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A climbing anchor consists of two strands of nylon webbing clipped to bolts in the rock. The webbing is clipped into the rope at the other end, with the webbing making angles of 22° and 35° with the vertical. What is the tension in each of the webbing strands if the combined mass of the rope and climber is 85 kg?

A climbing anchor consists of two strands of nylon webbing clipped to bolts in the rock. The webbing is clipped into the rope at the other end, with the webbing making angles of 22° and 35° with the vertical. What is the tension in each of the webbing strands if the combined mass of the rope and climber is 85 kg?

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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A climbing anchor consists of two strands of nylon webbing clipped to bolts in the rock. The webbing is clipped into the rope at the other end, with the webbing making angles of 22° and 35° with the vertical. What is the tension in each of the webbing strands if the combined mass of the rope and climber is 85 kg?

### Resolving Forces in Mechanics: A Simple Exercise In this exercise, we are given a diagram that depicts a system where forces are being resolved. This type of diagram is crucial for understanding how forces work in different directions and how they affect objects in mechanics. #### Diagram Explanation: The image shows a point where two forces meet, creating an angle with respect to each other, and a downward force. Here's a detailed description of the elements in the diagram: 1. **Forces and Angles**: - There are two inclined forces, each forming an angle with a vertical dashed line. - The angle on the left is labeled as 22 degrees. - The angle on the right is labeled as 35 degrees. 2. **Weight Force**: - A vertical arrow pointing downwards is representing the weight of an object. - The weight force is labeled as 85 kg. To convert this weight into force, we would multiply it by the acceleration due to gravity (9.8 m/s²). 3. **System Geometry**: - The two inclined lines meet at a point from which the vertical arrow starts. This point is essentially where the forces are combined. This system is often used to illustrate the principles of force resolution, where a single force is split into components that align with different angles. By understanding the angles and the weight force, one can employ trigonometric relationships to resolve the forces into their respective components. ### Practical Application: Such diagrams are central to solving problems in mechanics, particularly when dealing with static equilibrium problems, where the sum of all forces and moments must be zero. This helps in understanding how different forces balance each other out, ensuring the object remains in equilibrium. #### Steps for Resolution: 1. Decompose the weight force into components along the directions of the two inclined forces. 2. Use trigonometric functions (sine, cosine) based on the given angles to find these components. 3. Analyze the equilibrium conditions to explore the forces acting along the directions of the inclined lines. This exercise demonstrates the fundamental principles in physics and engineering related to force resolution and equilibrium.
Transcribed Image Text:### Resolving Forces in Mechanics: A Simple Exercise In this exercise, we are given a diagram that depicts a system where forces are being resolved. This type of diagram is crucial for understanding how forces work in different directions and how they affect objects in mechanics. #### Diagram Explanation: The image shows a point where two forces meet, creating an angle with respect to each other, and a downward force. Here's a detailed description of the elements in the diagram: 1. **Forces and Angles**: - There are two inclined forces, each forming an angle with a vertical dashed line. - The angle on the left is labeled as 22 degrees. - The angle on the right is labeled as 35 degrees. 2. **Weight Force**: - A vertical arrow pointing downwards is representing the weight of an object. - The weight force is labeled as 85 kg. To convert this weight into force, we would multiply it by the acceleration due to gravity (9.8 m/s²). 3. **System Geometry**: - The two inclined lines meet at a point from which the vertical arrow starts. This point is essentially where the forces are combined. This system is often used to illustrate the principles of force resolution, where a single force is split into components that align with different angles. By understanding the angles and the weight force, one can employ trigonometric relationships to resolve the forces into their respective components. ### Practical Application: Such diagrams are central to solving problems in mechanics, particularly when dealing with static equilibrium problems, where the sum of all forces and moments must be zero. This helps in understanding how different forces balance each other out, ensuring the object remains in equilibrium. #### Steps for Resolution: 1. Decompose the weight force into components along the directions of the two inclined forces. 2. Use trigonometric functions (sine, cosine) based on the given angles to find these components. 3. Analyze the equilibrium conditions to explore the forces acting along the directions of the inclined lines. This exercise demonstrates the fundamental principles in physics and engineering related to force resolution and equilibrium.
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