Where μ is the coefficient of friction and R is the normal reaction force.

The coefficient of friction (COF, μ) is a dimensionless scalar quantity which is the ratio of the force of friction, F _f, between two bodies and the normal reaction force, R.

The magnitude of the coefficient of friction depends on the materials in contact: steel on ice (in ice skating) has a low coefficient of friction; rubber sole on the ground (running) has a high coefficient of friction.

The greater the interaction between the molecules of the interfacing surfaces, the greater the size of the coefficient of friction.

Coefficients of friction range in value between zero and one, but can sometimes be higher.

When a force is applied to attempt to move a stationary object over another surface, we consider the coefficient of static friction. At some point, the force applied is sufficient to overcome the static friction and the object will begin to move. Once the object is in motion, we consider the coefficient of dynamic friction. The coefficient of dynamic friction is usually lower than the coefficient of static friction.

Consider maximizing and minimizing frictional influences in order to enhance performance.

For example:

• sports shoes (including spikes/cleats) and playing surface (grass, artificial surfaces, wood)

• winter sports (skiing, ice skating)

• use of a golf glove

• cycling on an indoor sloping velodrome.

Drag is the force or forces acting to oppose the motion of an object through a fluid medium such as air or water.

Limit to:

• surface drag: As a body moves through a fluid, its outer surface catches a layer of the fluid nearby, slowing it down compared to the fluid further away and so causing drag. This can be minimized by changing the surface to reduce the interaction between surface and fluid. Example: The use of shark-skin suits in swimming or shaving the swimmer’s body to make it smooth.

• form drag: As a body pushes against a fluid, the fluid pushes back (action and reaction). By streamlining the body and minimizing the surface area facing the direction of the motion, this type of drag is reduced. Example: Cyclists adopting a low profile position.

• wave drag: When a body moves along the surface of a fluid (usually water) some fluid is displaced to form a wave. These waves cause additional forces that oppose motion. Wave drag can be reduced by avoiding motion at the interface between air and water. Example: Swimming underwater for as long as is allowed at the start of a race.

Consider the influence of fluid viscosity, surface size, shape, texture and relative velocity on drag. For example:

• clothing for skiers, swimmers, runners, cyclists and base jumpers

• equipment for cycling (helmet and bicycle design)

• body position for a speed skater and swimmer. Drag increases dramatically with speed. (It increases as the square of the speed.)

Aim 8: Consider the economic implications of developing technologies to improve performance in sports.

Int: Consider the availability of performance-enhancing technologies in different parts of the world.