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.

M

_{R}V_{R}+ M_{B}V_{B}= (M_{R }+ M_{B}) V_{f}
(55.0
kg) (0 m/s) + (9800 kg) (6.70 m/s) = (9855 kg) (V

_{f})
V

_{f}= 6.66 m/s
We can then use this to find Regina’s acceleration, since
her initial velocity was 0 m/s.

V

_{f }= V_{o}+ at
6.66
m/s = 0 m/s + a(0.1s)

a
= 66.6 m/s

^{2}
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 10

^{7}Pa and the femur cross sectional area is 5 x 10^{-4}m^{2}. 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}m^{2})
Stress
= 7320000

7.32
x 10

^{6}Pa < 7 x 10^{7}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 10

^{7}Pa = F / A
7
x 10

^{7}Pa = F / (5 x 10^{-4}m^{2})
F
= 35000 N

F
= m a

35000
N = (55 kg) a

a
= 636 m/s

^{2}
V

_{f }= V_{o}+ at
V

_{f }= 0 m/s + (636 m/s^{2}) (0.1 s)
V

_{f }= 63.6 m/s
M

_{R}V_{R}+ M_{B}V_{B}= (M_{R }+ M_{B}) V_{f}
(55.0
kg) (0 m/s) + (9800 kg) V

_{B}= (9855 kg) (63.6 m/s)
V

_{B}= 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.

## No comments:

## Post a Comment