Image credit: Paramount Pictures
You know, this scene:
MythBusters did this song and dance a couple years ago, kind of. Our two faves, Jamie and Adam attempted to get onto a door together and it didn’t work.
Let me show you why.
First, let’s figure out if they could have actually fit on the door in terms of surface area. Kate Winslet (Rose) is 5’7”. She’s somewhat curled up and not reaching the full extent of the door. Let’s call the door 6 feet in length, 3 and a half feet in width, and 4 inches in thickness. The total area of the door is therefore 21 square feet. Kate Winslet is probably at the most 1 foot wide if she lay on her side. Leonardo DiCaprio (Jack) is 6’0” and also 1 foot wide on his side.Her total area would then be 5.83 square feet and his total area would be 6 square feet. Their total area (if not overlapping) would be 11.83 square feet, which is less than 21. So, from a purely geometric analysis, they both could have fit on the door.
However, unlike Rose with the Heart of the Ocean,1Seriously though, why would she throw a precious jewel into the ocean when she could have willed it to her granddaughter? we’re not going to abandon this just yet.
Anyway, in any fluid mechanics problem with a solid body, the buoyant force needs to be taken into account. When a weight displaces a volume of water, such as a boat, the buoyant force pushes upwards on the body to counteract the downward force.
Let’s take just the door. The door has its own weight, but a door floats in water, so we know that buoyant force must be enough to overcome the door’s weight downwards.
Now we add Jack and Rose. The average weight for a female who is 5’7” is about 120-150 lbs. I would ballpark her at 130 lbs.
The average weight for a male who is 6’0” is anywhere from 160-200 lbs, but Jack is a skinny fellow so let’s call him 160. This door looks heavy as heck, let’s say 70 lbs. To get their respective forces, we multiply by gravity, 32.2 feet per seconds squared.
Rose and Jack’s weights are distributed over the entire door, but because their center of mass is in the middle of the door to keep it from tipping, we can take an equivalent weight in the middle of the door.
By Archimedes principle, the buoyant force on the door is equal to the weight of the volume of water displaced by the door. For them to be comfortable and not freeze from water lapping at them, I would say at least two inches of the door need to be above water, labeled depth in the below table.
According to Newton’s Second Law, the sum of the forces on an object is equal to mass times acceleration. We need to sum the forces on the door to understand which way it is moving.
Case 1: Just Rose
Sum of the forces = Buoyant force-Door’s weight-Rose’s weight
Sum of the forces = 7032.48-2254-4186 = 592.48 pounds force
The net force is positive. This means that the door will stay afloat.
Case 2: Jack and Rose
Sum of the forces = Buoyant force-Door’s weight-Rose’s weight-Jack’s weight
Sum of the forces = 7032.48-4186-3864-5152 = -6169.52 pounds force
The net force is negative. This means that the door will sink. So no, both of them would not have survived if they had shared the door. Why didn’t he find a different door? That’s a question for a psychology major.