Behold a "hydro-car." You might see its like in the next James Bond movie; this real-life model could be useful for navigating urban waterways or during heavy flooding. Obviously, to propel your car through the water there must be some sort of propeller hidden under the chassis, but a more immediate and basic requirement is that your car must be able to float.
Now, we expect that your run-of-the-mill Toyota or Chevrolet is going to sink when flung into a body of water. But why is this? Is it because the car is too heavy, because it isn't watertight, both, or neither? Let's do a quick calculation based on Archimedes' principle to gain some insight into this important issue. Archimedes' famous principle states that the buoyant force acting on an object is equal to the weight of the volume of fluid displaced. For a floating object, the upward buoyant force must balance the downward force of the object's weight. So, is a normal car buoyant enough to float? Let's see...
First some approximations: We'll model the body of the car as rectangular, with the following dimensions: length 12 feet, width 5 feet, height (up to the bottom of the windows and ignoring the tires) 2 feet. This gives us a volume of 120 ft3 or 3.4 m3. We'll also assume that we don't want the water to get up to the level of the windows. To be safe, let's require that the car must float with a maximum of 50 percent (1.7 m3) of the body submerged.
If you think about it, you'll realize that the volume of the submerged part of the car is exactly equal to the volume of water it displaces. We can calculate the weight of that displaced water:
W = mg = DVg
m is the mass of the displaced water which is equal to its density
D (1000 kg/m3), multiplied by its volume
V (1.7 m3).
G is the acceleration due to gravity (9.8 m/s2). Plugging in the numbers we get W ≈ 16,700 N (or 3800 lb.). This is the buoyant force acting on the half-submerged floating car, and must be equal to its weight.
What does this tell us? 3800 pounds is pretty heavy for a car, especially one with the compact dimensions quoted above. So, according to our calculations, most normal cars should really float quite easily. If it weren't for those darn leaky doors!
Adam Weiner is the author of Don't Try This at Home! The Physics of Hollywood Movies.