# A SHM problem of floating

## 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

AlephZero
Science Advisor
Homework Helper
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.

Initially, $$F_b=dAy_o$$ where $$y_o$$ is the intial depth of the ship. The depth of the ship when its pushed down by a length dy (or y) is $$y_o+dy (or y_o+y)$$