Module 2B

Summary of Force, Displacement, Work, and Power in Athletic Movements

Introduction to Force Summation Over Displacement

• Transitioning from summing force over time to summing force over displacement.

• Example used: Counter movement jump (CMJ).

• Key components: Force-time curve, Displacement-time curve of the center of mass.

  • A red line indicates the minimum vertical displacement (bottom of the counter movement) with zero instantaneous velocity.

• Change in velocity during the jump: Initial and final velocity both zero, resulting in no net impulse at the minimum vertical displacement.

Force Displacement Curve

• Force displacement curve combines force-time and displacement-time information.

  • Represents force based on the center of mass position.

  • Initial interpretation may seem counterintuitive due to repeating displacements during CMJ.

• Focus for analysis: only the force-displacement aspect after the red line (bottom position).

Calculating Work

• Summing force over time: Calculated by finding area under the force-time curve (Impulse).

• For force over displacement: Calculate area under the force-displacement curve.

  • This area represents work done.

• Definition of work: Amount of energy transferred through force acting over displacement.

• Important note: Zero work is done during isometric actions (e.g., Isometric Mid-Thigh Pull - IMTP) where there is force but no displacement.

Deriving Relationships from Newton's Second Law

• Analogous to impulse-momentum relationship:

  1. Forces acting on the body due to gravity:

     • Express acceleration as gravitational acceleration ( ext{g}).

     • Work can be expressed as $W = m imes g imes h$ where $h$ is vertical displacement; this represents potential energy (PE).

     • PE is energy due to the height above a reference point.

• Introduction of external force causing acceleration:

  2. Work done can be presented as $W = rac{1}{2} mv^2$.

     • Recognized as kinetic energy (KE), which is energy due to motion.

• Combined results:

  • Work done is equal to the change in potential energy plus the change in kinetic energy:
    $W = ext{PE} + ext{KE}$.

  • This indicates increased mechanical energy if work is done on a body.

Principle of Energy Conservation

• In an isolated system, total energy remains constant unless work is done on the system.

• If work is done, energy increases by the amount of work performed.

• The new energy amount remains constant until further work is applied.

• Using CMJ as an example helps visualize the transformations between potential and kinetic energy throughout the jump.

Understanding Power

• Definition of power: Rate at which work is performed.

  • Power = $rac{dW}{dt}$, indicating work done over a time period.

• Careful distinction from everyday language:

  • Athletic power is often confused with explosiveness or force generated quickly, which may not coincide with mechanical definitions.

• Moving towards instantaneous power:

  • Using calculus, instantaneous power can be expressed as:
    $P = F imes v$ where $F$ is force and $v$ is velocity.

  • Important distinctions:

    • This is instantaneous power, not the definition itself, derived from the work-energy relationship.

Application of Power in Sports Conditioning

• Peak power in CMJ testing often used to evaluate lower body power.

• Desired correlation between vertical jump height and power output:

  • Typically moderate correlation (0.6 - 0.8); improvements in power do not guarantee proportional increases in jump height.

• Contrast between peak power and impulse:

  • Impulse shows a perfect correlation with jump height and is critical for performance assessments.

  • Visual representation shows challenges in correlating peak power to net impulse, especially since peak power occurs on the descending limb of the force-time curve.

• Peak values alone may not provide comprehensive insights into vertical jump performance; reliance on net impulse yields clearer predictive power.

Limitations and Practical Implications of Power Metrics

• Discussion surrounding the effectiveness of peak power:

  • Measures focus on an arbitrary segment of the force-time curve in jumps.

• Conclusively, power values alone do not accurately capture overall engagement dynamics in explosive activities.

  • Power analysis may be more relevant in endurance activities (cycling, rowing) where mechanical energy plays a significant role in performance outcomes.

  • In contrast, energy access limitations in explosive activities may overshadow power output factors.