Buoyancy Force question, having hard time starting.

[frozenguy]

Homework Statement

The 3m plank shown in section has a density of 800 kg/m³ and is hinged about a horizontal axis though its upper edge O. Calculate the angle theta assumed by the plank with the horizontal for the level of fresh water shown.

Homework Equations

Whats wrong with the editor? It isn't working properly for me at all.
B=rho*g*V
Sum of M_O=0

The Attempt at a Solution

I bolded in section because I was wondering what that meant exactly. Like I should only consider 1 meter in width? What about its thickness? Am I just supposed to use density of the plank to compare to density of water like in a ratio of some sorts?
I was thinking I need to find that distance from the centroid of buoyancy to the water line so I can find that length and then find theta.. But I'm not to sure on where to go.

 

[frozenguy]

Ok so I've been thinking this over more and I realized I need to take into account the water pressure force acting on the plank. So I have mg and the center of gravity, I have B at the centroid of the section under water, and I have the force of water pressure on the submerged part.

Sum around O=0 should give me my answer ya?

EDIT: I guess the water pressure is NOT a factor in this problem, or its included in the buoyancy.

 

[frozenguy]

Got it! The answer checks with the one provided from the book.

 

[berkeman]

Good job. I clicked into your thread yesterday, but didn't have time to be of help. Glad that you figured it out on your own!

 

[DeeNos]

As a scientist, it is important to approach problems systematically and logically. In this case, we can begin by defining the problem and identifying the key variables and equations involved.

First, we need to understand the concept of buoyancy force. This is the upward force exerted by a fluid on an object immersed in it. It is equal to the weight of the fluid that the object displaces. The buoyancy force can be calculated using the equation B=rho*g*V, where rho is the density of the fluid, g is the acceleration due to gravity, and V is the volume of the fluid displaced by the object.

Next, we need to determine the relevant variables in this problem. We are given the density of the plank (800 kg/m3), the length of the plank (3m), and the location of the hinge (O). We also know that the plank is immersed in fresh water, which has a density of 1000 kg/m3. We can use these values to calculate the buoyancy force acting on the plank.

To find the angle theta assumed by the plank, we need to consider the forces acting on it. The plank is hinged at one end, so there will be a reaction force at the hinge. The weight of the plank will also act downwards. Finally, there will be an upward buoyancy force acting on the plank. These forces must be balanced for the plank to be in equilibrium, so we can set up the equation Sum of MO=0, where MO is the moment of the forces about the hinge.

To solve for theta, we need to find the distance from the centroid of buoyancy to the water line. This can be done using the concept of center of mass. Since the plank is symmetric, the center of mass will be at the midpoint of the plank. From there, we can use simple trigonometry to find the length and then determine theta.

In conclusion, it is important to understand the concept of buoyancy force and how it applies to this problem. By identifying the relevant variables and using the appropriate equations, we can systematically solve for the angle theta assumed by the plank. It is also important to carefully consider the forces acting on the object and use principles such as center of mass to find the necessary distances.