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
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
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
Fluid mechanics question

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
Step by step
Solved in 4 steps with 1 images

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you


Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON

Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning


Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON

Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning

Fundamentals of Structural Analysis
Civil Engineering
ISBN:
9780073398006
Author:
Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:
McGraw-Hill Education


Traffic and Highway Engineering
Civil Engineering
ISBN:
9781305156241
Author:
Garber, Nicholas J.
Publisher:
Cengage Learning