It is well known that runners run more slowly around a curved track than a straight one. One hypothesis to explain this is that the total force from the track on a runner's feet--the magnitude of the vector sum of the normal force (that has average value mgmg to counteract gravity) and the inward-directed friction force that causes the runner's centripetal acceleration--is greater when running around a curve than on a straight track. Runners compensate for this greater force by increasing the time their feet are in contact with the ground, which slows them down. For sprinters running at 8 m/s around a curved track of radius 16 m, how much greater (as a percentage) is the average total force on their feet compared to when they are running in a straight line?
It is well known that runners run more slowly around a curved track than a straight one. One hypothesis to explain this is that the total force from the track on a runner's feet--the magnitude of the vector sum of the normal force (that has average value mgmg to counteract gravity) and the inward-directed friction force that causes the runner's centripetal acceleration--is greater when running around a curve than on a straight track. Runners compensate for this greater force by increasing the time their feet are in contact with the ground, which slows them down.
For sprinters running at 8 m/s around a curved track of radius 16 m, how much greater (as a percentage) is the average total force on their feet compared to when they are running in a straight line?
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