Buoyancy,volume of air inside barrel

In summary, the conversation discusses using a device to blow air into a plastic barrel in order to raise an anchor from the seabed. The force balance equation includes gravitational and buoyant forces and assumes that the mass of the barrel is negligible. The reasoning behind displacing water inside the barrel using Archimede's principle is also mentioned.
  • #1
Kqwert
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3

Homework Statement


We are using a device(as shown in the image) to blow air into a 200L plastic barrel. We want to know how much air (volume) that is needed to raise the anchor from the seabed.
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Homework Equations

The Attempt at a Solution


The anchor will start moving upwards when the sum of forces on it is zero. We have gravitational and buoyant forces. We need to "displace" an unknown amount of water inside the barrel by pumping air into the barrel, corresponding to V,air.

My force balance:
rho, water * g * V,anchor + rho, water*g*V,air - m,anchor*g - m, barrel*g = 0

The solution manual does not include the last term, i.e. m, barrel*g. I guess this is only possible because m, barrel is assumed very small compared to the anchor? Also: Is my reasoning regarding "displacing" an unknown amount of water inside the barrel correct, using Archimede´s principle?
 

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  • #2
If the mass of the barrel is not given, then you must assume that it is negligible. Your reasoning is correct.
 

1. How does the volume of air inside a barrel affect buoyancy?

The volume of air inside a barrel affects buoyancy by displacing water. As more air is added to the barrel, the volume of water that can be displaced increases, thus increasing the buoyant force. This is the principle behind how submarines and other watercraft can float.

2. Does the shape of the barrel affect buoyancy?

Yes, the shape of the barrel can affect buoyancy. A wider and shorter barrel will have a larger surface area and therefore displace more water, leading to greater buoyancy. A taller and narrower barrel, on the other hand, will have less surface area and therefore less buoyancy.

3. How does the density of the air inside the barrel factor into buoyancy?

The density of the air inside the barrel affects buoyancy because denser air will displace more water and therefore have a greater buoyant force. This is why helium, which is less dense than air, is used in balloons to make them float.

4. Can the volume of air inside a barrel change?

Yes, the volume of air inside a barrel can change. It can increase if more air is pumped in, or decrease if air is released. This change in volume will directly affect the buoyancy of the barrel.

5. How can the volume of air inside a barrel be measured?

The volume of air inside a barrel can be measured using a variety of methods, such as displacement by water, pressure sensors, or gas laws. The most common method is to use a graduated cylinder filled with water and submerge the barrel in it, measuring the amount of water that is displaced.

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