A Physics Lesson From Divergent

The movie Divergent was a box-office hit. It has a thrilling plot with danger, drama, and even a bit of romance! The movie is wildly entertaining as Tris is constantly having to prove herself by doing dangerous activities like throwing herself out of moving trains and jumping off of tall buildings into safety nets. However, if one were interested they could easily make the movie educational as well. 

For example, let's examine the scene below:



 

The clip shows Tris zip-lining from a skyscraper, plummeting down to ground level. Tris is so enthralled by the fantastic view that she almost forgets to pull the brake to stop herself. Luckily, by the time she does remember, she is able to stop herself completely before smashing her face into a metal wall. Because Tris is braking so suddenly, the brake heats up red. How would you solve for how much the brake heats up?


There's a few steps required to solve this problem. The first is to figure out how much potential energy Tris has at the top of the skyscraper. Potential energy is the amount of stored energy an object has because of its position. Tris is 150 meters above ground, therefore she has a significant amount of potential energy. 



Potential Energy = mgh 
mass of Tris = 55 kg,   gravity = 9.8 m/s2,   height of building = 150 m
P.E. = 55 kg 9.8 m/s150 m 
P.E. = 80850 J

As Tris descends down the zip-line, her potential energy transforms into kinetic energy, energy of motion. The law of conservation of energy states that the amount of potential energy Tris has must be the equal to her kinetic energy at the end of the zip-line. Therefore, her kinetic energy is also equal to 80850 J. We can solve for Tris's final velocity with the formula below.
Kinetic Energy =  1/2   x   m  x   v^2
kinetic energy = 80850 J,   mass of Tris = 55 kg,  velocity = ?
80850 J = 1/2 x 55kg x v^2
V = 54.23 m/s

Tris's final velocity would be 54.23 m/s on the zip-line, that's around 120 mph!


When Tris finally remembers to brake her kinetic energy is then transformed into heat. Again, the law of conservation of energy states that her kinetic energy (80850 J) must be transformed into heat (80850 J). Because of this we are able to solve for how much the brake heats up.

Q = m x    delta T
Q = 80850 J, mass of brakes = 3 kg, specific heat of steel = 452 J / kgC, change in temperature = ?
80850 J =  3 kg   452 J / kgC   delta T
delta T = 59.63 C


When Tris pulls the brake, it heats up about 60 degrees Celsius. In the scene the brake glows bright red. After doing some research on the heat at which steel becomes red in color, I have determined that the brake in that scene should not have turned red, but stayed its same color. Another science-fiction movie getting physics wrong...shocker!

Steel Color vs. Temperature 


Comments

Post a Comment

Popular Posts