## Thursday, December 5, 2013

### Ridiculousness

My teammate Jen was recently on the show "Ridiculousness" for a nasty fall she took a couple years ago.  I decided to calculate the force that Jen felt as she was put to a stop by the metal table.

I'm going to assume that as Jen jumps horizontally, she is an ideal projectile object.  Then I'm going to assume that she is moving at a constant velocity after she lands and that the concrete was a frictionless surface.
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I'm assuming that Jen was running at 3.6 m/s before she jumped, and the only force of acceleration acting on her is gravity (9.8 m/s^2).

initial velocity (x)= 3.6m/s
initial velocity (y) = 0 m/s
acceleration (x) = 0 m/s^2
acceleration (y) = 9.8 m/s^2
t = 2 s

final velocity (x) = 3.6m/s (no acceleration in x direction)

final velocity (y)= 0m/s + (9.8 m/s^2)(2 s)
final velocity (y) = 19.6 m/s

final velocity^2 = (19.6 m/s)^2 + (3.6 m/s)^2
final velocity when she hits the ground = 19.9 m/s

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She was then stopped by the table in what appears to be 2 feet (.6 m).  I will also assume she has a mass of 52 kg.

(1/2)(m)(vinitial)^2 + Wnc = (1/2)(m)(vfinal)^2
(1/2)(52 kg)(19.9m/s)^2 + Wnc = (1/2)(52 kg)(0m/s)^2
Wnc = 10,296 J

The table exhorted 10,296 J of work to bring Jen to a stop.  Using Work = (Force)(distance), we can determine that the force Jen felt from the table was..

10,296 = F (.6m)
F = 6177.6 N

Sounds painful.. no wonder she made it on TV.