Alright, physics time!
TL; DR As force of gravity is larger than that of buoyancy; Leo and Kate will be swimming with the fishes.
We can build a system of two forces. That produced by the force of gravity from the combined weights of Kate, Leo, and the door; and that of buoyancy.
1. Force of Buoyancy
Force of Buoyancy is (density)(volume)(acceleration of gravity)
We need to find the maximum force of buoyancy possible from the displacement of water of the plank/door. Lets assume the plank/door is approx. 2m x 0.75m x 0.06m
Yes, I'm saying the door is 6cm thick. Remember, this is the Titanic we are talking about, and I'm sure the doors would have been of the more.....grand variety. I realise the door isn't a perfect cuboid, but this is the movies. Who cares.
Density of water at 273K is approx 1000 kg * m-3 Acceleration of gravity at sea level is 9.81 m * s-2 Volume of the door is 2m * 0.75m * 0.06m = 0.09 m3
Substitute these values back into the original buoyancy formula:
(1000) * (9.81) * (0.09) = 882.9N <---- The maximum force that can be produced through buoyancy.
2. Force of Gravity
Lets assume Kate weighed 130lbs at the time (source: http://www.celebheights.com/s/Kate-Winslet-109.html). As for Leo? Obviously his weight will fluctuate due to his roles as an actor, but lets estimate that during Titanic he was 160lbs. (source: http://wiki.answers.com/Q/What_is_Le...ght_and_weight).
130lbs = 58.9kg 160lbs = 72.6kg
The mass of the door? Using the same dimensions from above, mass is density * volume. Lets take the estimate of 45lb/ft3 that jpesh1 used. This is about 720.8kg * m-3.
Therefore, the mass of the door is (720.8) * (0.09) = 64.9kg. Pretty reasonable mass for a door.
Now we have all our masses, we can combine them, multiply by the force of gravity, and then get a resulting force in newtons.
(64.9 + 58.9 +72.6)(9.81) = 1926.684N
3. Verdict
882.9N < 1926.684N
Force of buoyancy is less than Force of gravity. The two will sink.
Just sayin'
Also, I've no issue with anything that JKs done so far.
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