Fluids please help or start me off...thanks!?

Question

The beam (width) of the boat is 3.85 feet and the length is 18.00 feet. The sides are 4.20 feet high. The boat is floating in Charleston, SC harbor and is empty and drawing (How deep it sets in the water) 0.48 feet. As it sets the center of gravity is 1.60 feet above the bottom of the boat. The boat is loaded with 11, 250 pounds of cargo which moves the center of gravity upward by .26 feet. Find the empty weight of the boat and whether the boat is stable while both empty and loaded.

Answer 1

The first part is easy... the empty weight of the boat equals the mass of water displaced. To find the mass of water displaced need to calculate the volume of water displaced.

V= L of boat x W of boat x Draw of boat

V= 18 * 3.85 * 0.48= 33.26 ft3

Density of water is 62.4 lbs/ft3

Mass of water = 33.26 ft3 * 62.4 lbs/ft3

Mass= 2075.7 lbs

The stability is related to the turning moment, or the moment of inertia through the center of gravity versus the moment of inertia at a reference point. It has been a long time since I have done these calculations. I have copied a section from wikipedia about the parallel axis theorem which should be a good guide to finding the relavent section in your text book.

In physics, the parallel axis theorem can be used to determine the moment of inertia of a rigid body about any axis, given the moment of inertia of the object about the parallel axis through the object's center of mass and the perpendicular distance between the axes.

Let:

ICM denote the moment of inertia of the object about the centre of mass,

M the object's mass and d the perpendicular distance between the two axes.

Then the moment of inertia about the new axis z is given by:



This rule can be applied with the stretch rule and perpendicular axis theorem to find moments of inertia for a variety of shapes.



Parallel axes rule for area moment of inertia.The parallel axes rule also applies to the second moment of area (area moment of inertia);



where:

Iz is the area moment of inertia through the parallel axis,

Ix is the area moment of inertia through the centre of mass of the area,

A is the surface of the area, and

d is the distance from the new axis z to the centre of gravity of the area.

The parallel axis theorem is one of several theorems referred to as Steiner's theorem, after Jakob Steiner.

I noticed that the formulas did not copy from wikipedia, so you will have to check the reference to get the formulas... sorry about that