### Problem Statement: A \( m = 3.05 \, \text{kg} \) object hangs in equilibrium at the end of a rope (taken as massless) while a wind pushes the object with a \( F_w = 21.5 \, \text{N} \) horizontal force. Find the magnitude of the tension in the rope and the rope's angle from the vertical. The acceleration due to gravity is \( g = 9.81 \, \text{m/s}^2 \). **Output Fields:** 1. **Tension:** _____ N 2. **Angle:** _____ ° ### Diagram Explanation: On the right side, there is a diagram showing the setup: - A rope is hanging from a horizontal beam. - An object, represented by a green ball, is attached to the rope. - The ball is hanging at an angle from the vertical due to the wind blowing horizontally from the left. - The horizontal force \( F_w \) is labeled as "Wind" with an arrow pointing to the right. The diagram illustrates the forces acting on the object: - The gravitational force (downward). - The tension in the rope (along the rope). - The horizontal force applied by the wind.
### Problem Statement: A \( m = 3.05 \, \text{kg} \) object hangs in equilibrium at the end of a rope (taken as massless) while a wind pushes the object with a \( F_w = 21.5 \, \text{N} \) horizontal force. Find the magnitude of the tension in the rope and the rope's angle from the vertical. The acceleration due to gravity is \( g = 9.81 \, \text{m/s}^2 \). **Output Fields:** 1. **Tension:** _____ N 2. **Angle:** _____ ° ### Diagram Explanation: On the right side, there is a diagram showing the setup: - A rope is hanging from a horizontal beam. - An object, represented by a green ball, is attached to the rope. - The ball is hanging at an angle from the vertical due to the wind blowing horizontally from the left. - The horizontal force \( F_w \) is labeled as "Wind" with an arrow pointing to the right. The diagram illustrates the forces acting on the object: - The gravitational force (downward). - The tension in the rope (along the rope). - The horizontal force applied by the wind.
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:### Problem Statement:
A \( m = 3.05 \, \text{kg} \) object hangs in equilibrium at the end of a rope (taken as massless) while a wind pushes the object with a \( F_w = 21.5 \, \text{N} \) horizontal force. Find the magnitude of the tension in the rope and the rope's angle from the vertical. The acceleration due to gravity is \( g = 9.81 \, \text{m/s}^2 \).
**Output Fields:**
1. **Tension:** _____ N
2. **Angle:** _____ °
### Diagram Explanation:
On the right side, there is a diagram showing the setup:
- A rope is hanging from a horizontal beam.
- An object, represented by a green ball, is attached to the rope.
- The ball is hanging at an angle from the vertical due to the wind blowing horizontally from the left.
- The horizontal force \( F_w \) is labeled as "Wind" with an arrow pointing to the right.
The diagram illustrates the forces acting on the object:
- The gravitational force (downward).
- The tension in the rope (along the rope).
- The horizontal force applied by the wind.
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