A common small boat for use in quiet streams and lakes has a flat bottom and is

Question

A common small boat for use in quiet streams and lakes has a flat bottom and is approximately rectangular in shape like the smaller ones in this photo. For fishing they would be about 5.4 m long, 1.3 meters across at the bottom, and have a hull mass of 215 kg (475 lb weight) if made of aluminum. Along a side they would have a depth of 0.5 meter from the upper edge to the bottom.

The density of water is 1 g/cm3, or 1000 kg/m3. Assuming the boat's hull cross-section is a rectangle and that its sides are straight when it is put into water and that it is only immersed 10 cm, what is the upward force of the water (the buoyant force) on the boat?

How far into the water will it sink unloaded at equilibrium?

What is the maximum load that could be put into the boat in addition to its own mass that it could still float without being swamped by water over the sides?

Please explain your answers.

Explanation / Answer

buoyant force = mass of water replaced by object * gravity

Volume of water replaced by boat = 5.4*1.3*0.1 = 0.702 m^3

mass of water = Volume*density = 0.702*1000 =702 kg

Buoyant force = 702*9.81 = 6886.62 N

b.)

upto 50 cm it will not sink

c.)total volume 0f water replaced *density = M

M = 5.4*1.3*0.5*1000 = 3510 Kg

so maximum load = 3510 - 215 = 3295 Kg

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