Reprinted from the ACJ - September, 2003
I dropped a jar of mustard on my cat`s head this morning. I didn`t mean to. I was making a sandwich for lunch. He was eating out of his food bowl, directly below me. I bumped the jar, it rolled, fell and `Clunk`, brained him. He yelped, jumped straight up and ran for kingdom come; wondering what he had done wrong. I felt bad because, not only do I kind of like him, but I also took guilty relief in the fact that had it missed his head it probably would have cracked a tile in my new kitchen floor.
The incident got me to thinking. Just how hard did that jar hit him? Being and engineer I couldn`t let it rest at `Darn hard`. The fact that I was also struggling to come up with a Health Watch article explains why you are hearing about it at all.
We have all done it. Open a cabinet, take something out. Bend over to use the tool, or whatever. Stand up to put it away and `Crack`, the top of your head meets the cabinet corner. I always think (after @#$%!$#@) `How could I have hit it that hard?` `I just stood up; it`s not like I took a running start and Head-butted it`. The answer is Pounds-Force. It is the secret to `blunt force trauma`.
I am going to get a little fast and loose with the science here, but remember this isn`t a thesis; it is a humorous article about bumping your noggin. Newton`s second law of motion states Pounds-Force (F) = Mass(m) x Acceleration(a). Thus the more an object weighs and the faster it is moving the more it will hurt when you stop it with your melon. The most common form of acceleration we encounter is gravity. Gravity has an acceleration of 32 feet per second squared. So if a 1 pound object falls for 1 second the apparent pounds it hits with (F) is 1 Lb x 32 ft/s2 = 32 Lbf. So if my mustard jar weighs 8 oz (0.5 Lb), like the label says, and fell for a second, it hit the little guy like it weighed 16 Lbs. No wonder he likes mayo. A 1 Lb hammer hitting your finger at twice the speed of gravity, as you swing it, feels like 64 Lb. You turn around, take 1 step, `Pow`, Mr. forehead meet Mr. hoist arm. We walk at about 5 miles per hour which is about 7 feet per second. That`s 2 steps. So in a half a second you were able to ram your 10 Lb head into the hoist at 40 Lbf. The same is true of the cabinet we hit earlier. But, in that situation, the force is concentrated in a smaller area (the corner of the cabinet). That concentrated force may be enough to overcome the elasticity of your skin. Result; four stitches and a goose egg. Ever drop the remote control on your bare foot? Feels like it weighed 8 lbs.
Legend has it that Isaac Newton discovered gravity when an apple hit him in the head. In actuality the apple hit his cat. But he noticed that the light weight apple hit with a force that made it seem much heavier. He reasoned that something else must be acting on the apple to accelerate it. Viola! Gravity.
For a dropped object the acceleration is constant at the speed of gravity. So the weight of the object becomes important. Get hit with a tennis ball from out of the blue and it stings. Make it a baseball and it may knock you out. Make it a jar of mustard and you get an angry cat. The lesson here is that falling objects build up a lot of force. Be careful when storing things on shelves. Never walk under a scaffold with workers above. If someone yells `Heads Up`; don`t! Duck and cover.
The other controlling factor is the speed with which an object is moving when you stop it with a body part. That is why the 1 Lb hammer hurts like the Diken`s when it hits your thumb at swinging speed. But the 75 # convenience store door only taps you on the back as the closing mechanism slowly releases air. If you control the speed, and the weight, of falling, swinging or flying objects, you control the danger they present.
I realize that I have given you a lot to think about in this article. So as you calculate the force with which this article will hit the circular file. I`m going to see if my cat wants part of this sandwich.
The above article was written by David M. Brown, Chief Engineer of Johnson Manufacturing Company, Inc. and is published by JOHNSON with the expressed approval of the National Automotive Radiator Service Association and the Automotive Cooling Journal. Other reproduction or distribution of this information is forbidden without the written consent of JOHNSON and NARSA/ACJ. All rights reserved.
JOHNSON MANUFACTURING COMPANY
14 Lost Grove Road / PO Box 96 / Princeton, Iowa 52768-0096
Phone 563-289-5123 or Fax 563-289-3825