How High Must a 400 lb Mass Be Dropped to Achieve a 3.5g Impact?

[starr_logic]

Hello all, I have a gravitational problem that I need help with figuring out. Its not actual homework but work related. I have a mass of 400 lb (large person) that needs to impact the ground at 3.5g. How do I calculate how high the mass needs to be dropped from to achieve the 3.5g? Its been a long time since physics classes and I need a refresher! Let me know if I missed any pertinent info. Thanks in advance!

 

[Dick]

How much acceleration the person experiences when impacting depends not only on the height but on how he lands. If he lands on his feet stiff legged he will experience much greater acceleration than if he flexes his knees. But it is a pretty simple calculation. Suppose he falls a distance D before he starts braking and then brakes to a stop in a distance B. The energy he acquires from gravity before stopping is m*g*(D+B) (g=9.8m/s^2). To stop in a distance B requires he absorb that energy with a braking force F acting over a distance B. So F*B=m*g*(D+B). F=m*a where 'a' is his acceleration (Newton's law). So m*a*B=m*g*(D+B). Cancel the m and rearrange and get a/g=(D+B)/B. So his acceleration in units of g is (D+B)/B. Now you can see that as B becomes small the corresponding acceleration becomes large. If you want a/g=3.5 then just estimate a value for B corresponding to his landing style and figure out D.