math in the news: issue 53
TRANSCRIPT
Why the Titanic Sank
The Titanic was a British ship that set sail on April 10, 1912. It made two stops before heading toward New York. It never made it there. It sank on April 15 after hitting an ice berg.
What happened to the Titanic?Click on this video to see the sequence of events that led to
the sinking of the Titanic. http://youtu.be/qCv1jKHfFiY
Where is the Titanic now?Click on this video to see footage of
the wreck of the Titanic.http://youtu.be/6Z7REEnwKOQ
Why the Titanic Sank
To get a sense of how massive the Titanic was, this illustration gives an idea of the scale of the ship.
Why the Titanic Sank
The key to sailing a ship of this size is to make sure the density of the ship is such that it will float on water. Density is defined as the ratio of mass to volume.
Why the Titanic Sank
The density of water is defined as 1. So in order for the Titanic to float, it needed a density less than 1.
Why the Titanic Sank
To simplify the calculation of density, let’s assume that the bulk of the ship is in the shape of a triangular prism, as shown here.
Why the Titanic Sank
The net on the left shows the three dimensions used to calculate the volume of a triangular prism.
Why the Titanic Sank
The length, width, and height measurements are those of the Titanic. The mass of the ship was 46,000 tons.
Why the Titanic Sank
The measurements provided yield a density of 0.41 for the Titanic, well below the density needed to float. This also means that the Titanic could still take on water before sinking.
Why the Titanic Sank
Once the Titanic started taking on water, its mass would increase while its volume decreased. This is shown in the expression above. Losing volume and gaining mass is a deadly combination that will lead to a ship sinking.
Why the Titanic Sank
We can graph the function representing the changing density to see where it intersects the graph y = 1. This is the point where the ship has taken on too much water, making its density greater than 1.
Why the Titanic Sank
Once the ship gained about 40% more mass in water, then the ship had too much density to float. One of the features that was intended to prevent too much water was the set of 16 water-tight sections of the ship.
Why the Titanic Sank
However, when the Titanic struck the ice berg, five (possibly six) compartments were damaged. This would have allowed enough water to sink the Titanic.
Or would it?Click on this video to see what additional problems emerged
with these water-tight compartments.
http://youtu.be/xZ8Olj0xs4Q
Why the Titanic Sank
Do you think if the 16 compartments had been fully water tight that the Titanic might have stayed afloat long enough for the passengers to be rescued?