# Fluid Question and density tension etc.

• amaris
In summary, the conversation discusses various problems related to density, mass, and pressure. The first question involves determining the maximum mass that can hang from a Styrofoam sphere without sinking in water, while the second question is about the percentage difference in air pressure between the top and bottom of a gym. The third question involves finding the mass density of a floating cylinder, and the fourth question involves calculating the tension in a string holding a partially submerged rock. The individual has attempted to solve these problems but has encountered difficulties and is seeking urgent help.
amaris
1)Styrofoam has a density of 300kg/m^3. What is the maximum mass that can hang without sinking from a 40.0 cm-diameter Styrofoam sphere in water?

Found density of styrofoam per cm^3...then got lost

2)A gym is 14.0m high, what is the percentage difference between air pressure at the top of the gym and on the ground of the gym?

no clue whatsoever

3)A 6.00 cm-tall cylinder floats in water with its axis perpendicular to the surface. The length of the cylinder above water is 1.30 cm. What is the cylinder's mass density?

I took the height of the cylinder that was submerged and divided it over the total height to find the volume that was submerged then multiplied that by the density of water -.-

4)2.60 kg rock whose density is 4100 kg/m^3 is suspended by a string such that half of the rock's volume is under water. What is the tension in the string?

somehow or another I arrived at the answer of 25.5, not quite sure how but either way it was wrong.

I know it sounds like you're doing my entire hmwk assignment, but this is merely less than half of what I've done already. :(

need desperate urgent help...

edit: solved the first qn on my own

Last edited:
show that you try to solve the problem first

2. look at the psi difference. There is air in the room, so there must be pressure from that at the bottom of the room that doesn't exist at the top

3. Use bouancy force? maybe? Looks promising

4. same as 3.

...

Hello, it seems like you are struggling with some density and fluid mechanics problems. Let me try to help you understand these concepts better.

Firstly, density is defined as the mass per unit volume of a substance. In the case of Styrofoam, it has a density of 300kg/m^3, which means that for every cubic meter of Styrofoam, it has a mass of 300kg. To find the maximum mass that can hang from a Styrofoam sphere without sinking, we can use the equation: density = mass/volume. Since we know the density and the volume (given by the diameter of the sphere), we can rearrange the equation to solve for mass. So, the maximum mass that can hang from a 40.0 cm-diameter Styrofoam sphere would be 300kg/m^3 x (4/3)π(0.2m)^3 = 6.3kg.

Moving on to the second question, we need to understand the concept of air pressure. Air pressure is the force exerted by the weight of air above a certain point. The higher the altitude, the lower the air pressure because there is less air above that point. So, in this case, we can calculate the percentage difference between the air pressure at the top of the gym (14.0m) and on the ground (0m) using the equation: percentage difference = (higher value - lower value)/lower value x 100%. Therefore, the percentage difference between the air pressure at the top and ground of the gym would be (14.0m-0m)/0m x 100% = infinity. This is because there is no air pressure at 0m, so the percentage difference would be infinite.

Next, for the third question, we need to use the concept of buoyancy. A floating object displaces a volume of water equal to its own weight. So, in this case, the volume of the submerged part of the cylinder is equal to its weight. We can use the equation: density = mass/volume to find the density of the cylinder. The mass of the cylinder is equal to the weight of the submerged part, which can be calculated by multiplying the density of water (1000 kg/m^3) by the volume of the submerged part (6.00cm x 6.00cm x 1.30cm = 46.8cm^

## 1. What is fluid tension?

Fluid tension refers to the force that is exerted on the surface of a liquid due to the cohesive forces between the molecules of the liquid. It is responsible for the formation of droplets and the surface tension of liquids.

## 2. How is fluid density measured?

Fluid density is typically measured by using a hydrometer, which is a device that measures the specific gravity of a liquid. The specific gravity is the ratio of the density of the liquid to the density of water at a specific temperature.

## 3. How does fluid pressure change with depth?

Fluid pressure increases with depth due to the weight of the fluid above pushing down. This is known as hydrostatic pressure and is described by the equation P = ρgh, where P is the pressure, ρ is the fluid density, g is the acceleration due to gravity, and h is the depth.

## 4. What is the difference between a liquid and a gas?

The main difference between a liquid and a gas is the strength of the intermolecular forces between the molecules. In a liquid, the molecules are close together and have strong cohesive forces, whereas in a gas, the molecules are farther apart and have weaker forces. This results in different physical properties such as density, compressibility, and viscosity.

## 5. How does the shape of a container affect fluid behavior?

The shape of a container can affect the behavior of a fluid in several ways. For instance, a narrow container will cause the fluid to rise to a higher level due to capillary action. The shape can also affect the flow of the fluid, with wider containers allowing for faster flow than narrow ones. Additionally, the shape can also impact the pressure distribution within the fluid.

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