# Q & A: Getting hit in the head with a rock

Q:
Just theoretical physics for a dorky game of Hackmaster: Assuming you could propel a rock (spherical, weighing 1 lb) to a force of 1000 foot-pounds, how much damage would that rock do to a human in each of these cases, and differentiating between the rock breaking on impact, or the rock maintaining its shape, for: 1) head shot, 2) upper torso, 3) lower torso, and 4) a limb (pick one?)? Thanks.
- Seth H (age 17)
Texas
A:
Dear Seth, don't try this experiment at home.
First of all lets get the foot-pounds into an equivalent energy for a one pound rock.  By the way, a foot-pound has units of energy, not force.  I feel more comfortable working in metric units so using the conversion factor of  1 foot-pound = 1.356 Newton-meters so set E = 1356.  A Newton-meter is the same as a Joule.   Now one pound is equal to 0.454 kilograms. Equating this energy with kinetic energy,  E = 1/2 mv2 , we can solve for the velocity of the rock obtaining v2 = (2 E)/m, or, doing the arithmetic;  v =  77.24 meters per second.  Converting back to English units using 1 m/sec = 2.24 mph you get 173 miles per hour.
I don't think you would like to be hit anywhere on your body by a one pound object going at 173 mph.

LeeH

Another way to see that is that 1000 ft-lbs of energy in a 1 lb object gives it the same energy as if it were in free frictionless fall for 1000 ft. Same conclusion. Mike W.

(published on 01/19/2011)