Buoyancy 4Q. A balloon uses hot air to provide its lifting capability. Prior to its release it is tethered to the ground by a steel cable. If the gondola, weights, passengers, and material weigh 2000 lb, determine the tension in the cable when the balloon is inflated as a sphere having a diameter of 60 ft. Assume that the hot air has a specific weight of 0.040 lb/ft³ and the ambient air has a specific weight of 0.070 lb/ft^3 Buoyant force Weight of "hot" air 2000 lb Cable tension

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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**Buoyancy**

**4Q.** A balloon uses hot air to provide its lifting capability. Prior to its release, it is tethered to the ground by a steel cable. If the gondola, weights, passengers, and the material weigh 2000 lb, determine the tension in the cable when the balloon is inflated as a sphere with a diameter of 60 ft. Assume that the hot air has a specific weight of 0.040 lb/ft³ and the ambient air has a specific weight of 0.070 lb/ft³.

**Diagram Explanation:**

The diagram illustrates the forces acting on a hot air balloon tethered to the ground:

- The **balloon** is represented as a sphere filled with hot air.
- The **buoyant force** acts upward due to the difference in specific weights between the ambient air and the hot air inside the balloon.
- The **weight of the hot air** within the balloon acts downward.
- The gondola is depicted below the balloon with a downward arrow representing the **2000 lb weight** of the gondola, weights, passengers, and material.
- A downward arrow labeled **cable tension** indicates the tension in the steel cable tethering the balloon to the ground.
Transcribed Image Text:**Buoyancy** **4Q.** A balloon uses hot air to provide its lifting capability. Prior to its release, it is tethered to the ground by a steel cable. If the gondola, weights, passengers, and the material weigh 2000 lb, determine the tension in the cable when the balloon is inflated as a sphere with a diameter of 60 ft. Assume that the hot air has a specific weight of 0.040 lb/ft³ and the ambient air has a specific weight of 0.070 lb/ft³. **Diagram Explanation:** The diagram illustrates the forces acting on a hot air balloon tethered to the ground: - The **balloon** is represented as a sphere filled with hot air. - The **buoyant force** acts upward due to the difference in specific weights between the ambient air and the hot air inside the balloon. - The **weight of the hot air** within the balloon acts downward. - The gondola is depicted below the balloon with a downward arrow representing the **2000 lb weight** of the gondola, weights, passengers, and material. - A downward arrow labeled **cable tension** indicates the tension in the steel cable tethering the balloon to the ground.
Expert Solution
Step 1: Given

weight= 2000 lb

diameter= 60ft

radius = 30 ft

specific weight (hot air) = 0.040 lb/ft3

specific weight (ambient air) = 0.070 lb/ft3

We have to apply the buoyancy force concept

To find :

Tension in the cable 

steps

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