## To understand how do boats and ships float, we will first make one with the help of “Archimede´s principle”

Now, imagine we want to b**uild a boat that carries 5 people**, **each of this persons weight 100kg** (about 220 lbs), so, how can we make the boat?

So, Archimede’s principle sustains that, for the boat to be able to float, the weight of the boat should be equals to the buoyancy force exerted by the fluid

$Wboat+persons=Buoyancy$

Now, here is the tricky part, let us assume that the boat weights 200 kg. Wait what? Just like that?

No, this weight will change depending on the dimensions we are going to find and the material of whatever you are going to build the boat is going to weight

$Mboatpluspersons*g = ρfluid*g*Vsubmerged$

*If you want to know why does $Buoyancy= ρfluid*g*Vsubmerged**$ this is a result of newton’s law free body diagram analyzed within a (whatever the shape it has) plate, you can find this is Fluids mechanics from Cengel 7 ^{th} edition chapter 3 section 3-7 buoyancy and stability*

$(500kg + 200kg) * 9.81 m/s^2 = 1000 kg/m^3 * 9.81 m/s^2 *Vsub$

$Vsub=0.7m^3$

Now, here is the important part, you have to make sure that there is $0.7 m^3$ submerged in the water.

ions of the boat,

*Front view of the boat*

Making the deck bigger (part where people is standing), would make the boat heavier, and you would have to change the total weight of the boat by taking it into consideration in the your calculations

If the boat has a squared or something like a block shape, then the ship dimensions would be, the deck plus the the volume that should be submerged for it to be able to float

$Vsub=cube root of $0.7 m^3$ =$0.7^1/3$

$Vsub=0.8879×0.8879×0.8879$ m

What if I don’t want it to be so tall, if I reduce its height, then width and length should compensate in how much I am reducing its height to.

Let us say, that we want to reduce its height to one third.

$Vsub=0.8879 x0.8879*3 x0.8879/3$

$Vsub=0.8879×2.66×0.3 m$

Now, this will be the new dimensions of the submerged volume, now make sure to understand that these are not the dimensions of the boat, this is just the dimensions of the lower part of the boat that is going to be submerged, you can make the deck at will, you just have to remember that making it bigger will make the boat weight more and also remember that this boat is just **designed for 5 people that weight 100 kg.**