Calculate Distance Buoy Sinks w/ Man on Top

In summary, the conversation discusses the calculation of the additional distance a 810-kg cylindrical can buoy will sink when a 69.0-kg man stands on top of it in salt water. Two methods are considered, one involving the weight of the buoy and the man, and the other involving the man's weight being equal to the weight of a volume of water with the same radius as the buoy. The correct result is obtained when considering the slightly higher density of salt water compared to pure water.
  • #1
alexfloo
192
0

Homework Statement


A 810-kg cylindrical can buoy floats vertically in salt water. The diameter of the buoy is 0.900 m. Calculate the additional distance the buoy will sink when a 69.0-kg man stands on top.


Homework Equations


B = ρ{water}Vg


The Attempt at a Solution


I've tried this two ways:
1.) I set up B = Wgt of the buoy, with V = πr2L, and solved for L. Then I set up the same problem with the weight of the buoy plus that of the man and solved again, then subtracted.

2.) The man's weight is equal to the weight of some volume of water. If that water were arranged into a cylindrical formation with radius r = .45m, it would have some length L. This should be equal to the distance the buoy sinks.

A = πr2 = .6362
V = AL = .6362L
ρ(water)V = 636.2L = mass of water

636.2Lg = 69g
L = 69/636.2 = .1085

This is exactly the same result I got for the first same method (as I would expect) but it's apparently wrong. Even more confusing, the web-homework system advised me:

"Not quite. Check through your calculations; you may have made a rounding error or used the wrong number of significant figures."

While the numbers listed here are abbreviated, I did the work on my calculator and never actually rounded anything. Any ideas as to what I'm missing?
 
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  • #2
Haha okay, I've been staring at this for at least an hour but I just realized the buoy floats in SALT water. The density I used was just slightly to low.
 
  • #3
Salt water is slightly more dense than pure water. This may be contributing to the problem.

EDIT: Okay, you got there just ahead of my suggestion! Well done.
 

What is the purpose of calculating the distance a buoy sinks with a man on top?

The purpose of this calculation is to determine the buoyancy of the man on top of the buoy. This information can then be used to estimate the amount of weight the buoy can support and to ensure the safety of individuals using the buoy.

What factors affect the distance a buoy sinks with a man on top?

The distance a buoy sinks with a man on top is affected by several factors, including the weight of the man, the buoyancy of the buoy, and the density of the surrounding water.

How do you perform the calculation for the distance a buoy sinks with a man on top?

To calculate this distance, you will need to use the buoyancy formula, which takes into account the weight of the man, the buoyancy of the buoy, and the density of the water. You can then solve for the distance by rearranging the formula.

What units should be used to measure the weight, buoyancy, and density in this calculation?

The weight should be measured in newtons (N), the buoyancy in newtons (N), and the density in kilograms per cubic meter (kg/m^3). It is important to use consistent units throughout the calculation to ensure accurate results.

Are there any safety precautions to consider when performing this calculation?

Yes, it is important to ensure that the buoy and the man on top are both in a safe and stable position before taking any measurements. Additionally, proper safety equipment should be worn when working near bodies of water.

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