# F = MA 2011 Exam # 8 (Fraction of an object above surface of water)

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In summary: So as long as the block is not deformed, the buoyant force will always be proportional to the fraction below water. In summary, we use the equations F_app = F_g - F_b and F_b = F_g to find the apparent weight and buoyant force of a block of wood submerged in water. By setting these equations equal to each other and solving for the fraction of the block below water, we can determine that 2/5 of the block will be visible above the surface of the water when it is floating. This relationship holds true for blocks of any density, as long as they are not deformed.
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## Homework Statement

8. When a block of wood with a weight of 30 N is completely submerged under water the buoyant force on the block
of wood from the water is 50 N. When the block is released it ﬂoats at the surface. What fraction of the block will
then be visible above the surface of the water when the block is ﬂoating?
(A) 1/15
(B) 1/5
(C) 1/3
(D) 2/5
(E) 3/5

## Homework Equations

F_app = F_g - F_b
For floating objects:
F_b = F_g

## The Attempt at a Solution

So, to start off, we plug into the first equation to find the apparent weight underwater:
F_app = 30 - 50
F_app = - 20N
I can intuitively see why the answer is 2/5, but can't find the physics of it.

If a fraction β of the block is above the water, then what is the buoyant force on the block?

Hint: The buoyant force is proportional the volume of the block that is underwater

Did you mean β below the water? If so, then the buoyant force would be β(mg)

Ok let's take β below water, but that's not correct. For example, you are told that if the block is fully submerged, then the buoyant force is 50N.

Turn the hint I gave before into an equation. If a fraction β is below water, then

Buoyant force = kβ

Now you know that the buoyant force is 50N when β = 1. Put these into the equation to find k.

Ok, so:
F_b = F_g
β(50) = 30
β = 3/5
so 3/5 is below the water; this means 2/5 is above.
Is this reasoning sound?

Yep, that's correct.

Thanks, so in general on these types of problems, keep in mind that:
The buoyancy force is directly proportional to the fraction below the water, given it is of uniform density.
Right?

The block doesn't have to be of uniform density though. The buoyant force is simply the weight of the displaced water, which is proportional to the volume of the block below water.

## 1. What is the equation F = MA used for?

The equation F = MA, also known as Newton's second law of motion, is used to calculate the force (F) applied to an object based on its mass (M) and acceleration (A).

## 2. How is the equation F = MA related to the 2011 Exam # 8 question?

The 2011 Exam # 8 question involves finding the fraction of an object that is above the surface of water, which requires the use of the F = MA equation to calculate the force of buoyancy on the object.

## 3. What is the significance of the fraction of an object above the surface of water?

The fraction of an object above the surface of water is important in determining the buoyant force on the object and whether it will float or sink in the water.

## 4. How is the F = MA equation applied to this question on the 2011 Exam # 8?

The F = MA equation is used to calculate the buoyant force (F) on the object, where the mass (M) is the mass of the water displaced by the object and the acceleration (A) is the acceleration due to gravity.

## 5. Are there any other factors that may affect the fraction of an object above the surface of water?

Yes, factors such as the density and shape of the object, the density of the water, and any additional forces acting on the object can also affect the fraction of the object above the surface of water.

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