Powering Up Relativistic Baseball

There’s a cute post on the consequences of a pitcher throwing a baseball at 90% of the speed of light (see Relativistic Baseball).  (cute for geeky people like me, at least).  The author assumes that the baseball somehow accelerates from rest to 90% of light speed without worrying about how that occurs.  But, as a chemical engineer I have to wonder about the energy requirements for achieving 0.9c, so I did a calculation on the change in kinetic energy of a baseball from rest.

High school physics tells us the kinetic energy goes from zero at rest to ½mv^2 , and apparently a baseball has a mass of about 145 g.  So the change in kinetic energy would be 5.6 x 10^15 Joules.  But wait!  In Wikipedia I discover that this will be incorrect at such high speeds, where classical mechanics doesn’t quite work.  (Engineers rarely deal with relativistic mechanics, so I didn’t learn that before.)  The correct calculation is apparently based on relativistic kinetic energy, which is equal to  mc^2/(sqrt(1-v^2/c^2)-mc^2  (sorry, I haven’t figured out how to do equations in WordPress yet).  Using this relationship, I get the energy requirement to be 1.8 x 10^16 Joules, somewhat higher than the classical mechanics calculation. 

How much energy is that?  Well, it is equivalent to 5 million MWh (megawatt-hours), which is the typical output of a CANDU 900 MW reactor (again, according to Wikipedia)over a period of about 7 months.  I’d like to see the arm of a pitcher who could deliver that much energy to a baseball in the span of a second or two!


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