### Understanding Forces Acting on a Hot-Air BalloonThe hot-air balloon in Figure 1 is being held to the ground with two ropes. The ropes have tension \( T_1 \) and \( T \). The hot-air balloon has a vertical upward force of 500N.#### Explanation of Forces:- **Vertical Upward Force**: The balloon experiences a vertical force of 500 Newtons (N), which acts upwards.- **Tension Forces in Ropes**: There are two ropes that are holding the balloon to the ground, each having a tension denoted as \( T_1 \) and \( T \).This setup is a classic example used in physics to understand the balance of forces and the concept of tension in ropes. In practical scenarios, calculations can be made to determine the tensions in the ropes based on the vertical force and the angles at which the ropes are attached to the balloon.### Visual Representation:*There is one figure associated with this text which is referenced but not provided here. Typically, such a figure would illustrate:*1. A hot-air balloon with two ropes attached to it.2. Arrows indicating the tension forces \( T_1 \) and \( T \) in each rope.3. An upward arrow showing the vertical force of 500N exerted by the balloon.The diagram would help visualize the directions of the forces and the interaction between the tension in the ropes and the upward force on the balloon. This example is useful in teaching topics such as equilibrium of forces, vector resolution, and the principles of dynamics in classical mechanics. **Physics Lesson: Understanding Force and Tension in Static Equilibrium**This diagram illustrates a hot air balloon anchored to the ground using two tethers. The situation can be analyzed using the principles of static equilibrium to understand how the forces balance each other out. ### Diagram Description:- **Hot Air Balloon**: Positioned at the intersection of the vertical and horizontal planes.- **Upward Force (500 N)**: An upward force of 500 Newtons (N) is acting on the balloon.- **Anchoring Tethers**: Two tethers (T1 and T2) are holding the balloon in place. - **Tether 1 (T1)**: Stretches vertically to a ground anchor point at \( Y = 10.0 \, m \) from the ground level. - **Tether 2 (T2)**: Stretches horizontally to a ground anchor point located \( X = 6.0 \, m \) horizontally from the balloon's base and 3.0 m horizontally from T1's ground anchor.### Axes:- **Y-Axis**: Vertical axis representing the height in meters (\( m \)).- **X-Axis**: Horizontal axis representing the horizontal distance in meters (\( m \)).### Key Points in the Diagram:- The origin (0,0) is located at the base of the hot air balloon.- The tether 1 (T1) runs vertically from the origin (0,0) to a point 10 meters up the Y-axis.- The tether 2 (T2) runs from the origin (0,0) diagonally to a ground anchor point 3.0 meters to the left and 6.0 meters to the right on the X-axis.### Analysis:The forces in the vertical and horizontal directions need to be balanced to keep the balloon in static equilibrium. The tension forces in T1 and T2, along with the upward force of 500 N, achieve this balance. **Vertical Forces**: - \( T1 \) component in vertical direction must counteract the 500 N upward force.**Horizontal Forces**:- \( T2 \) component must balance itself and any lateral force to maintain equilibrium.### Concept Application:This diagram helps us understand tension forces and equilibrium in a real-world example. This knowledge is crucial for fields like engineering and physics, where calculating and balancing forces accurately can

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Answered: 10.0 m. Y 500 N T₁ 3.0 m 6.0 m X

Science

Physics

10.0 m. Y 500 N T₁ 3.0 m 6.0 m X

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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