# Fluid Mechanics - Floating Bodies

• blazin247nc
In summary, a solid block with a specific gravity of 0.9 is floating with 75% submerged in water and 25% submerged in an unknown fluid. To find the specific gravity of the unknown fluid, the buoyant forces from both liquids should be considered. Using this approach, the density of the unknown fluid is calculated to be 600 kg/m^3.
blazin247nc
Fluid Mechanics -- Floating Bodies

## Homework Statement

A solid block with specific gravity 0.9 floats so that 75% of the body is submerged in water and the other 25% sits in an unknown fluid layered above the water. Find the specific gravity of the unknown fluid.

density of water = 1000 kg/m^3
density of the block = 900 kg/m^3 (from SG)

## Homework Equations

For floating bodies W = Fb

W = d*g*V
Fb = d*g*Vdisplaced

## The Attempt at a Solution

W = Wblock + Wfluid
Wblock = 900*9.8*(a+b) ----->length and width cancel when equations are set equal
Fb = 1000*9.8*b -------->a = height of block above water (.25) b= below water (.75)

This is where I get lost. I know I need to incorporate the weight of the unknown fluid pushing down on the block, but does the weight of the fluid only include the displaced weight?

where:

W = 900*9.8*(a+b) + d-fluid*9.8*a ? But when I do this I get a negative density :(

Hi blazin247nc,

blazin247nc said:

## Homework Statement

A solid block with specific gravity 0.9 floats so that 75% of the body is submerged in water and the other 25% sits in an unknown fluid layered above the water. Find the specific gravity of the unknown fluid.

density of water = 1000 kg/m^3
density of the block = 900 kg/m^3 (from SG)

## Homework Equations

For floating bodies W = Fb

W = d*g*V
Fb = d*g*Vdisplaced

## The Attempt at a Solution

W = Wblock + Wfluid
Wblock = 900*9.8*(a+b) ----->length and width cancel when equations are set equal
Fb = 1000*9.8*b -------->a = height of block above water (.25) b= below water (.75)

This is where I get lost. I know I need to incorporate the weight of the unknown fluid pushing down on the block,

No, that is not right since you are already using the buoyant force from the water. There are two ways you could deal with the fluid forces acting on the objects in these types of problems.

The first way is to find the force pushing down on the top of the object due to the liquid pressure, and the force pushing up on the bottom of the object due to the water pressure. In this problem, those sum of those two forces (one is positive, one is negative) would have to equal the weight of the object.

The second way (which is normally the best way) is to think in terms of the buoyant forces from both of the liquids. The buoyant forces are upwards, because the pressure is greater the deeper you go.

These are alternate approaches; the problem in your approach is that you are mixing them and using the buoyant force of the water, and the force downard from the unknown liquid. The total buoyant force already comes from adding together the individual forces on the top and bottom of the object. Does that help?

but does the weight of the fluid only include the displaced weight?

where:

W = 900*9.8*(a+b) + d-fluid*9.8*a ? But when I do this I get a negative density :(

OK, I see what I was doing wrong now. I got 600 kg/m^3 as the density of the mystery fluid. Seems like a more reasonable answer than -200 :P

## 1. How do objects float in fluids?

Objects float in fluids due to a concept known as buoyancy. This is the upward force exerted by a fluid on an object that is partially or fully submerged in it. The buoyant force is equal to the weight of the fluid that the object displaces. If the buoyant force is greater than the weight of the object, it will float.

## 2. Why does an object's shape affect its ability to float?

An object's shape affects its ability to float because it determines its volume and surface area. Objects with a larger surface area relative to their volume, such as a boat, will experience a greater buoyant force and therefore are more likely to float. Objects with a smaller surface area relative to their volume, such as a rock, will experience a smaller buoyant force and are less likely to float.

## 3. Can an object float in any fluid?

Technically, an object can float in any fluid, including gases like air. However, the density of the fluid will determine how easily the object will float. For example, objects with a low density, like a balloon filled with helium, will float easily in air due to the buoyant force. On the other hand, objects with a higher density, like a brick, will not float in air because the buoyant force is not strong enough to overcome the weight of the object.

## 4. What is the difference between a floating body and a sinking body?

A floating body is an object that remains at the surface level of a fluid due to the balance between its weight and the buoyant force. A sinking body is an object that submerges in a fluid due to the weight of the object being greater than the buoyant force. The key difference is the relative strength of the buoyant force compared to the object's weight.

## 5. How does the density of an object affect its ability to float?

The density of an object plays a significant role in its ability to float. The higher the density of an object, the more likely it is to sink in a fluid. This is because the object will displace a smaller volume of fluid, resulting in a smaller buoyant force. Conversely, objects with a lower density will float more easily as they displace a larger volume of fluid, resulting in a stronger buoyant force.

Replies
8
Views
2K
Replies
2
Views
2K
Replies
16
Views
2K
Replies
6
Views
1K
Replies
13
Views
2K
Replies
10
Views
10K
Replies
18
Views
2K
Replies
2
Views
1K
Replies
4
Views
1K
Replies
13
Views
3K