FM Explorers recently discovered a sunken ship which they would like to raise. T

Question

FM

Explorers recently discovered a sunken ship which they would like to raise. This ship is approximately hemispherical m shape with a radius of 5 m and lies 30 m below the surface of incompressible fresh water. The mass is further estimated to be 250,000 kg. Also being engineers, the explorers decide to raise the ship by adding ping-pong balls to its interior until it floats to the surface. Each ping-pong ball is 2.5cm in diameter and filled with air. The outer shell of the ball can be neglected. What is the total downward force on the ship? Assume that the ship is a solid hemisphere in contact with the bottom. Answer hint: 23,000,000 N How much buoyancy force does a single ping-pong ball provide? Answer hint: 6.4 N How many ping-pong balls will be required to raise the ship? Is this plan reasonable? What would the total downward force on the ship be if it were not firmly attached to the ground such that water was in contact with the flat surface of the hemisphere? How many ping pong balls would be required for this case? Answer hint: 115,750 N

Explanation / Answer

a)

Volume of ship = 2/3*pi*r^3 = 2/3*3.14*5^3 = 261.67 m^3

Volume of water above the ship = 3.14*5^2*30 - 261.67 = 2093.33 m^3

Mass of water above the ship = density*volume = 1000*2093.33 = 2,093,330 kg

Total mass of ship + water above the ship = 250,000 + 2,093,330 = 2,343,330 kg

Total downward force = mg = 2,343,330 *9.81 = 22,988,100 N (approx. 23,000,000 N)

b)

Volume of ball = 4/3*3.14*2.5^3 = 65.417 cm^3

Buoyancy force = weight of displaced water = 1000*(65.417*10^-6)*9.81 = 0.64 N (The answer provided in hint seems to be off by a decimal.)

c)

22,988,100 = n*0.64

No. of balls needed, n = 35,918,907

No. of balls that be "fitted" in the ship = 261.67 / (65.417*10^-6) = 4,000,031

Since 35,918,907 > 4,000,031, plan is not feasible.

d)

Buoyancy force on ship = 1000*261.67*9.81 = 2,566,983 N

Total downward force = 250,000*9.81 - 2,566,983 = 114, 483 N

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