Thursday, March 4, 2010

Kinetic Energy

The kinetic energy equation…

E=(1/2)m v^2

This is the Newtonian famous equation for Kinetic Energy. Note the terms are related as follows:

E(energy) in Joules
M(mass) in kilograms
V(velocity) in meters per second

Now the nature of this equation is fascinating to real world encounters. First it can be noted that is it very similar to the famous relativistic equation e=mc^2. We will cover the relation of these two equations in later blogs, but for now it’s useful to use Einstein’s equation to remember the very useful Newtonian equation for kinetic energy.

How is this interesting in real life?

First from the equation you can see that the energy is the square of its velocity. Considering this if you double your speed you increase your kinetic energy by 4 times…if you triple your speed you increase your kinetic energy by 9 times.

Second, Newtonian kinetic energy is frame dependent, which means if an object is moving in relation to an object it has kinetic energy, but if two objects are moving with the same velocity and direction they have no kinetic energy in relation to each other.

Now if we apply this information to real life objects we find something amazing. A common pebble if traveling at sufficient speed can have greater energy then the equivalent amount of TNT….just from its speed. Some interesting speed to energy ratios:

These can be figured using the equation E=(1/2)m v^2:

Speed necessary for 1 gram rock to have same energy as 1 gram TNT:

2300 Meters per second – 2.3 Km/s – 1.43 miles/s – 5150 mp/h

Note it is theorized that the sr-91 Aurora manned spy plane is believed to reach speeds of 5000mp/h. At those speeds if it impacted the ground the energy released would be equivalent to its weight in TNT just from kinetic energy.

The International Space Station currently orbits at a speed of roughly 17,000 mp/h, at that speed its kinetic energy is roughly 9 times that of TNT. This is significant when it comes to space debris. If a piece of debris even the size of a quarter, which weighs in at approximately 6 grams was to impact the space station at these speeds, the energy released would be the equivalent of 54 grams of TNT and would at the least be troublesome. This would explain why NASA currently tracks over 19000 pieces of space junk as small as 4 inches. The May 2009 Hubble repair mission assigned to the space shuttle was nearly scrubbed due to the 1 in 180 chance for a strike with space debris. In addition the ISS has had to undergo modification of its orbit to avoid potential strikes. Space debris is a menace and it’s the kinetic energy of such impacts that is at fault.

Kinetic energy is also significant when it comes to earth impacts with meteoroid or comets. One June 30, 1908 such an encounter occurred. An object from space burst over the Siberian forest releasing massive amount of energy. This object, likely moving potently in excess of 50,000 mph and possibly many tens of meters across burst with energy in excess of 10 Megatons, 1000 times the energy released over Hiroshima. Additionally a crater in Mexico known as the Chicxulub crater is believed to be the result of an impact with a celestial object of significantly greater size at possibly 6 miles in diameter. The result was a release of energy in excess of 100,000,000 megatons, and may well have been the cause of the Cretaceous–Tertiary extinction event, that extinguished a large swath of bio-diversity.

One final note. Often one will hear of the military using projectiles from tanks that are called kinetic energy penetrators, or KE-munitions. These rounds contain no explosive; rather they are made of depleted uranium which is very dense and very heavy. Traveling in excess of ½ mile per-second these rounds impart 3 ½ tons of force upon impact. And when used effectively the results are often referred to as a “kinetic kill”.

Next week on to moving atoms and heat…

1 comment:

  1. awesome! Love the blogs, keep them coming. Todd