Q.The maximum static friction available to an athlete is given by fₛ^(max) = μₛ N. A sprinter wears spiked shoes mainly in order to:

Sprinters rely on static friction to generate forward propulsion. When an athlete pushes off the ground, the foot exerts a backward force on the track. According to Newton's third law, the track exerts an equal and opposite forward force on the foot. This forward force is the static friction, which propels the athlete forward. For maximum acceleration, the athlete needs to maximize this static friction without slipping.

The maximum static friction available is given by fₛ^(max) = μₛ N, where μₛ is the coefficient of static friction and N is the normal reaction force. Spiked shoes are designed to increase the effective resistance to sliding.

1. reduce the normal reaction force This option is incorrect. Reducing the normal reaction force N would directly decrease the maximum static friction fₛ^(max), making it harder for the athlete to push off without slipping. Sprinters aim to maximize friction, not reduce it.
2. increase the grip by creating a mechanical interlock with the track This option is correct. The spikes on a sprinter's shoes dig into the track surface, creating a physical or mechanical interlock. This interlock significantly increases the resistance to relative motion between the shoe and the track. It effectively prevents the shoe from sliding backward, allowing the athlete to exert a much greater backward force on the ground, which in turn generates a larger forward static friction force for propulsion. This mechanism enhances the "grip" far beyond what smooth rubber would provide.
3. reduce the athlete's inertia …

To understand why sprinters wear spiked shoes, we must first consider the role of friction in athletic performance, especially in sprinting. Friction is a force that opposes relative motion or the tendency of motion between two surfaces in contact. For a sprinter, the ability to accelerate rapidly depends on their capacity to push backward against the track. According to Newton's Third Law, the track then pushes forward on the sprinter with an equal and opposite force. This forward force is the static friction force.

The maximum static friction (fₛ^(max)) that can be generated between the athlete's shoe and the track is given by the formula fₛ^(max) = μₛ N, where μₛ is the coefficient of static friction and N is the normal reaction force. To achieve maximum acceleration, a sprinter needs to maximize this static friction, allowing them to exert a greater backward force without their feet slipping.

Let's analyze each option:

1. reduce the normal reaction force The normal reaction force (N) is the force exerted by the surface perpendicular to the contact area. On a flat track, it is primarily determined by the athlete's weight and any vertical acceleration. Reducing the normal reaction force would directly decrease the maximum static friction available (fₛ^(max) = μₛ N), which is counterproductive for a sprinter who needs more friction to push off powerfully. Spiked shoes do not reduce the normal reaction force.
2. increase the grip by creating a mechanical interlock with the track This is the primary reason sprinters wear spiked shoes. The small, sharp spikes on the sole of the shoe penetrate the surface of the track. This penetration creates a mechanical interlock between the shoe and the track material. This mechanical interlock significantly increases the effective coefficient of static friction (μₛ). A higher μₛ directly leads to a higher maximum static friction (fₛ^(max)), allowing the sprinter to apply a much greater backward force against the track without slipping. This increased grip translates into more efficient transfer of force and greater forward propulsion, leading to faster acceleration. …