Maximum Horizontal Acceleration in a Sprint

Introduction:
In order to determine the maximum horizontal component of acceleration of an athlete in a sprint, we need to consider the coefficients of static and kinetic friction between the shoes of the athlete and the ground.

Explanation:
The maximum horizontal component of acceleration can be determined by analyzing the forces acting on the athlete in motion. In this case, we need to consider two scenarios - when the athlete is at rest (static friction) and when the athlete is in motion (kinetic friction).

1. Static Friction:
When the athlete is at rest, the maximum horizontal component of acceleration is limited by the maximum static friction force. The formula to calculate the maximum static friction force is given by:

F_static = μ_static * N

where F_static is the maximum static friction force, μ_static is the coefficient of static friction, and N is the normal force acting on the athlete.

2. Kinetic Friction:
Once the athlete starts moving, the maximum horizontal component of acceleration is limited by the maximum kinetic friction force. The formula to calculate the maximum kinetic friction force is given by:

F_kinetic = μ_kinetic * N

where F_kinetic is the maximum kinetic friction force, μ_kinetic is the coefficient of kinetic friction, and N is the normal force acting on the athlete.

Normal Force:
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is equal to the weight of the athlete, which can be calculated using the formula:

N = m * g

where m is the mass of the athlete and g is the acceleration due to gravity.

Calculation:
Let's assume the mass of the athlete is 60 kg.

1. Calculation of Normal Force:
N = m * g = 60 kg * 10 m/s^2 = 600 N

2. Calculation of Maximum Static Friction Force:
F_static = μ_static * N = 0.6 * 600 N = 360 N

3. Calculation of Maximum Kinetic Friction Force:
F_kinetic = μ_kinetic * N = 0.5 * 600 N = 300 N

Conclusion:
Therefore, the maximum horizontal component of acceleration of the athlete in a sprint is limited by the maximum kinetic friction force, which is 300 N.