Question

Do the best you can with this one. Show all your work that reaches the answer. The third part is not too easy and for that you will have to think very carefully. A boat has a total mass, including the load in it, of 200,000 kg (roughly a weight of 220 tons in our weight units). The boat is shaped like a barge, with a length of 30 meters and a width of 15 meters. You may assume that the bottom of the boat is flat. (So, think of the boat having the shape of a rectangular cooking pan.) As with any boat, part of the hull is under water and the rest is above water. It floats. (a) What is the weight of the boat in Newtons? (b) What is the buoyant force supplied by the water (in Newtons)? (c) How far below the surface of the water is the bottom of the boat? (For this last part, remember that part of the hull of all boats is underwater, as part of any hull must be if it is to be able to displace water.)

Answer 1

PART A:

Mass of the boat m_b = 2000000 kg.

Acceleration due to gravity g = 9.8 m/s².

The weight of the boat

PART B:

After the boat is left in the water, the boat is suspended in the water so the effective force on the boat must be zero.

So the buoyant force is equal to the weight of the boat, i.e.

PART C:

We know that buoyant force is equal to the weight of the displaced liquid; or the mass of displaced liquid is equal to the mass of the body floating above it.

So, the mass of the water displaced

The density of the water

So, the volume of the water displaced

Now let us calculate the area of the bottom of the boat

So the height of the boat underwater can be given by

So the underwater height of the boat is 4.44 m.