal. Components are detailed along the North (N) and East (E) directions: - \( W \) is resolved into components \( W_E \) (East) and \( W_N \) (North). - \( C \) is resolved similarly into \( C_E \) and \( C_N \). The vector \( R \) is the resultant of \( W \) and \( C \) with its components expressed as the sum of corresponding components of individual forces. The smaller diagram on the right represents angular measurements. It labels a 30-degree angle with an adjacent force \( F_y \), showing calculations for the components: - \( F_x = -F \cos(30^\circ) = -180 \cos(30^\circ) = -155 \) - \( F_y = F \sin(30^\circ) = 180 \sin(30^\circ) = 90 \) This calculation verifies the force components along the specified axis. ### Additional Notes - **Last Revised**: 07/17/2015 - This content is categorized under "Force Vectors – 3.5" and can be beneficial for understanding vector resolution in physics, particularly in dealing with forces in two dimensions.
Transcribed Image Text:## Transcription of Educational Content on Force Vectors ### Text Explanation **Figure 6: A force \( W \) due to wind and a force \( C \) due to current produce a resultant \( R \) along the diagonal of the force parallelogram.** The components of \( R \) along any axis are the sum of the components of \( W \) and \( C \) along that axis. This demonstrates a critical property of the resultant of two forces: if two forces act together on the same object, the resultant force along any axis is the sum of the components of the two forces along that axis. This is known as the **Component Rule for Adding Vectors.** **Component Equations:** 1. \( R_E = W_E + C_E \) 2. \( R_N = W_N \) In these equations, the components \( W_E, W_N, C_E, \) and \( C_N \) may be positive or negative. --- ### Diagram Explanation The diagram on the left illustrates vectors \( W \) (wind force) and \( C \) (current force) forming a parallelogram, with the resultant vector \( R \) along the diagonal. Components are detailed along the North (N) and East (E) directions: - \( W \) is resolved into components \( W_E \) (East) and \( W_N \) (North). - \( C \) is resolved similarly into \( C_E \) and \( C_N \). The vector \( R \) is the resultant of \( W \) and \( C \) with its components expressed as the sum of corresponding components of individual forces. The smaller diagram on the right represents angular measurements. It labels a 30-degree angle with an adjacent force \( F_y \), showing calculations for the components: - \( F_x = -F \cos(30^\circ) = -180 \cos(30^\circ) = -155 \) - \( F_y = F \sin(30^\circ) = 180 \sin(30^\circ) = 90 \) This calculation verifies the force components along the specified axis. ### Additional Notes - **Last Revised**: 07/17/2015 - This content is categorized under "Force Vectors – 3.5" and can be beneficial for understanding vector resolution in physics, particularly in dealing with forces in two dimensions.
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