Very recently, I was scrolling on Facebook trying to procrastinate on some of the work I have to do this week. As I was scrolling through the endless stream of news, cat videos, fail videos, etc., I saw a post talking about whether Jack could have survived at the end of the Titanic and whether or not to condemn Rose as a cold-hearted person for not letting Jack join her on top of the floating door. Since we have recently covered the topic of buoyancy, I decided I should give a crack at it and see whether or not Jack could have survived.
In order to start this problem, we need to use the equation for the force of buoyancy:
Fb = Density (fluid) x Volume (fluid displaced) x g
We know that the acceleration due to gravity is 9.8 m/s^2. For the density of the fluid, or freezing ocean water in this case, we can estimate the density to be about 1070 kg/m^3 (https://www.windows2universe.org/earth/Water/density.html). The only thing missing is the volume of the ocean water displaced. For simplicity's sake, we will assume that the door on which Rose was just completely submerged. Thus, if we find the volume of door, we can use this in calculating our buoyancy force. The dimensions of the door can be estimated to be 2.00 m by 1.00 m by 0.125 m, giving a volume of 0.250 m^3 (http://physicsbuzz.physicscentral.com/2012/09/sorry-girls-titanic-doors-were-made-of.html). Now that we have this information, we can calculate the buoyancy force acting on the floating door:
Fb = 1070(0.250)(9.8) = ~2620 N
In order to determine whether both Rose and Jack could have gotten on the floating door and lived, we need to figure out the force of gravity acting against the buoyancy force. The force of gravity is given by
Fg = (m [door] + m [Rose] + m [Jack])g
By simply googling the weights of Kate Winslet and Leonardo DiCaprio, we can use 63 kg and 75 kg for the masses of Rose and Jack respectively. We now only need the mass of the door. One of the woods used to make the doors of the Titanic was oak, which has a density of 770 kg/m^3 (https://www.engineeringtoolbox.com/wood-density-d_40.html). By multiplying this density by the volume of the door, we find the mass of the door to be 192.5 kg. With this information in hand, we are ready to calculate the force of gravity, which is found to be:
Fg = (192.5+63+75)(9.8) = ~3240 N
We see that Fg > Fb if both Jack and Rose are on the door at the same time. This means that the door would have sank if both Jack and Rose were on it, ultimately meaning they would have died. To confirm that the door wouldn't sink with just Rose on it and confirm that the movie did not have bad physics (at least in this instance), we can calculate the force of gravity if it were just Rose on the door.
Fg = (192.5+63)(9.8) = ~2500 N
We see that Fg < Fb in the case where Rose is the only one on the door, confirming that she could be on top of the door without it sinking. Thus, despite the cries and calls of all those fans of Jack who claim he could have been saved, we see that there would have been no way for both Jack and Rose to be on top of the door without it sinking. One of them had to die in the end for the other to have a chance to survive.
Thanks for reading.