L25 - Energy

• Defining Energy:

  • Definition: the capacity or ability to do work
  • Many forms:
  • Thermal, chemical, nuclear, electromagnetic & mechanical
  • Mechanical Energy is measured in Joules (J)
  • Produced from muscle & what sporting equipment is designed for
  • To absorb or transfer energy
• Mechanical Energy Forms:

  • Kinetic energy - related to a body’s motion
  • Linear or rotational
  • Linear kinetic energy is calculated as 1/2 the body’s mass (m) multiplied by the square of its velocity (v)
  • Ek = (½ * m) * v^2
  • Velocity more important as it is squared
  • Rotational kinetic energy is calculated using the mass moment of inertia (I) of the body in motion & its angular velocity (ω)
  • E<k = ½ * I * ω^2
• Mechanical Energy Forms:

  • Potential energy - energy of position or deformation
  • 2 forms

  1. Gravitational potential energy, which is the potential of a body to do work as a function of height (h) with respect to a reference surface where g is gravitational acceleration
  2. Deformation energy or strain energy, which is the energy stored in a body by virtue of its deformation
• Mechanical Energy Forms:

  1. Gravitational potential energy, which is the potential of a body to do work as a function of height (h) with respect to a reference surface where g is gravitational acceleration

  • Ep = m * g * h
  • Height = CoM from the ground
• Mechanical Energy Forms:

  • 2. Deformation energy or strain energy, which is the energy stored in a body by virtue of its deformation
  • Mathematically describing the amount of energy will depend upon the material properties of the deformable body
  • Ie no single equation can describe the deformation of all bodies
  • More important for sport performance & equipment
  • Deforms to absorb energy, to give energy back to system
• Mechanical Energy Forms - Deformation:

  • Es = ½ * k * Δ x^2
  • k = constant; each material have a strain factor/constant
  • How much resistance to deformation
  • Protective equipment look at k value (resistance to deform), how much energy store in equipment (so not transferred to body)
  • Guidelines for k for most sports like sprinting & pole vaulting
  • Change in Δx^2 = the distance
  • eg a string in a bow, how much energy can store in bow
  • pole vault, how much reform & how much returned
  • How much bend/flex in hockey stick (more weight, more flex), bending stick allows to put more energy into hitting the puck
• Assumptions: Mechanical Energy:

  • Total mechanical energy (TME) is the sum of the linear kinetic, angular kinetic, & positional potential energy + strain energy
  • Sum of all forms of energy
  • TME = Ek + E<k + Ep = ( ½ m v^2 ) + ( ½ I ω^2 ) + (m g h)
  • TME = scalar quantity
  • Ignore strain as assume bones are rigid & changing
  • Is a bad assumption as bones do deform (all the time)
  • Mechanical strain is what makes them strong
  • Equations is hard to know how much deformation is taking place at bone so is ignored
  • Although… We often assume the body is rigid or non deformable
• Principles: Conservation of Energy:

  • Gravity is a conservative Force
  • If primary external force (in the air/falling)
  • When gravity is the only acting external force a body’s mechanical energy remains constant
  • (PE + KE) = C
  • PE = potential energy; KE = Kinetic energy
  • C = conserved/constant
  • Won’t change when in air, but the potential & kinetic energy trade off
  • Peak = 0 velocity/kinetic energy, all potential energy
  • As get further from peak = potential energy decrease, kinetic energy increase
• Principles: Conservation of Energy:

  • What are some of the key points in this statement?
  • Energy is neither created or destroyed (thermal dynamics)
  • Can’t generate/create energy that way
  • Lose in one gain in the other (trade off bw/ potential & kinetic energy)
  • Have to be in the air, no other forces acting on you (energy conserved in air)
• Principles: Conservation of Energy (ball example):

  • Total Energy = Ek + Ep

  1. Max velocity = max kinetic energy
  2. As the ball ascend the potential energy increases while kinetic energy decreases bc/ gravity is slowing the flight
  3. At the peak of trajectory the v^2 of the ball = 0 thus no kinetic energy. h = maximum = max potential energy
  4. Downward flight the reverse change in energy occurs
• Principles: Conservation of Energy (ball example):

  • Experiment: throwing ball look at transfer of energy
  • Moment released greatest velocity lowest potential; as move up velocity decreased and potential increased
  • Potential highest at peak height
  • When closed system, no other external forces acting
• Principles: Conservation of Energy:

  • Trampolining/gymnastics
  • Energy from mat, same idea as above
• Law of Conservation of Mechanical Energy:

  • If the resultant force acting on a body is a conservative force then the body’s total mechanical energy will be conserved
  • Resultant force will be conservative if all external forces are conservative
  • A force is conservative if it does no work around a closed path (motion cycle)