A 75 kg runner taking part in a 200 m dash must run around the end of a track that has a circular arc with a radius of curvature of 32 meters. if he completes the 200 m dash in 20.33 s and runs at constant speed throughout the race, what is the magnitude of his centripetal force as he runs the curved portion of the track?

F = - 226.7874N

Explanation:

Initially we must determine the speed at which the runner runs that is given by the following equation:

v = velocity = (200m) / (20.33s) = 9.8377 m/s

To determine the centripetal force of the corridor in the curve we must use the following equation:

Fc = centripetal force = - m * ω² * r

m = mass of the runner

ω = angular speed

r = ratio of the curve

The angular velocity is the swept angle per unit of time, so we determine that perimeter has a complete turn of the curve, 2π radians, and calculate the time it would take to travel it to the runner to know the angular velocity it takes:

Perimeter = 2π * r = 2π * 32m = 201.0619m

The time it would take to travel would be:

t = (201.0619m / 9.8377 m/s) = 20.4379s

ω = (2π) / (20.4379s) = 0.3074 (rad/s)

After obtaining these values we can calculate the centripetal force to which the runner is exposed in the curve:

F = - 75kg * (0.3074 rad/s) ² * 32m = - 226.7874N

The minus sign corresponds to the sense of force being outward of the radius of curvature.