Area Moment of Inertia & Stability of Floating Bodies

In summary, the conversation revolves around finding the area moments of inertia for a ship with a rectangular waterline area. The mass of the ship and two cargo containers is given, along with the length and width of the waterline. The question is asking for the length of a specific point, and the given values are GM, GG', h, and an angle. The speaker is unsure which values to use for b and h in the equation for finding I/V. They are seeking assistance in determining the correct values.
  • #1
lirexin
4
0
Just totally confused which value to use to get the area moments of inertia with this question

The ship was initially looks like this the mass of the ship is 5000 tonnes two heavy cargocontainers each of mass 73,370 Kg each
assume that the ship has a rectangular waterline area, with length 94.85m and width 12m

123123.jpg


12.jpg


The question is asking the length of BG and hence find the length of G'B'
Ive been told that GM=47.7028(m) GG'=2.5(m) h=4.41154(m)(sink height) the angle is 3(degree)
What I've done was using the equation GM = I/V-BG then BG = I/V-GM
For the I/V part I = bh^3/12 from the textbook the problem is which value is b and which value is h?
 
Engineering news on Phys.org
  • #2
Any one help
 

1. What is area moment of inertia and why is it important in studying floating bodies?

Area moment of inertia, also known as second moment of area, is a measure of the distribution of an object's mass around its axis of rotation. In the context of floating bodies, it is important because it determines the body's resistance to bending or deformation under external forces.

2. How is the area moment of inertia calculated for a floating body?

The area moment of inertia for a floating body can be calculated by integrating the product of the squared distance from the axis of rotation and the cross-sectional area of the body over the entire body.

3. What factors affect the stability of a floating body?

The stability of a floating body is affected by the location of its center of buoyancy, the shape and size of the body, and the density of the fluid it is floating in. The higher the center of buoyancy and the smaller the area moment of inertia, the more stable the body will be.

4. How does the shape of a floating body affect its stability?

The shape of a floating body plays a significant role in its stability. Bodies with a larger area moment of inertia, such as cylinders or spheres, are more stable than bodies with a smaller area moment of inertia, such as flat plates. This is because the distribution of mass in these shapes creates a larger resistance to bending.

5. Can the area moment of inertia be manipulated to improve the stability of a floating body?

Yes, the area moment of inertia can be manipulated by changing the shape, size, or density of the body. By increasing the area moment of inertia, the stability of the body can be improved. This is why ships and boats are designed with a wide, curved hull to increase their stability in water.

Similar threads

I Moment of inertia of human body with limbs at an angle
    • Mechanics
Replies
12
Views
345
Understanding the Value of the Second Moment Of Area
    • Mechanical Engineering
Replies
7
Views
2K
Understanding Kinetic Energy: Moment of Inertia and Rotational Motion
    • Advanced Physics Homework Help
Replies
5
Views
897
Calculating the Second Moment of Area for Floating Bodies
    • Introductory Physics Homework Help
Replies
2
Views
1K
Angular acceleration of plank hanging off edge with a weight
    • Introductory Physics Homework Help
Replies
7
Views
301
IC Engine Connecting Rod Mass Moment of Inertia Measurements
    • Mechanical Engineering
Replies
2
Views
959
How can I calculate the moment of inertia of any object?
    • Mechanics
Replies
10
Views
1K
Moment of Inertia with pulley and two masses on a string (iWTSE.org)
    • Introductory Physics Homework Help
Replies
8
Views
8K
Torque and Moment of Inertia of a Lever Arm
    • Mechanics
Replies
2
Views
2K
Moment of inertia formula help
    • Introductory Physics Homework Help
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top