How fat DOES a man have to be to stop a runaway trolley?
Check my math/physics please.
I wanted to make an animation exploring a trolley problem from a physics standpoint rather than a moral philosophy standpoint, inspired by some of the comments here
Now my brain is fried trying to figure it out.
I figured I'd keep it simple (but not simple enough) by focusing on a scenario where the trolley pushes the man in front of it, and the increased friction stops the trolley.
Assuming a 15000lb
trolley moving at 15mph
a required stopping distance of 300 yards
and an assumed kinetic coefficient of friction of 0.68
I'm coming up with a 184 pound man, which is a lot smaller than I intuitively thought, so I figured I should double-check I'm not making a dumb mistake.
Assuming I convert them all into kg metres/second and metres
(speed^2*mass)/(distance*2) = Force in Newtons required to stop it
And then convert the newtons to pounds, and apply the coefficient of friction to get what he has to weigh to add that force from his friction.
So I combine all that with the metric conversions, and I get something like this:
Weight in lbs = ( 15mph * 0.4470 mps/mph )^2 *15000lb * 0.4535 kg/lb * 0.2248lb/N / ( 300yd * 0.9144m/yd *2 *0.68 )
Which comes out to only a 184lb man.
Check that I have correctly used formulas for stopping and force, please, though I will also entertain discussion of what other factors I'm ignoring if they would change the result drastically.
For the coefficient of friction I used an example I found for "tires on a dirt road" because I didn't feel like dragging someone along the ground. And my other assumptions were to give the possibility of stopping it as much credence as I could.