Friday, November 23, 2012

Mean Girls Physics

By Beth Shore
Towards the end of the movie, Mean Girls, Regina George is struck by a bus and suffers a neck fracture. This scene can be seen here:

(Time 1:20)

            So, in the spirit of Bad Movie Physics, I wanted to look at whether Regina should have fractured other bones, such as her femurs. To do this, I had to make some assumptions. Assuming the time of the collision was 0.1 s, Regina weighs about 55 kg and the bus weighs 9800 kg, and the bus was traveling the school zone limit of 15 mph (or 6.7 m/s), we can use the inelastic collision equations to figure out final velocity of the bus and Regina.

            MRVR + MBVB = (MR + MB) Vf
            (55.0 kg) (0 m/s) + (9800 kg) (6.70 m/s) = (9855 kg) (Vf)
            Vf = 6.66 m/s

We can then use this to find Regina’s acceleration, since her initial velocity was 0 m/s.
            Vf = Vo + at
            6.66 m/s = 0 m/s + a(0.1s)
            a = 66.6 m/s2

Then, we can use this acceleration to find force.
            F = ma
            F = (55 kg) (66.6 m/s)
            F = 3660 N

Finally, from the homework we know that the ultimate sheer strength of the femur is 7 x 107 Pa and the femur cross sectional area is 5 x 10 -4 m2. Assuming the majority of the force is going to her femurs (as they are at the level of the bumper of the bus, which is where she would be hit first), we can see whether they should break or not.
            Stress = F/A
            Stress = (3660 N) / (5 x 10 -4 m2)
            Stress = 7320000
            7.32 x 106 Pa < 7 x 107 Pa, so her femurs would not break at this speed.

How fast, then, would the bus have to be going to break her femurs?
            7 x 107 Pa = F / A
            7 x 107 Pa = F / (5 x 10 -4 m2)
            F = 35000 N

            F = m a
            35000 N = (55 kg) a
            a = 636 m/s2

            Vf = Vo + at
            Vf = 0 m/s + (636 m/s2) (0.1 s)
            Vf = 63.6 m/s

            MRVR + MBVB = (MR + MB) Vf
            (55.0 kg) (0 m/s) + (9800 kg) VB  = (9855 kg) (63.6 m/s)
            VB = 64 m/s

Which is about 143 mph. So Regina’s femurs are safe, especially when you consider that the force would likely be spread over more of her body than just her femurs. However, other bones may break, as the femur is the strongest and longest bone in the whole body.
In conclusion, at least in this section, Mean Girls does not ignore the laws of physics and is not an example of a movie with bad physics. 

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