Now thats its morning I have a new look at things.
Assuming all things except weight and velocity are equal.
Scenario 1: Heavy Chopper, call its weight 10, moving at a velocity 10. Has a momentum of 100 and impacts a block of wood with F=500, from equations F=ma, which turns to F=.5mv^2(original velocity)-.5mv^2(final velocity which is 0).
Scenario 2: Light chopper, weight =5, moving at velocity 20. Has same momentum as scenario 1=100, but has a F=1000 using same equation above.
Both knives impact the same 100 weight block of wood which ideally absorbs the entire Force and reacts by moving. Since the block of wood can not freely move in the direction of the force it then reacts in a negative Force towards the knife. Lets say 80% of its energy was absorbed into the ground and the other 20% comes back. That means a F=100 impacts the large knife, which means it will want to 'rebound' with velocity =~4.5 . The F on the light knife is 200, which with its smaller weight means it tries to rebound with a velocity of =~6.3(no calculator here, so someone correct my math if its wrong.) This would seem to indicate why a smaller knife feels like it recoils more. If we stop here the light knife has exerted more force on the wood, which given all other things are equal, would mean it has cut deeper.
But, lets keep going. You are still applying a force on the knife. Your arm absorbs most of the recoil of the knife but you are still pressing down on the blade with as much pressure as you can, equal in both knives cases. Since you are applying the same force to each knife at this point but the lighter knife is reacting more negatively towards you with a greater force there is now a greater force being applied to the heavy knife, remember this is all happening in an instant. You send a larger force to the wood with the heavy knife this time. The wood reacts again, and the knives again, and again and again until all energy is used up in friction or absorbed by some other means. Each time the wood reacts with a force on the knives, the smaller knife will react more, so its energy back to the wood will diminish faster than the heavy knife. This sinusoidal curve will show which knife ultimately transfers the most energy into the wood.
If you have ever seen a computer analysis of a knife stabbing something it is actually the second force applied to the knife that generally penetrates what it is puncturing, not the first. This is why most ballistic vests are not good against knife attacks as they are designed to defeat a single large energy transfer. The force behind a knife is much different than a bullet and you can not use the same principles to compare energy transfer of the 2. There is a constant force applied to the knife, where a bullet only has an initial energy transferred to it by the expansion of gasses behind it. There are lots of reactions happening that we can not even feel and I would venture a guess that if someone did the same computer analysis on a block of wood being chopped we would see the same sinusoidal graph come out that you see in stabs. Moral of the story, get out and chop something.
Disclaimer: I am not a physics teacher nor even a current physics student. I deal more with static loads in my day to day and leave dynamic ones to the people who know better.
Its too early in the morning to have my head hurting, time to get some meat on the smoker!! Chop this with your physics book.
... darn failing AOL internets. so yes or no on that part is cool.
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