Fluid Question and density tension etc.

[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

 

[Hunterbender]

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.

 

[thomate1]

...

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^