Question
E A barge is 60 ft long, 20 ft wide, and 8 ft deep. When
empty, it weighs 210000 lb , and its center of gravity is
1.5 ff above the bottom. Is it stable when floating in
water?
empty, it weighs 210000 lb , and its center of gravity is
1.5 ff above the bottom. Is it stable when floating in
water?
Ask by Ross Bowman. in the United States
Nov 13,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The barge is stable when floating in water because the metacentric height (75 ft) is greater than the center of gravity height (1.5 ft).
Solution
To determine if the barge is stable when floating in water, we need to calculate the metacentric height (GM) of the barge. The barge is stable if the metacentric height is greater than the center of gravity height.
Given:
- Length of the barge (L) = 60 ft
- Width of the barge (W) = 20 ft
- Depth of the barge (D) = 8 ft
- Weight of the barge when empty (W) = 210000 lb
- Center of gravity height above the bottom (CG) = 1.5 ft
The metacentric height (GM) is calculated using the formula:
Let’s calculate the metacentric height (GM) of the barge.
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Remove the parentheses:
- step2: Multiply the terms:
- step3: Reduce the fraction:
The metacentric height (GM) of the barge is 75 ft.
Now, we need to compare the metacentric height (GM) with the center of gravity height (CG) to determine if the barge is stable when floating in water. If the metacentric height is greater than the center of gravity height, the barge is stable.
Given:
- Center of gravity height above the bottom (CG) = 1.5 ft
Since the metacentric height (GM) is 75 ft and the center of gravity height (CG) is 1.5 ft, the barge is stable when floating in water because the metacentric height is greater than the center of gravity height.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
To determine the stability of the barge when floating in water, we can use the concept of metacentric height (GM). A stable vessel must have a positive GM, which means the center of buoyancy (B) must be below the center of gravity (G). Since the center of gravity is 1.5 ft above the bottom, we consider the barge’s dimensions to find the center of buoyancy, which will rise as the vessel displaces water. If the metacentric height is greater than zero, the barge should be stable.
In water, the barge’s displaced volume is calculated by multiplying its dimensions. The stability can be further assessed by examining the righting arm (the distance between the center of gravity and the center of buoyancy). A righting arm that is larger than zero contributes to the vessel’s stability, especially in a heeled position. Therefore, even when empty, if the GM is positive, the barge can be considered stable.
To solidly confirm your findings, some real-world boat stability tests can be helpful, like observing how well it righted itself after being tilted. Stability also varies with loading conditions, so ensuring proper weight distribution and avoiding top-heavy loads can prevent potential capsizing. Engaging in regular safety checks and potentially utilizing ballast can enhance the barge’s sturdiness on the water.
