Is the Olympic running race fair? I noticed that the 200-meter sprints are conducted on curved tracks. (See this video: world championship semifinals 2009)
Isn't that weird? I mean, just look at the curvatures of each lane! 



(Source)
Since they use staggered start lines, the total track length is the same. But the person on the innermost lane would have to do more work as compared to the one on the outermost lane. He would have to put in an additional amount of work against friction to counter the extra centrifugal force. 
(The extra centrifugal force is roughly 2 Newtons from my calculation).
I believe that the winners of a running race are the ones who do more work against the friction. So, don't you think the runners in the inner lanes should be given an advantage?
 A: From the point of view of an ideal machine that is not slipping on the ground, friction does not do any work.  $W = \vec F \cdot \vec d$, but as the shoe does not slip, the distance moved against friction is zero, so the work is also zero.
Another way to think about it is that in a constant-speed turn, the velocity is tangent to the curve, while the centripetal force required is radial to the turn.  The dot product is zero and again, no work is required to perform the turn.  
All the losses from the runner are from other sources (air drag, inelastic impacts with the ground and internal to the leg, muscles being used to decelerate limbs, etc.)  You could certainly make an argument that running in a tight turn is biomechanically a disadvantage, but saying that energy loss is due to friction or required centripetal forces wouldn't be correct.
A: Runners generally prefer the middle lanes, and that's where the highest-seeded runners usually get assigned.  While it is true that the tighter curve of the inner lanes means that you effectively have more weight on your feet (by about 1% relative to the outermost lane), it is also considered an advantage to be able to see your competitors during the race, which you can't at the beginning if you start out in front of them (as you do in the outermost lane).
