|Just let him up there, darn it!|
Photo courtesy of www.dailynewsdig.com
Buoyancy is the force that makes something float. It depends on the volume of the floating object and the density of the liquid in which it is floating. For something to remain above the water level, the bouncy force must be greater than the force of gravity pulling down on the object.
In the case of Rose, Jack and the door, the buoyancy force of the ice cold salt water pushing up on them must be greater than the force of their combined weight. The force pushing up depends on the volume of the object submerged and the density of the water in which it is floating. So lets see how that stacks up. Looking at the raft in stills from the movie and looking up Kate Winslet's height, we can estimate that the raft is about 6'x3'x5" and the density of ice cold salt water is 1000kg/m^3. Our heros would survive only if the top of the raft were at least at the water level. So let's assume the volume submerged is that of the full door, 0.254 m^3 (keeping it all in metric). Multiply this by the density of salt water and the pull of gravity and you find that the buoyant force is 2490N.
If the weight of Jack+Rose+door is greater than 2490N, they are all in hot water (or, I guess freezing cold water). Seeing as there was much controversy of Kate Winslet's weight, it was easy to find out that at the time of the movie she weighed 125lbs, or 549N. It was a little harder to track down Leo's weight, but he topped out at a whopping 161lbs or 715N.
Finding the weight of the door is a bit trickier. Weight is volume times density times the pull of gravity, but its not clear what the door is made of. There were three types of wood commonly used on the Titanic, teak, oak and pine with densities of 980kg/m^3, 770 kg/m^3 and 420 kg/m^3 respectively. If the door were teak, the weight would be 2,440N, oak would be 1,147N and pine tops out at 617N.
Teak would barely float on its own so Rose and Jack would be headed into an eternity of sappy music together. If the door were pine, the total force of Jack+Rose+Door would be 2,313N and all would have been well in the world of middle school girls across the globe. But darn you Mr. Cameron, pine was simply not good enough for your movie! The door was most likely oak which has a weight of 1,920N so adding the adorable couple would give a weight of 3,185N, just a little too heavy. Subtract Jack and you get a force of 2,470N, just light enough to float and allow Rose to go on and live a long and happy life as Jack's frozen body spent continued to bob in the ocean. Before he died in his melodramatic, tear-jerking manner, he made her make him a promise.
"You must do me this honor. Promise me you'll survive. That you won't give up, no matter what happens, no matter how hopeless. Promise me now, Rose, and never let go of that promise."
She wouldn't have had to make that promise if James Cameron had just used pine!
*Mathlete would like to note that she feels the movie would have been improved with teak doors and only rewatched the ending grudgingly in the name of science.