Buouyancy force and Archimedes' principle

In summary: As you wrote in your first post, balance of forces must be fulfilled after loading the fish. The additional weight of the fish must be compensated by additional displaced water. Just equal the mass of the loaded fish (##\rho_FV_F##) and the mass of the displaced water (##\rho_WV_W##); the gravitational acceleration(s) ##g## cancels each other on both sides of the equation. You stick with one unknown (##V_W##) for which you have one equation to solve for it.
  • #1
lin1430
3
0
How much more will the volume of a fishingboat go under water, if I load the boat with 3.0m^3 fish with the density 0.90kg/dm^3?

Fish : 3.0m^3
Density of fish: 0.90kg/dm^3?

Homework Equations



Archimedes principle: density * volume * g[/B]

The Attempt at a Solution



Tried setting upward force = downwards force (mg)

substituting m for ro*V[/B]

changing V to A*h, then finding h. But it is obviously wrong.
 
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  • #2
Ahoihoi @physicsforum!

Unfortunately it's not possible to comprehend your attempt to solve the problem. Please try to write down all of your steps, explaining your used symbols.

The principle of Archimedes states that the buoyancy force acting on a body corresponds to the weight (force) of the displaced fluid. My first guess, after reading your post, would be that you mixed up the density of the water and the fish...
 
  • #3
This was my attempt
 

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  • #4
lin1430 said:
This was my attempt

I think it would be easier to calculate the additionally displaced volume of water, when the fish is loaded on the boat. You can calculate that with the equation below your drawing, all you need is the values for the densities of fish and water and the volume of fisch you want to load. The data of the fish is provided as you wrote in your first post. Do you have any density given for the water? If not, I propose to use 1 kg/dm^3. But with these three values you are able to calculate the displaced volume by the weight of the fish. I don't know if this is already the demanded answer or if you have to calculate how much the boat will immerge (if the geometry of the boat is given).
 
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  • #5
stockzahn said:
I think it would be easier to calculate the additionally displaced volume of water, when the fish is loaded on the boat. You can calculate that with the equation below your drawing, all you need is the values for the densities of fish and water and the volume of fisch you want to load. The data of the fish is provided as you wrote in your first post. Do you have any density given for the water? If not, I propose to use 1 kg/dm^3. But with these three values you are able to calculate the displaced volume by the weight of the fish. I don't know if this is already the demanded answer or if you have to calculate how much the boat will immerge (if the geometry of the boat is given).

Sounds good. The density of water is to be 1kg/dm^3. I do not have to calculate how much the boat wil immerge, just how much additional change will happen. But how would I proceed to calculate the displaced volume by the equation under my drawing?
 
  • #6
lin1430 said:
Sounds good. The density of water is to be 1kg/dm^3. I do not have to calculate how much the boat wil immerge, just how much additional change will happen. But how would I proceed to calculate the displaced volume by the equation under my drawing?

As you wrote in your first post, balance of forces must be fulfilled after loading the fish. The additional weight of the fish must be compensated by additional displaced water. Just equal the mass of the loaded fish (##\rho_FV_F##) and the mass of the displaced water (##\rho_WV_W##); the gravitational acceleration(s) ##g## cancels each other on both sides of the equation. You stick with one unknown (##V_W##) for which you have one equation to solve for it.
 

Related to Buouyancy force and Archimedes' principle

1. What is buoyancy force?

Buoyancy force is the upward force exerted on an object immersed in a fluid, such as water or air. It is caused by the difference in pressure between the top and bottom of the object, with the higher pressure at the bottom pushing up on the object.

2. What is Archimedes' principle?

Archimedes' principle states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid that is displaced by the object. This means that the heavier the object, the more water it will displace and the greater the buoyant force will be.

3. How does the shape of an object affect its buoyancy?

The shape of an object can greatly affect its buoyancy. Objects that are more dense and compact, such as a rock, will sink in water because they displace a small amount of water. On the other hand, objects that are less dense and have a larger surface area, such as a boat, will float because they displace a greater amount of water.

4. Can the buoyancy force be greater than the weight of an object?

Yes, the buoyancy force can be greater than the weight of an object if the object is less dense than the fluid it is immersed in. In this case, the object will float on the surface of the fluid because the upward buoyant force is greater than the downward force of its weight.

5. How is buoyancy force used in everyday life?

Buoyancy force is used in a variety of ways in everyday life. It is essential for objects to float in water, such as ships and boats. It is also used in swimming and scuba diving equipment to help the user stay afloat. Additionally, it is utilized in hot air balloons and blimps to provide lift and allow them to fly.

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