A ship with a mass of 2.00x105 kg must displace 200 m3 of water to float. This conclusion is derived from the principle of buoyancy, which states that the buoyant force must equal the weight of the ship. The calculation utilizes the density of water, which is 1.00x103 kg/m3, and the formula for buoyant force, Fb = pfVg, where pf is the density of water, V is the volume of displaced water, and g is the acceleration due to gravity. The units of density must be consistent to ensure accurate results.
PREREQUISITESStudents studying physics, naval architects, marine engineers, and anyone interested in understanding the principles of buoyancy and ship design.
so is itNessdude14 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.
chaotiiic said:so is it
g*(2.00x10^5) = (1.00x10^3)*V*g
g cancels
V = 200,000/1000 = 200m^3
ok thanksNessdude14 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.