Linear Energy and Kinetics

Linear Energy Overview

  • Concepts in Linear and Angular Kinematics

    • Chapters Overview:

    • Chapter 9: Linear Kinematics

    • Chapter 10: Angular Kinematics

    • Chapter 11: Linear Kinetics

    • Chapter 12: Angular Kinetics

  • Additional Review Sources:

    • Canvas: Set06B PS, W&Z C 3 Basic Biomechanics

    • KJF Physics Textbook: Chapters 4-6, 9

    • Khan Academy: AP/College Physics 1

Kinematics vs Kinetics

  • Kinematics:

    • Area focused on motion components:

    • Linear Position, Velocity, Acceleration (P, V, A)

    • Angular Position, Velocity, Acceleration (Θ, ω, α)

    • Time (t)

  • Kinetics:

    • Examines causes of motion:

    • Mainly forces

    • Includes torque, impulse, momentum, work, power, energy

Energy Basics

  • Definition:

    • Energy is the capacity to perform work.

    • Units:

    • Joules (J), where 1 J = 1 Nm

  • Types of Mechanical Energy:

    • Kinetic Energy (KE):

    • Formula: KE = 1/2 m v²

    • Gravitational Potential Energy (PEg):

    • Formula: PEg = m * g * h

    • Where g = acceleration due to gravity, h = height

    • Potential Strain Energy (PEs):

    • From deformation

    • Formula: PEs = 1/2 k Δx²

    • k = spring constant (stiffness)

Work-Energy Relationship

  • Work (U) is equal to the change in an object's energy:

    • Formula:

    • U = ΔME + Q (where Q = non-conservative energy losses)

    • U = work from external forces excluding gravity

    • Change in Energy:

    • U = ΔKE + ΔPEg + ΔPEs + Q

Example of Kinetics and Energy Transformation (Runner with Air Resistance)

  • Forces Affecting Motion:

    • Fgx – Fa = m·ax (forces along x-axis)

    • Fgy – Fw = m·ay (forces along y-axis)

Application in Exercises (e.g., Biceps Curl)

  • Energy transformations when executing a bicep curl can be modeled as:

    • U = ΔKE + ΔPEg

    • Where U = F̄ · Δp

    • The change in energy corresponds to the mechanical work done.

Lifting and Lowering Objects

  • Forces and Work for Raising/Lowering Objects:

    • Average force required equals the weight of the object.

    • Formula relationship:

    • U = ΔKE + ΔPEg + ΔPEs + Q

  • For Horizontal Movement:

    • Average force required equals zero if net displacement is zero.

Effects of Friction on Work

  • Work required for lifting/lowering an object increases if friction is present:

    • U = m * g * h + Q (friction)

Hooke's Law and Spring Energy

  • Formula:

    • Fs = -k ∙ Δx ( (spring force) )

    • k = spring constant (N/m)

    • Restoring force direction is opposite to displacement.

  • Work done on the spring:

    • Potential Energy in Spring:

    • U = 1/2 k Δx²

    • Energy is derived from the area under the force vs. displacement curve.

Example Calculation with Springs

  • Example: Stretching a TheraBand:

    • If k = 500 N/m and Δx = 0.1 m:

    1. Calculate force required:

      • Fs = 500 * 0.1 = 50 N

    2. Calculate work done:

      • U = 1/2 * 500 * (0.1)² = 2.5 J

    3. Average force required:

      • F̄ = 1/2 * k * Δx = 25 N

Conclusion

  • Understanding energy types and their transformations is crucial for analyzing movement and performance in sports like volleyball and exercises.