Volume of water a ship must displace to float

[chaotiiic]

Homework Statement

What volume of water must a ship that masses 2.00x10^5 kg displace to float?

Homework Equations

density = mass/volume
density of water = 1.00x10^3

The Attempt at a Solution

200,000/1000 = 200 m^3
im guessing that in order to float you must displace your own volume. I've read other answer you have to displace your own mass

 

[Nessdude14]

Think of a free body diagram of a ship floating on water. There's a force from the weight of the ship, and since the ship isn't sinking or rising, the force of buoyancy from the water must equal that of the weight of the ship.
The equation for buoyant force is: F_b=p_fV_fg
In your case, p_f is the density of water, and V_f is the volume of water displaced by the ship (your unknown variable.)
Find the volume of displaced water which makes this buoyant force equal to the weight of the ship, and you're done. Hope this helps.

 

[chaotiiic]

Think of a free body diagram of a ship floating on water. There's a force from the weight of the ship, and since the ship isn't sinking or rising, the force of buoyancy from the water must equal that of the weight of the ship.
The equation for buoyant force is: F_b=p_fV_fg
In your case, p_f is the density of water, and V_f is the volume of water displaced by the ship (your unknown variable.)
Find the volume of displaced water which makes this buoyant force equal to the weight of the ship, and you're done. Hope this helps.

so is it
g*(2.00x10^5) = (1.00x10^3)*V*g
g cancels
V = 200,000/1000 = 200m^3

 

[Nessdude14]

so is it
g*(2.00x10^5) = (1.00x10^3)*V*g
g cancels
V = 200,000/1000 = 200m^3

Looks good. One thing you need to be sure of is your units on the water density. The density you used was in kg/m^3 which happens to be just what you needed for your problem to come to an answer of m^3. Always work through the units along with the numbers.

 

[chaotiiic]

Looks good. One thing you need to be sure of is your units on the water density. The density you used was in kg/m^3 which happens to be just what you needed for your problem to come to an answer of m^3. Always work through the units along with the numbers.

ok thanks