A 1,200Kg crate is sunk in the harbor and sits on the bottom a depth of 30m. The

Question

A 1,200Kg crate is sunk in the harbor and sits on the bottom a depth of 30m. The crate is square and measures 3m on each side. A plan to raise the boat using ping pong balls has been put in place. The boat is sealed so that the ping pong balls can be added to the boat and will remain in the boat displacing enough water to raise it to the surface. An average ping pong ball is 4 cm in diameter. Ping Pong balls have a typical mass of 2.7g and 0.2% of them are poorly made and will take on water. How many will you need? Can you fit than many in the crate?

Explanation / Answer

according to archimedes principle or acc. to buoyant force:

buoyant force - W( weight of water displaced) = mass of ball * g * n

where n = no. of balls

Density *volume *g - density of water * volume * g = m *g*n

mass of crate - 1 * (3*3*30) = 0.0027 * n : because ( volume displaced = 3*3*30)

1200 - 270 = 0.0027 * n

n = 3.44 * 10 ^5 balls

and 0.2 % of 'n' are poor balls

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