The latest animated feature from Pixar, Up, is the studio’s first contribution to the current fashion for 3D movies. I’ve written about 3D technology in two previous columns (Journey to the Center of the Earth and Monsters vs. Aliens) so I will not go into that in this review.
Up tells the story of widower Carl Fredrickson as he journeys to the South American landmark Paradise Falls with an accidental companion, Russell, a young Wilderness Explorer. Russell appears on Carl's doorstep hoping to earn his "helping the elderly" badge, but ends up a reluctant companion when Mr. Fredrickson’s house takes flight under a vast collection of helium balloons. Their trip to Paradise Falls includes a violent storm, à la The Wizard of Oz, but the pair land safely in South America. Russell and Carl have a series of adventures and work together to save a rare bird from a maniacal adventurer/explorer, Charles Muntz.
Others with an interest in science and movies have calculated how many helium balloons it would really take to lift a small house and determined the roughly 30,000 shown falls far short. There is a significant oversight in these calculations, though, since the helium also has to bear the weight of the balloons as well as the house, but it is more interesting to me to use this film to talk about why a helium balloon floats in the first place.
Buoyancy is the net upward force on any object submerged in a fluid. Most of us are familiar with the fact that we feel lighter when we get in a swimming pool, ocean, or bathtub. Anyone who has tried to push a beach ball under water has felt the substantial upward (buoyant) force on the ball. The size of the buoyant force is a property of the volume of the object and the density of the fluid the object is in: it is equal to the weight of the fluid displaced by the submerged object. For example, a submerged 2-liter bottle would displace 2 liters of water, which weigh about 20 Newtons (N), so the buoyant force on that bottle would be 20 N in the upward direction. If you filled the same 2-liter bottle with sand, it would weigh a lot more than 20 N, and it would sink because the buoyant force would be less than the object’s weight. Fill the bottle with oil and it will weigh a bit less than 20 N, and it will float. Salt water is denser than fresh water, so objects that just barely float in salt water will sink in fresh water.
It might be a little strange to realize we are displacing a fluid (air) as we walk around on the surface of the Earth. Since the average 70 kg (700 N) person has a volume of only 0.07 cubic meter, and the density of the atmosphere is only 1.48 kg/m3, the buoyant force on the average person is only about 1 N, which isn’t enough to be noticeable. Helium balloons, on the other hand, are so light the buoyant force on them is greater than their weight, so they float in air. Another way to get a balloon to float is to heat the air inside it, which makes it less dense than the surrounding air, so the buoyant force is greater than the weight of the balloon and basket.
Now, given that Mr. Fredrickson’s house is floating essentially motionless in the air, the net force on it must be zero. That means that the balloons are pulling up on the house with the same size force as the Earth pulling down. In that situation, one person could move the house to the side relatively easily, but once the house got moving, a force would have to be applied to make it stop. I expect wind would be a real problem, since even a light breeze blowing on such a large surface (the house and balloons) would be enough to push the house along. This brings me to my main concern with the floating house.
Several times in the film, a substantial number of balloons are popped, with surprisingly little effect. This is a problem, when the forces up and down are delicately balanced: removing just a few balloons would reduce the upward force on the house, and since the weight of the house does not change, it would sink. Near the end of the film, Carl does take this into account when he removes most of the movable property in the house in order to get it off the ground again. This is a dramatic scene, with Carl making a break from his past by discarding possessions he has held on to so long. Unfortunately, for the physics of his floating house to work, he should have been tossing out a little at a time through the course of the movie.
As in other recent Pixar films (such as WALL-E, review here), a clear message of conservation and concern for the environment comes through in Up, and Carl’s wife Ellie is a strong (if absent) female character. Physics and physical science teachers can certainly use the floating house to discuss buoyancy and balanced vs. unbalanced forces.
Jacob Clark Blickenstaff is Assistant Professor of Physics and Assistant Director of the Center for Science and Mathematics Education at the University of Southern Mississippi. He can be reached at jacob.blickenstaff@usm.edu.
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