Beaker of water and bouyancy in a sink

• Physics197
In summary, the conversation discusses an experiment where a beaker is placed in a sink and its behavior when filled with water. By observing that the beaker floats when less than half full and sinks when more than half full, the density of the material of the beaker can be determined. Using the equations Fb = pVg and P2 = P1 + Pgh, the weight of the beaker can be calculated and compared to the weight of the displaced water. By finding the difference between the two, the volume of the beaker can be determined and used to calculate its density. The density was found to be just under 1400 kg/m^3.
Physics197

Homework Statement

You place a glass beaker, partially filled with water, in a sink. The
beaker has a mass of 517 g and an interior volume of 280 cm3. You now start to fill the sink with water and find, by experiment, that if the beaker is less than half full, it will float; but
if it is more than half full, it remains at the bottom of the sink as the water rises to its brim. What is the density of the material of which the beaker is made?

Fb = pVg
P2 = P1 + Pgh

The Attempt at a Solution

We know that the beaker just floats when it is half full.
In this case the volume of water in it is half 280 = 140 cm3
Given the density of water you can calculate the mass of water now in the half-full beaker.
If you add the mass of water to the mass of the beaker now, you get the total mass (and hence weight) that is just supported by the upthrust of the water.
The volume of water that is supporting the beaker is equal to the external volume of the beaker. This means you can calculate the external volume.(Archimedes)
The difference between the two volumes is the volume of the glass.
You know the mass of the glass so you can find its density.

Thanks, that's what I needed, just an explanation.

In short, is the weight of an object that is floating always going to equal the weight of the displaced water which equals density of the water * volume displaced * gravity?

It just seemed like we blew through this topic in class.

And if you have worked this out did you get just under 1400 kg/m^3 for the density?

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1. How does the buoyancy of a beaker of water in a sink work?

The buoyancy of a beaker of water in a sink is based on Archimedes' Principle, which states that the upward buoyant force on an object in a fluid is equal to the weight of the fluid that the object displaces. When the beaker is placed in the sink, the water in the sink pushes back against the beaker, creating an upward force that counteracts the weight of the beaker and its contents. This allows the beaker to float in the water.

2. What factors affect the buoyancy of a beaker of water in a sink?

The buoyancy of a beaker of water in a sink is affected by several factors, including the density of the water, the volume of the beaker, and the weight of the beaker and its contents. The more dense the water, the greater the buoyant force. Similarly, a larger beaker will displace more water and experience a greater buoyant force. Lastly, the weight of the beaker and its contents can also impact the buoyancy.

3. How does the shape of the beaker affect its buoyancy in a sink?

The shape of the beaker can impact its buoyancy in a sink. A beaker with a wider base will have a larger surface area in contact with the water, creating a greater upward buoyant force. On the other hand, a beaker with a narrower base will have a smaller surface area and experience less buoyant force. Additionally, the shape of the beaker can also affect its stability in the water.

4. Can the temperature of the water in the sink affect the buoyancy of the beaker?

Yes, the temperature of the water in the sink can affect the buoyancy of the beaker. As the temperature of the water increases, its density decreases, resulting in a decrease in the buoyant force acting on the beaker. This means that the beaker will sink deeper into the water. Similarly, colder water will have a higher density and create a greater buoyant force, causing the beaker to float higher in the water.

5. How is the concept of displacement related to the buoyancy of a beaker of water in a sink?

The concept of displacement is crucial to understanding the buoyancy of a beaker of water in a sink. When the beaker is placed in the water, it displaces a certain volume of water equal to its own volume. This displaced water creates an upward force on the beaker, allowing it to float. This principle also applies to objects with irregular shapes, as they still displace a volume of water equal to their own volume, resulting in a buoyant force.

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