A boat floats with 25% of its volume under water. a. What is the boatâs density?

b. If the boat was made from 500 kg of metal, what is the volume of the boat? (Assume the air in the boat has negligible mass and density)

c. What mass of cargo will cause the boat to float 75% below the water?

(a) 250 kg/m^3

(b) 2 m^3

(c) 1000 kg

Explanation:

(a) Let V be the total volume of the boat.

Volume immersed = 25 % of total volume = 25 V / 100 = V / 4

Let the density of boat is d.

Density of water = 1000 kg/m^3

Use the principle of flotation

Buoyant force on the boat = weight of the boat

Volume immersed x density of water x g = Volume x density of boat x g

V / 4 x 1000 x g = V x d x g

d = 250 kg/m^3

(b)

mass = 500 kg

density = 250 kg/m^3

V = mass / density = m / d = 500 / 250 = 2 m^3

(c) Let the mass of cargo is m.

Volume immeresed = 75 % of total volume = 75 x 2 / 100 = 1.5 m^3

Buoyant force = weight of boat + weight of cargo

1.5 x 1000 x g = 500 g + m g

1500 = 500 + m

m = 1000 kg