Friction and Drag (HL)

Introduction

In the realm of Sports, Exercise, and Health Science (SEHS), understanding the principles of friction and drag is crucial. These forces significantly affect the performance and efficiency of athletes and the dynamics of various sports activities. This study note will delve into the intricate details of friction and drag, covering key concepts such as fluid resistance, terminal speed, projectile motion with air resistance, and wave phenomena.

Fluid Resistance & Terminal Speed

Drag Forces and Their Effects on Motion

Drag force is a type of friction that acts opposite to the relative motion of any object moving with respect to a surrounding fluid. This could be air (aerodynamic drag) or water (hydrodynamic drag).

• Equation for Drag Force: $$ F_d = \frac{1}{2} C_d \rho A v^2 $$ where:
  • $F_d$ is the drag force,
  • $C_d$ is the drag coefficient,
  • $\rho$ is the fluid density,
  • $A$ is the cross-sectional area,
  • $v$ is the velocity of the object.
• Example: A cyclist experiences drag force as they ride. The faster they go, the more significant the drag force they encounter, which requires more power to maintain speed.

Lift and Its Interaction with Drag Forces

Lift is a force perpendicular to the direction of motion, often encountered in sports like skiing, where athletes use lift to their advantage to reduce friction.

• Example: In skiing, skiers use their body position to create lift, reducing the drag force and allowing them to move faster.

Drag Force and Speed Relationship

Drag force increases with the square of the speed of the object. Thus, doubling the speed quadruples the drag force.

Note

As speed increases, the drag force becomes more significant, requiring exponentially more energy to overcome.

Friction

Nature of Friction and Its Impact on Motion

Friction is a force that opposes the relative motion of two surfaces in contact. It plays a crucial role in sports by providing the necessary grip and control.

Static vs. Dynamic Friction

• Static Friction: The frictional force that prevents relative motion between surfaces.
• Dynamic (Kinetic) Friction: The frictional force acting when surfaces are in relative motion.
• Equation for Friction: $$ F_f = \mu F_n $$ where:
  • $F_f$ is the frictional force,
  • $\mu$ is the coefficient of friction (static or dynamic),
  • $F_n$ is the normal force.

Factors Affecting Friction

• Surface Texture: Rough surfaces increase friction.
• Normal Force: Greater normal force increases friction.
• Material Properties: Different materials have different coefficients of friction.

Example

In basketball, players rely on the friction between their shoes and the court to make quick stops and changes in direction.

Conversion of Kinetic Energy into Heat

Friction converts kinetic energy into thermal energy, which is why objects slow down and eventually stop due to friction.

Projectile Motion with Air Resistance

Effects on Distance and Height

Air resistance reduces both the distance and height of a projectile. Unlike in a vacuum, where projectiles follow a parabolic path, air resistance causes a more complicated trajectory.

Angle, Speed of Release, and Projectile Path

• Optimal Angle: Without air resistance, the optimal angle for maximum range is 45 degrees. With air resistance, this angle is less.
• Speed of Release: Higher speeds increase air resistance, reducing the range.

Example

A soccer player must account for air resistance when shooting the ball. Kicking the ball at a higher angle or speed will result in different trajectories compared to a vacuum.

Terminal Velocity

Concept of Terminal Velocity

Terminal velocity is the constant speed that a freely falling object eventually reaches when the resistance of the medium prevents further acceleration.

• Equation for Terminal Velocity: $$ v_t = \sqrt{\frac{2mg}{\rho A C_d}} $$ where:
  • $v_t$ is terminal velocity,
  • $m$ is mass,
  • $g$ is acceleration due to gravity,
  • $\rho$ is fluid density,
  • $A$ is cross-sectional area,
  • $C_d$ is drag coefficient.

Interaction of Drag Force and Gravitational Pull

At terminal velocity, the drag force equals the gravitational pull, resulting in zero net acceleration.

Air Resistance & Projectile Motion

Horizontal Component of Projectile Velocity

Air resistance reduces the horizontal velocity component, causing the projectile to decelerate more rapidly than it would in a vacuum.

Range and Maximum Height Reduction

Air resistance shortens the range and reduces the maximum height of a projectile.

Common Mistake

Ignoring air resistance in calculations can lead to overestimating the range and height of a projectile.

Hydraulics and Stream Flow

Factors Affecting Water Flow

• Gravity: Drives water flow in channels.
• Frictional Resistance: Opposes water flow, influenced by channel roughness.

Turbulent vs. Laminar Flow

• Turbulent Flow: Chaotic and irregular, increases frictional resistance.
• Laminar Flow: Smooth and regular, decreases frictional resistance.

Channel Shape and Roughness

• Shape: Wider and deeper channels reduce frictional resistance.
• Roughness: Smoother channels reduce frictional resistance.

Example

In swimming, athletes aim to reduce turbulent flow around their bodies to swim faster.

Wave Phenomena (HL Only)

Simple Harmonic Motion (SHM)

• Defining Equations: $$ x(t) = A \cos(\omega t + \phi) $$ where:
  • $x(t)$ is displacement,
  • $A$ is amplitude,
  • $\omega$ is angular frequency,
  • $t$ is time,
  • $\phi$ is phase constant.

Energy Changes in SHM

Energy in SHM oscillates between kinetic and potential forms.

Single-Slit Diffraction and Interference Patterns

• Diffraction: Bending of waves around obstacles.
• Interference: Superposition of waves leading to constructive and destructive patterns.

Doppler Effect

Change in frequency or wavelength of a wave in relation to an observer moving relative to the wave source.

Example

The Doppler Effect is observed in sports when a fast-moving ball produces a noticeable change in sound frequency as it passes by.

Impulse and Momentum

Calculating Impulse

Impulse is the change in momentum of an object when a force is applied over a time interval.

• Equation for Impulse: $$ J = \Delta p = F \Delta t $$ where:
  • $J$ is impulse,
  • $\Delta p$ is change in momentum,
  • $F$ is force,
  • $\Delta t$ is time interval.

Worked Examples

Example

A soccer player kicks a ball, applying a force of 50 N over 0.1 seconds. The impulse imparted to the ball is: $$ J = 50 , \text{N} \times 0.1 , \text{s} = 5 , \text{Ns} $$

Conclusion

Understanding the principles of friction and drag is essential in SEHS as they influence the performance and dynamics of sports activities. Mastery of these concepts allows for better analysis and optimization of athletic performance.