Wednesday, 23 November 2011

What Is Kinetic Energy?

I have the distinct impression most science writers are English majors and not schooled in physics. Why do I think this? Because kinetic energy is bandied about as though it were a force. We hear that a meteor will strike with hundreds of thousands of foot pounds of energy or a rifle bullet strikes with thousands of foot pounds of energy. It's all rubbish. Kinetic energy is a formula devised by Isaac Newton to enable you to calculate the potential energy of an object in motion. He expressed it as ke (kinetic energy) = 1/2 m V2. Seems simple enough until you try a simple example. We know if you drop something here on earth that gravity accelerates it at about 32.2 feet per second toward the center of the earth. So in 1/4 of a second our object will attain a velocity of about 8 feet per second and travel about 1 foot. In another 1/4 second it will reach about 16 feet per second and travel an additional 3 feet for a total of 4 feet. We see a graph of velocity versus time is a straight line but the distance traveled quadruples for each doubling of time. It does this because it accumulates velocity with time and moves further with each increment of time.

So let's try a simple example. We will drop a 1 pound mass 1 foot. The velocity it attains in one foot is the same velocity that would enable it to rise 1 foot if it were traveling in the opposite direction. It is called symmetry. Physical processes usually exhibit symmetry. Up and down are mirror images of each other. So, back to our 1 pound mass dropped 1 foot. We know this is a foot pound by definition. So we multiply 1 pound by 8 squared for 64 and halve it for an answer of 32. Long way from 1 foot pound so what is the problem? The problem is m is used in Newtonian mechanics to mean many things. In the momentum equation (momentum = mv) m is 1 pound - BUT- in the kinetic energy formula m is expressed in what Newton termed a slug. A slug is that mass which when acted upon by a force of 1 pound accelerates at 1 foot per second. Since we know gravity would accelerate it at 32.2 feet per second but a force of 1 pound accelerates it at 1 foot per second a slug is obviously 32.2 lbs. It is the gravitational constant, little g, over 1. So he coined a new unit of mass with the gravitational constant neatly ensconced within it.

Why you may ask. Well because we get the correct answer if we take our original answer and divide by 32. It is 1 which is the correct answer. Since v changes only 32 feet per second we see at high levels of v the potential energy is enormous. But remember this is potential energy only if you can extract work by lowering it on a rope or in an elevator. That's why a .308 bullet may possess around 3000 foot pounds because in a vacuum it will rise losing only 32 feet per second in its travel. If you think it imparts 3000 foot pounds to a deer it does not. Newton also said for every action there is an equal and opposite reaction. This is the kick on the butt plate of the rifle. If it were 3000 foot pounds you can be confident in the knowledge no one would fire the rifle a second time. Kinetic energy is not a force. The impact energy is its momentum. Kinetic energy just expresses how high it can rise.

Kinetic energy is much more impressive when talking about impacts though so marketing people and English majors describe motion in terms of kinetic energy.

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