Volume of water a ship must displace to float

In summary, the volume of water that a ship with a mass of 2.00x10^5 kg must displace to float is 200 m^3. This can be calculated using the equation Fb=pfVfg, where pf is the density of water and Vf is the volume of displaced water. By setting the buoyant force equal to the weight of the ship, we can solve for Vf and find that it is equal to 200 m^3. It is important to always check units when solving problems involving density and volume.
  • #1
chaotiiic
26
0

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
 
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  • #2
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: Fb=pfVfg
In your case, pf is the density of water, and Vf 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.
 
  • #3
Nessdude14 said:
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: Fb=pfVfg
In your case, pf is the density of water, and Vf 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
 
  • #4
chaotiiic said:
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.
 
  • #5
Nessdude14 said:
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
 

What is the volume of water a ship must displace to float?

The volume of water a ship must displace to float is equal to the weight of the ship divided by the density of water. This is known as the Archimedes' principle, which states that the upward buoyant force on an object in a fluid is equal to the weight of the fluid that the object displaces.

How is the volume of water a ship must displace calculated?

The volume of water a ship must displace can be calculated by measuring the weight of the ship and knowing the density of water. The density of water is typically 1 gram per cubic centimeter (g/cm3). Therefore, if a ship weighs 100,000 grams, it will displace 100,000 cubic centimeters (or 100 liters) of water.

Does the shape of the ship affect the volume of water it must displace?

Yes, the shape of the ship does affect the volume of water it must displace. A ship with a wider bottom will displace more water compared to a ship with a narrower bottom, even if they have the same weight. This is because the wider bottom creates more surface area, resulting in a greater displacement of water.

What happens if the volume of water a ship must displace is greater than its weight?

If the volume of water a ship must displace is greater than its weight, it will float. This is because the upward buoyant force will be greater than the downward force of gravity. The ship will continue to float until its weight equals the weight of the water it is displacing.

Can a ship sink if it displaces the correct volume of water?

Yes, a ship can still sink even if it displaces the correct volume of water. This can happen if the weight of the ship is not evenly distributed or if it encounters rough seas or strong currents. In these cases, the buoyant force may not be strong enough to keep the ship afloat, causing it to sink.

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