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The record of the women's 200 m is 21.34 sec. If all racers at that speed, how much more force would be needed by the racer in lane 1 to stay in her lane than by racer in lane 8. Assume that all racers weigh 534 N. The track is a 400 m Olympic track.

You need more data to answer this. 200 m races are run around a curve. You need to know the radius of curvature R of lanes 1 and 8 as they go around the curve at one end of the track. Find that information, and then use the formula
F = M V^2/R
to get the lateral centripetal force required to stay in a lane. It will be higher for the inside lane.

According to
(Broken Link Removed)
each lane is 1.22 meters wide. Lane 1 has a radius of curvature of 36.8 meters

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