This weekend, I had the opportunity to watch the great movie Inception with Leonardo DiCaprio. I’ll try not to spoil too much but I saw some interesting physics in the movie.
For those of you that don’t know, the movie is based on the concept of dreams. Leo’s character explains that, using some (likely illegal) sedatives, it’s possible to enter other people’s dreams so that you can extract some piece of knowledge from the dreamer’s subconscious. When we share dreams, the people not actually dreaming can alter the physics of the world to create anything they want.
To wake up from a dream, a person needs a “kick” or a falling sensation that will cause the mind to force itself to wake up. After some googling, I found that this is a real phenomenon call a “Hypnic Jerk.” This is the feeling you get when you’re falling asleep and suddenly the inner ear misperceives the relaxation of falling into slumber as a downward acceleration despite laying still. The brain responds by jolting the arms and legs to prevent you from hurting yourself.
To get this kick, Leo and his co-characters devise a plan of driving a van off a bridge to use the change in acceleration as the falling sensation and jolt themselves awake. Using the average weight of a van with 6 people (c.75kg each) is 4450kg. Acceleration due to gravity would be:
Fg=m x g = 4450kg x 9.8m/s^2 = 43,160 N
If they were to fall from a 30m bridge, then they would fall in 3.50 seconds with a final velocity of 34.4m/s.
∆y=yot + ½ a t2 , 30m= (0m/s)t + ½ (9.8m/s2)t2= 3.50s
Vf = vo+at = 0m/s + (9.8m/s) (3.50s) = 34.3m/s
The movie gives a time change ration of 1min time to 20min of dream time. Thus, with this ratio, the fall in the first dream would be:
3.50s = (1min/60s) (20 min / 1min) = 1.2min (70s) in the second dream and 24min (1440s) in the third dream.
Thus, in the second dream, the characters would experience an acceleration of
A=∆v/∆t = (34.3m/s – 0m/s)/ 70s = 0.49m/s2. However, they are in freefall so it’s as if they are floating.
Because of this freefall, they use an explosive to crash an elevator so that the velocity (an acceleration) change on impact feels like falling. The explosion uses the law of conservation of momentum to propel the elevator. They will have no initial momentum because neither are moving (Using the average mass of an elevator and the values for C4):
∆p= 0, po=0, ∴ Melevatorvelevator = mbombvbomb, (1200kg)(v)=(1kg)(-8000), v= 6.67m/s
Thus, when the elevator collides with the ceiling the change in velocity would be
The acceleration, will be a=∆v/∆t= (6.67m/s- 0m/s)/.25s =26.7 m/s2
Therefore, the people would definitely feel the acceleration and would be jolted awake.