How Can I Calculate the Weight and Compression of a Submerged Coffee Can?

[2112]

Math isn't a strong point of mine, and hope someone could give me a valid response to this.
I'm still working on underwater physics, and have two questions.
First, if I had a 34 oz coffee can that I want to submerge below water to a depth of 8 feet, how many pounds would it take to get the can down that far, the can is opened at the bottom trapping the air in while being submerged, part two would be at the depth of 8 foot, how can I determine the amount that the air is compressed within the can.
I would figure it out myself, but getting underwater in a pool in Ohio at the present time would be just abit to cold.

 

[berkeman]

You don't need a pool, you just need to use some math. No excuses. Show us your work, and we'd be happy to help you.

1st cut -- how much does 34 oz of water weigh? 2nd cut, how much does 34 oz of air compress at that depth? 3rd cut -- solve the problem.

 

[m2003]

Calculating the weight and compression of a submerged coffee can can be done using basic principles of physics and fluid mechanics. To determine the weight needed to submerge the can to a depth of 8 feet, you will need to use the equation W = ρVg, where W is the weight, ρ is the density of the fluid (in this case, water), V is the volume of the can, and g is the acceleration due to gravity (9.8 m/s^2). The volume of the can can be calculated using the formula for the volume of a cylinder, V = πr^2h, where r is the radius of the can and h is the height (or depth in this case) that the can will be submerged to. Once you have calculated the volume and density of the can, you can plug those values into the equation to determine the weight needed to submerge it to a depth of 8 feet.

To determine the amount that the air is compressed within the can at a depth of 8 feet, you will need to use the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature (in Kelvin). At sea level, the air pressure is approximately 14.7 psi, but at a depth of 8 feet, the pressure will increase due to the weight of the water above it. You can use the equation P2 = P1 + ρgh, where P2 is the pressure at a depth of 8 feet, P1 is the initial pressure at the surface, ρ is the density of water, g is the acceleration due to gravity, and h is the depth. Once you have calculated the pressure at a depth of 8 feet, you can use it in the ideal gas law equation to determine the new volume of the air inside the can. The difference between the initial volume and the new volume will give you the amount of compression that has occurred.

I hope this explanation helps you understand how to calculate the weight and compression of a submerged coffee can. Keep in mind that these calculations are based on ideal conditions and may vary slightly in real-world situations.