It is FROZEN everywhere!! Almost anyone today can say they have seen, know or heard of a little musical film phenomenon called Frozen. It was released by Walt Disney Pictures on November 23, 2013. It was directed by Chris Buck and Jennifer Lee and produced by Peter Del Vecho. Along with loveable characters, catchy musical numbers and wide popularity, Frozen has become the highest grossing animated film of all time. When making an animated feature, in order to grab an audience’s attention, there needs to be a good, solid story. Without a good story, the film will not be as memorable and an audience may quickly lose interest. In addition to the story, animators have to create believably in their characters and their environment. Physics is a huge contender in helping create these believable environments.
Based on the Hans Christian Andersen fairy tale The Snow Queen, Frozen tells the story of two sisters, Anna and Elsa of Arendelle. Elsa has supernatural powers that Anna is very fond of. After an accident, Anna’s memory is changed so that she will never remember her sister’s powers. After the tragic death of their parents, Elsa is forced to take over the thrown as queen. However, since neither Anna nor anyone knows of her supernatural powers, she is self conscious about being accepted. Her powers are later discovered and fearing for her life Elsa flees the kingdom, covering it in snow and ice. It is thanks to her sister Anna and a few other friendly characters that they are able to save the kingdom and give Elsa her confidence back. In this world of Frozen, creative modifications to physics are made to create a believable yet imaginative environment in which the characters exist.
Although this film is widely acclaimed, there are several instances where they laws of physics are changed or ignored. This is present through paths of action, nature elements in the environment, unrealistic falling and weather conditions. During Anna’s search for her sister, she meets a man by the name of Kristoff and his reindeer Sven. As they are headed towards the north mountain, they begin to get chased by wolves, causing them to be cornered at a cliff and they decide to jump.
According the Newton’s Law of Inertia, an object with moves with constant, uniform motion until acted on by an unbalanced force. In this sequence we see Anna, Kristoff and Sven getting ready to jump from a lower mountain cliff to the higher mountain cliff across from them.
Although Kristoff cuts the rope so Sven can push himself off. Both Sven and Anna make it to the next mountain while Kristoff barely makes it and is then pulled up; they all survive. However, if Newton’s Law of Inertia were present in this scene their path of action would have been closer to that of the sleigh. The sleigh in this scene is the unbalanced force. In addition to the gravitational pull they characters would have, this unbalanced force would have caused all three characters to actually “fall” in a more downward motion/path of action, rather than continue upwards. In addition, given the distance they need to travel, chances are neither character would have actually made it from one mountain top to the next; maybe get close but not exactly land on top of the next mountain.
In continuation with the Law of Inertia, there is what is called Inertia and Drag. In animation, drag is the effect that occurs when material such as hair or clothing, follows behind the rest of a character’s motion. Drag is affected by the inertia of an object, in this case the character. During the musical number “Let It Go” we see Elsa walking alone on a mountain. There is clear indication of some wind, as shown by the falling snow. Although it is not a strong force, it is present.
The focus in this scene is her cape and element of wind. When she sings “well now they know” she takes off her glove, throws it into the air and spins. Her cape, in this instance, does an almost 360 and after the glove exits the screen, the snow and the wind disappear. Now there is a sense that there is no additional force going against the character as she continues to walk. About twenty seconds later there is a sudden force of wind, causing her cape to drag and lift up behind her.
So the drag occurs first, by the character’s motion and second by the sudden force of wind. The drag in this scene is not consistent and is altered to fit the song. If the wind element was present throughout the entirety of the song, even if it built up gradually, her cape would have started to drag earlier and towards the end the would not be the only object dragging. Drag can also occur when a character moves in a quick fashion.
When Elsa does a half spin after releasing her glove, her cape drags up and a centrifugal force causes it to open outwards. Judging by the force Elsa uses to spin and knowing the wind element is almost eliminated and given that the material of her cape is probably a little heavier than regular clothing, it probably would not have spun and dragged as wide as it did.
You will notice there are a lot of mountain shots and scenes in this film that do not quite follow the laws of physics. There are two more example in which a mountain, or mini mountain, are involved. In this first scene we see Anna, Kristoff and Olaf once again being cornered to a cliff.
Kristoff informs the audience that the distance is a “100 foot drop” and there is about twenty feet of snow below them. This, according to him, means that when they fall and land “it will be like landing on a pillow.” When the characters do land you see them about half covered in snow then get up and continue on with their journey. The following scene has a similar case.
In this scene, Elsa and Anna are both young children. Anna asks Elsa to catch her by making mini snow mountains for her to jump on. When Elsa has a hard time keeping up she slips and accidentally strikes Anna causing her to fall on a snow hill and roll to the ground.
These two scenes are examples of the lack of terminal velocity due to air resistance and unbalanced forces. In the first scene with Anna, Kristoff and Olaf they fall what is said to be one hundred feet and land of about 20 feet of snow. Terminal velocity states that for a size and shape, the object that weighs more has a higher terminal velocity. This would not affect Olaf as much, given that he is a snowman and would most likely blend into the snow below. However, Anna and Kristoff are human. Judging from the scene, the drop seems to be much longer than one hundred feet. If this is true, then Anna and Kristoff's terminal velocity would be very high and fast. Because of this they would not have survived the landing, regardless of there being plenty of snow.
In the second scene with young Elsa and Anna, Anna also has a lower terminal velocity. In this situation there is an unbalanced force that causes her fall, Elsa’s miss. This causes Anna to fall straight down into a snow mountain. Due to the density of that mountain, she rolls off and gradually slows down until hitting the floor. The snow is not a large amount and due to Anna’s relative weight, her terminal velocity would have been higher than what the scene presents. Yes the snow slows her down but given that the floor is hard and covered in ice, Anna could have potentially have hit her head/body a bit harder, causing some bruising. Given these examples, it is clear that in the world of Frozen the terminal velocity is much lower, such that you would survive, despite falling a great distance.
The largest elements in this film are ice and snow. The film starts with the season of summer. After Elsa flees due to her fear, she freezes over the kingdom. The fact that the entire kingdom is frozen for a majority of the film brings on the final, broken law of physics: Thermodynamics and heat flow is almost nonexistent.This applies the third law of Thermodynamics which states that as a system approaches absolute zero, the entropy (or heat absorbed or emitted) of a system approaches minimal value. The villagers and all other characters cannot survive long in the frozen atmosphere. As the kingdom continues to get colder and colder, the heat flow from the villagers is less and less.
On the other hand Elsa appears to have no heat flow whatsoever. She is neither affected by the season of summer nor the fact that the kingdom’s temperature is probably below freezing. This would mean that Elsa’s temperature and that of freezing are the same. Given this is an animated film, of course, everyone survives and no one is put in any grave danger due to the temperature of the given climate.
I saw this film twice in the movie theaters because I loved it so much. I was very pleased with the overall look of the film, it’s musical numbers and the twist ending. I never gave much thought on the physics, or lack of, in the this film until this term paper. It is amazing what animation can do. That’s the beauty of it. One can exaggerate, use un-realistic settings or elements, and break laws in order to create an engaging feature film. Although the laws of physics are purposely broken and this film may be a bit of a “fixer upper,” it makes for the magical element in the story and believability in the world that is FROZEN.
