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A SHM problem of floating

  • Thread starter crossfacer
  • Start date
  • #1
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Homework Statement


There is a ship of mass M floating on a river. The upper portion of the ship has a uniform cross-sectional area A and the density of water is d. Now the ship is displaced a further depth y into the water and released.
What is the resultant force acting on the ship when it is displaced a further depth y into the water?

The Attempt at a Solution


d = m / v where m is the mass of water and v is volume of water being pushed by ship
m = d (A*y)
net F= Mg - mg
net F= g [ M - d (A*y) ]


The correct answer is F= - dgAy. Why isn't the weight of the ship taken into account?
Thank you so much!
 

Answers and Replies

  • #2
AlephZero
Science Advisor
Homework Helper
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The ship is floating on the river. So the buoyancy force for the part of the ship that was below the waterline when y = 0 equals its weight Mg.
 
  • #3
Initially, [tex]F_b=dAy_o[/tex] where [tex]y_o[/tex] is the intial depth of the ship. The depth of the ship when its pushed down by a length dy (or y) is [tex]y_o+dy (or y_o+y)[/tex]
 

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