Final answer:
The average total force on a sprinter's feet is infinitely greater when running on a curved track compared to running in a straight line.
Step-by-step explanation:
To calculate the percentage by which the average total force on a sprinter's feet is greater compared to running in a straight line, we need to compare the centripetal force experienced by the sprinter on the curved track to the force required to run in a straight line. The centripetal force can be calculated using the formula:
Fc = (mv^2) / r
Where Fc is the centripetal force, m is the mass of the sprinter, v is the velocity, and r is the radius of the curved track.
To find the percentage difference, we can subtract the force required to run in a straight line from the centripetal force and divide it by the force required to run in a straight line, then multiply by 100 to express it as a percentage.
Let's plug in the values:
Mass of the sprinter (m) = 60.0 kg
Velocity (v) = 8.0 m/s
Radius of the track (r) = 20 m
First, let's calculate the centripetal force:
Fc = (60.0 kg)(8.0 m/s)^2 / 20 m
Fc ≈ 192 N
Next, let's calculate the force required to run in a straight line:
Fstraight = ma
Since the sprinter is running at a constant velocity, there is no acceleration, so the force required to run in a straight line is zero.
The percentage difference is:
Percentage difference = (Fc - Fstraight) / Fstraight x 100
Percentage difference = (192 N - 0 N) / 0 N x 100
Percentage difference = undefined
Therefore, the average total force on the sprinter's feet is infinitely greater when running on a curved track compared to running in a straight line.