Y1

Large river boats and barges such as in the painting below share a similar construction with the the common small boat in the photos for use in quiet streams and lakes. They typically have a flat bottom and are approximately rectangular in shape as you can see. 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 might have a depth of 0.6 meter (about two feet) from the upper edge to the bottom, though the smallest ones are not that deep.

The density of water is 1 g/cm³, or 1000 kg/m³. Assume that the boat's hull cross-section is a rectangle and that its sides are straight to make a floating box. When it is put into water if it were immersed 15 cm, what would be the upward force of the water (the buoyant force) on the boat?

1. How far into the water will this boat sink, unloaded, at equilibrium?

2. 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 0.6 m sides?

Much bigger versions are used to transport heavy loads on rivers, as barges pushed by tugboats, and to transport equipment and personnel for landing on ocean shores or to provide aid under adverse conditions.

3. A typical river barge is 10 meters wide and 60 meters long, designed typically to handle 1400 "short tons". A short ton is 2000 pounds or 907 kg. With the on-going drought in the eastern continental US, barge traffic on the Mississippi River is stalled because the water depth is insufficient in some pools to accommodate a loaded barge. How deep should the water be, at a minimum?