What is the Apparent Weight of an Iron Block Submerged in Water?

In summary, the density of iron is 8 times larger than the density of water. An iron block with a weight of 800 N is weighed in air and when completely submerged in water, it has an apparent weight of 700 N. To determine this, the formula for apparent weight and buoyant force were used. The block's mass, volume, and buoyant force were calculated based on its weight, and the density of iron and water.
  • #1
Aoiumi
23
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Homework Statement


The density of iron is 8 times larger than the density of water. An iron block has weight 800 N when it is weighed in air. When the block is weighed when completely submerged in water, the apparent weight is...
The answer is 700 N but I don't know how this is determined.

Homework Equations


Apparent weight is equal to mg minus Fb
Fb = ρfgVf


The Attempt at a Solution


Apparent weight = 800N - Fb
Fb = x(9.8)Vf
Density of iron is 8x
 
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  • #2
Aoiumi said:

Homework Statement


The density of iron is 8 times larger than the density of water. An iron block has weight 800 N when it is weighed in air. When the block is weighed when completely submerged in water, the apparent weight is...
The answer is 700 N but I don't know how this is determined.

Homework Equations


Apparent weight is equal to mg minus Fb
Fb = ρfgVf

The Attempt at a Solution


Apparent weight = 800N - Fb
Fb = x(9.8)Vf
Density of iron is 8x
If the block has a weight of 800 N, what is its mass? From this result, if its density is ρB, what is its volume? If it is totally submerged in water, with this volume, what is the buoyant force on the block (given that the density of water is 1/8 of ρB)?
 
  • #3
800N = m (9.8 m/s^2)
m = 81.6 kg

If Density of iron: ρ = m/v
ρ = 81.6 / v

How do I express ρ?
 
  • #4
Water is more dense than air, so it will push the block up. It will seems the block will weigh less. But I think that how deep the block is in the water matters too. It's apparent weight will be different in the bottom of a pool and in the bottom of the ocean. I'm not really sure though
 
  • #5
You don't need to find the mass explicitly.
You wrote a formula for Fb.
Write a similar one for the weight of the block (W).
And compare the two. You know W. You can easily find Fb and then the apparent weight.
 
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  • #6
Aoiumi said:
800N = m (9.8 m/s^2)
m = 81.6 kg

If Density of iron: ρ = m/v
ρ = 81.6 / v

How do I express ρ?
You just leave it algebraic. v = 81.6/ρB
This is the volume of the block, so the buoyant force exerted by the water on the block is:
[tex]F=9.8 ρ_Wv=(81.6)(9.8)\frac{ρ_W}{ρ_B}=800\frac{ρ_W}{ρ_B}[/tex]
Does that make sense?
 
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  • #7
That makes sense. Thank you!
 

FAQ: What is the Apparent Weight of an Iron Block Submerged in Water?

What is density and how is it calculated?

Density is a measure of how much mass is contained in a given volume of a substance. It is calculated by dividing the mass of the substance by its volume. The units of density are typically grams per cubic centimeter (g/cm3) in the metric system and grams per milliliter (g/mL) in the English system.

How does density affect the apparent weight of an object?

Density does not directly affect the weight of an object. However, the apparent weight of an object may change in different environments due to the effects of buoyancy. In a denser medium, an object will experience greater buoyant force, making it feel lighter. In a less dense medium, an object will feel heavier.

What is the relationship between density and buoyancy?

Density and buoyancy are inversely related. The more dense an object is, the less buoyant force it will experience in a fluid. This is because the object displaces a smaller volume of fluid compared to a less dense object of the same size and shape. This is why objects made of denser materials, such as iron, sink in water while less dense objects, like wood, float.

How does temperature affect the density of a substance?

Temperature does affect the density of a substance. In general, as the temperature increases, the density of a substance decreases. This is because as the temperature increases, the particles of the substance gain more energy and move farther apart, taking up more space and decreasing the density. However, there are some exceptions, such as water, which has its highest density at 4 degrees Celsius.

How is density used in real-world applications?

Density is an important concept used in many real-world applications. For example, it is used in the construction of buildings and bridges to determine the strength and stability of materials. It is also used in the production of various products, such as food and cosmetics, to ensure the correct amount of ingredients are used. Additionally, density is used in the study of weather and oceanography to understand the movement of air and water masses.

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