**Title: Calculating Tensions in Shoelaces Using the Component Method** **Overview:** When tying shoes, a person typically holds the shoelaces at specific angles and applies a downward force. In this scenario, a force of 20 lbs is applied. This exercise will demonstrate how to use the component method to determine the tensions \( T_1 \) and \( T_2 \) in each shoelace. **Diagram Explanation:** The image illustrates two hands holding shoelaces with tensions \( T_1 \) and \( T_2 \), pulling at angles of \( 30^\circ \) and \( 40^\circ \) from the horizontal line, respectively. The combined effect of these tensions counters a direct downward force of 20 lbs at the point where the shoelaces meet. **Steps to Solve:** 1. **Break Down Forces:** - Resolve the tensions \( T_1 \) and \( T_2 \) into their horizontal and vertical components. - For \( T_1 \): - Horizontal component: \( T_{1x} = T_1 \cos(30^\circ) \) - Vertical component: \( T_{1y} = T_1 \sin(30^\circ) \) - For \( T_2 \): - Horizontal component: \( T_{2x} = T_2 \cos(40^\circ) \) - Vertical component: \( T_{2y} = T_2 \sin(40^\circ) \) 2. **Equilibrium Conditions:** - Since the system is at equilibrium, the sum of the vertical components must equal the downward force, and the horizontal components must cancel out. - Vertically: \( T_{1y} + T_{2y} = 20 \, \text{lbs} \) - Horizontally: \( T_{1x} = T_{2x} \) 3. **Solve the Equations:** - Use these equations to solve for \( T_1 \) and \( T_2 \). Understanding how to resolve and calculate forces in this manner is essential when applying physics concepts to real-world scenarios, such as ensuring stable and secure knots when tying shoes.
**Title: Calculating Tensions in Shoelaces Using the Component Method** **Overview:** When tying shoes, a person typically holds the shoelaces at specific angles and applies a downward force. In this scenario, a force of 20 lbs is applied. This exercise will demonstrate how to use the component method to determine the tensions \( T_1 \) and \( T_2 \) in each shoelace. **Diagram Explanation:** The image illustrates two hands holding shoelaces with tensions \( T_1 \) and \( T_2 \), pulling at angles of \( 30^\circ \) and \( 40^\circ \) from the horizontal line, respectively. The combined effect of these tensions counters a direct downward force of 20 lbs at the point where the shoelaces meet. **Steps to Solve:** 1. **Break Down Forces:** - Resolve the tensions \( T_1 \) and \( T_2 \) into their horizontal and vertical components. - For \( T_1 \): - Horizontal component: \( T_{1x} = T_1 \cos(30^\circ) \) - Vertical component: \( T_{1y} = T_1 \sin(30^\circ) \) - For \( T_2 \): - Horizontal component: \( T_{2x} = T_2 \cos(40^\circ) \) - Vertical component: \( T_{2y} = T_2 \sin(40^\circ) \) 2. **Equilibrium Conditions:** - Since the system is at equilibrium, the sum of the vertical components must equal the downward force, and the horizontal components must cancel out. - Vertically: \( T_{1y} + T_{2y} = 20 \, \text{lbs} \) - Horizontally: \( T_{1x} = T_{2x} \) 3. **Solve the Equations:** - Use these equations to solve for \( T_1 \) and \( T_2 \). Understanding how to resolve and calculate forces in this manner is essential when applying physics concepts to real-world scenarios, such as ensuring stable and secure knots when tying shoes.
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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Transcribed Image Text:**Title: Calculating Tensions in Shoelaces Using the Component Method**
**Overview:**
When tying shoes, a person typically holds the shoelaces at specific angles and applies a downward force. In this scenario, a force of 20 lbs is applied. This exercise will demonstrate how to use the component method to determine the tensions \( T_1 \) and \( T_2 \) in each shoelace.
**Diagram Explanation:**
The image illustrates two hands holding shoelaces with tensions \( T_1 \) and \( T_2 \), pulling at angles of \( 30^\circ \) and \( 40^\circ \) from the horizontal line, respectively. The combined effect of these tensions counters a direct downward force of 20 lbs at the point where the shoelaces meet.
**Steps to Solve:**
1. **Break Down Forces:**
- Resolve the tensions \( T_1 \) and \( T_2 \) into their horizontal and vertical components.
- For \( T_1 \):
- Horizontal component: \( T_{1x} = T_1 \cos(30^\circ) \)
- Vertical component: \( T_{1y} = T_1 \sin(30^\circ) \)
- For \( T_2 \):
- Horizontal component: \( T_{2x} = T_2 \cos(40^\circ) \)
- Vertical component: \( T_{2y} = T_2 \sin(40^\circ) \)
2. **Equilibrium Conditions:**
- Since the system is at equilibrium, the sum of the vertical components must equal the downward force, and the horizontal components must cancel out.
- Vertically: \( T_{1y} + T_{2y} = 20 \, \text{lbs} \)
- Horizontally: \( T_{1x} = T_{2x} \)
3. **Solve the Equations:**
- Use these equations to solve for \( T_1 \) and \( T_2 \).
Understanding how to resolve and calculate forces in this manner is essential when applying physics concepts to real-world scenarios, such as ensuring stable and secure knots when tying shoes.
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