Sunday, September 13, 2015

A Study of the Messiness of Death by Rail Gun

The year is 1996. The movie, Eraser. The muscles and guns hero....Arnold Schwarzenegger.

So Arnold is at the warehouse, and decides to give the Bad Guys a taste of their own creation. That is, violent death by railgun. But how realistic is the violence, for both parties involved?

First, we want to find out exactly how much firing one of those hurt.

With the law of conservation of momentum, we can use the equation:

Where a=Arnold and b=bullet

So for the values, I found:

Ma= 113kg (the Governator is reported to weight about 250lb)
Mb= 0.1kg
Vi,a= 0m/s
Vi,b= 0m/s
Vf,a= ?
Vf,b= 1.80x108m/s (I interpreted "near the speed of light" as 60% of the full 3x108m/s)

To calculate Arnie's final velocity:

Since the left side zeroes out, we can rearrange the equation to
Vf,a = -MbVf,b M

Fill in the fun parts
Vf,a = (0.1kg)(1.80x108m/s) / 113kg
the kgs cancel out to give the final units of m/s

And this is his final velocity
Vf,a 1.6x105m/s

While only traveling at 0.05% of the speed of light, that's still 356,078mph and probably won't feel good even in his smithereened state.

yeah that's gonna hurt

Next, we find out what this feels like to be on the receiving end.

Where v=Victim and b=bullet

Mv85kg (these guys didn't look too hefty)
Vf,v/b= ? (determined as one value if we're assuming the bullet stuck and they traveled together)

The equation for this
V(Mv + Mb) = MvVi,v+MbVi,b

Arranges down to
Vf  = MbVi,b Mv + Mb

And with the values plugged in
Vf  = (0.1kg)(1.80x108m/s) 85.1kg

Vf  = 2.1x105m/s
The victim is sent flying by the projectile from the rail gun at a speed of 2.1x105m/s, or 472,819mph......ouch.

Conclusion: This movie was not depicted nearly as violently as it should've been.

1 comment:

  1. I like it! Good job! I like the bolded numbers, the proper subscripts on the variables. Very neat! And the calculation appears to work out correctly.