# A solid cylinder of uniform density of 0.85 g/cm3 floats in

• Spartan73
In summary, X, the height of the upper surface of a solid cylinder floating in a glass of water, will be affected by the following changes to the initial system: 1. Replacing the cylinder with one of the same height and diameter but with a density of 0.83 g/cm3 2. Removing some of the water from the glass 3. Pouring a liquid with a density of 1.06 g/cm3 into the glass 4. Replacing the cylinder with one of the same density and height, but 1.5 times the diameter 5. Replacing the cylinder with one of the same density and diameter, but half the height 6. Pouring a liquid with a density of
Spartan73

## Homework Statement

A solid cylinder of uniform density of 0.85 g/cm3 floats in a glass of water tinted light blue by food coloring.
https://s1.lite.msu.edu/res/msu/kashy/physicsLib02/32_Fluids1_Pascal_Arch/graphics/archimedes.gif
Its circular surfaces are horizontal. What effect will the following changes, each made to the initial system, have on X, the height of the upper surface above the water? The liquids added do not mix with the water, and the cylinder never hits the bottom. The cylinder is replaced with one that has the same height and diameter, but with density of 0.83 g/cm3.
Some of the water is removed from the glass.
A liquid with a density of 1.06 g/cm3 is poured into the glass.
The cylinder is replaced with one that has the same density and height, but 1.5× the diameter.
The cylinder is replaced with one that has the same density and diameter, but with half the height.
A liquid with a density of 0.76 g/cm3 is poured into the glass.

## The Attempt at a Solution

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Spartan73 said:
solid cylinder of uniform density of 0.85 g/cm3 floats in a glass of water tinted light blue by food coloring.

try to work out and show on template so that we can contribute

Spartan73 said:

## Homework Statement

A solid cylinder of uniform density of 0.85 g/cm3 floats in a glass of water tinted light blue by food coloring.
https://s1.lite.msu.edu/res/msu/kashy/physicsLib02/32_Fluids1_Pascal_Arch/graphics/archimedes.gif
Its circular surfaces are horizontal. What effect will the following changes, each made to the initial system, have on X, the height of the upper surface above the water? The liquids added do not mix with the water, and the cylinder never hits the bottom. The cylinder is replaced with one that has the same height and diameter, but with density of 0.83 g/cm3.
Some of the water is removed from the glass.
A liquid with a density of 1.06 g/cm3 is poured into the glass.
The cylinder is replaced with one that has the same density and height, but 1.5× the diameter.
The cylinder is replaced with one that has the same density and diameter, but with half the height.
A liquid with a density of 0.76 g/cm3 is poured into the glass.

## The Attempt at a Solution

I
N
I
N
N
D[/B]
For the third one, draw a diagram showing the two liquids and the cylinder.
For the fifth one, please explain your reason for saying no change.
For the last one, note that X is defined as the height of the top of the cylinder above the water.

## 1. What causes the cylinder to float?

The upward force of buoyancy, which is equal to the weight of the displaced fluid, causes the cylinder to float.

## 2. How does the density of the cylinder affect its buoyancy?

The density of the cylinder plays a crucial role in determining its buoyancy. If the density of the cylinder is less than that of the fluid it is placed in, it will float. If the density of the cylinder is greater than that of the fluid, it will sink.

## 3. Does the shape of the cylinder affect its buoyancy?

Yes, the shape of the cylinder does affect its buoyancy. A cylinder with a larger cross-sectional area will displace more fluid and therefore have a greater buoyant force. A longer cylinder will also displace more fluid and have a greater buoyant force.

## 4. Can the cylinder float in any type of fluid?

No, the cylinder can only float in a fluid that has a lower density than the cylinder. If the fluid has a higher density, the cylinder will sink.

## 5. What happens if the cylinder is pushed under the surface of the fluid?

If the cylinder is pushed under the surface of the fluid, it will experience a greater force of buoyancy due to the increased amount of fluid it is displacing. This will cause the cylinder to rise back up to the surface.

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