- Practice: A rectangular boat has a width of 5 cm, a length of 8 cm, and a mass of 150 g. How far will the boat sink into liquid with a density of 1.2 g/mL? Check your answer.

the boat will sink 3.125 cm

Explanation:

According to Archimedes principle of buoyance, the buoyant force exerted on the part of the boat immersed in the liquid must  be equal to the weight of the fluid that was displaced. And if the boat is floating, the boat's weight must equal that buoyance force:

Weight boat = Weight of liquid displaced

boat's mass x g = mass of liquid displaced x g

simplifying "g":

boat's mass = mass of liquid displaced

In the case of the boat, its mass = 150 gr, and the volume of its submerged part is: 5 cm x 8 cm x h  With "h" the unknown we need to find (amount the boat sunk into the liquid).

Then:

boat's mass = 150 grams

Recall that density = Mass/Volume  -->  mass = Volume x density

mass of liquid displaced = volume x density = 5x8xh cm^3 x 1.2 g/mL

Recall as well that 1 mL = 1 cm^3 therefore:

mass of liquid displaced = 40 h x 1.2 grams = 48 h grams

solving for "h" (which will come in cm):

150 = 48 h

then h = 150/48 = 3.125 cm