Somebody has to do it...
Let's assume that the door is about 7ft x 3ft x 2in. This would be approximately equivalent to 2.13m x 0.91m x 0.05m. V=2.13*0.91*0.025=0.1 m^3.
The density of water can be approximated to 1000 kg/m^3 although it would be slightly less given that the temperature of the water was around 0C.
We have to look up the density of different types of wood used on the Titanic.
Oak: 0.6-0.9 (* 10^3 kg/m^3)
Teak:0.6-0.9 (* 10^3 kg/m^3)
Maple 0.6-0.75 (* 10^3 kg/m^3)
We'll give Rose the benefit of the doubt and say that the density of the wood is at its minimum possible value (assuming that the door was solid) at 600 kg/m^3.
With this info we get the mass of the door to be more like 28kg (61 lbs) which seems more plausible than 10kg, but if you go through the calculations with 10kg, you can see that this difference doesn't really matter.
We then ask, "At what additional weight would the door no longer stay afloat?" This would be when the buoyant force equals the force of gravity on the door and whatever weight is on it. Instead of doing all those calculations, we can make a simple equality: (the mass of the door + maximum additional mass)/(volume of the door) = density of water. (28+M)/0.1=1000. M = 72 kg. This would be enough to hold up either Jack (70 kg) or Rose (50 kg) alone but not both (120 kg). Thus, all Jack can do is hold on to the edge with the majority of his body submerged. Body heat is lost 25 times faster in cold water than in cold air as poor Jack found out.
http://www.youtube.com/watch?v=pXvlKYcdSc0#t=0m51s