Answer:
F= -226.7874N
Step-by-step 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.