Work-Energy Theorem

• Principles: Transfer of Energy

  • Transfer of energy is the mechanism by which energy is passed from one body to another
  • Work is required to transfer energy
• Principles: Transfer of Energy

  • Transfer from one system to another
  • Not perfectly conserved as some energy is lost by friction, air resistance, heat (with contact from friction), sound - all take energy so slows down over time
  • Closed system no other energy can be put in
• Principles: Transfer of Energy

  • What happens to system after put work on it (when no work is occurring)
  • Transfer energy from one system (you) to another (ball)
  • More energy transfer further its going to go
  • Either get more energy by more strength or back ball more absorptive
  • eg golf ball flat with contact and releases as teardrop shape (point at club); amount of energy stored changes shape of ball
  • Amount of deformation increases with more work
  • Materials/elasticity of ball help increase energy transfer
• Work-Energy Theorem:

  • The energy associated with the work done by the net force doesn’t disappear after the net force is removed (or becomes 0), it is transformed into the Kinetic Energy of the body
  • We call this the Work Energy Theorem
  • W = E2 - E1
  • The net work done by all forces acting on the body equals the change in kinetic energy
• Work-Energy Theorem:

  • If we want it to absorb or return/release the energy
  • Bike helmets to release energy by dejoining bonds (chuck away after crash), plastic shell for lower friction when hit ground to stop head rotating (there to skid) - so if have crack also chuck away
  • Cricket helmet takes a lot of hits/repeated impacts
  • Hockey helmet: resilient material (designed to deform in particular way), spread area of deformation (over shell of helmet), when recoils shoot ball back out/returns energy; good for high velocity not low (such as concussion - different)
• Work-Energy Theorem:

  • If we want it to absorb or return/release the energy
  • Ball designed to absorb & return energy
  • If not designed for it system breaks because not made to return energy so all that it can do is release it (de-join bonds)
  • So if put to much energy into body/muscles/ligaments get injuries
• Work-Energy:

  • We apply a force on the ball through a distance which increases the velocity of the ball from 0 to its release velocity
• Work-Energy Theorem:

  • Work changes the energy of the system
  • W = E2 - E1
  • We can show this mathematically
  • W = F x a
  • W = m a s
  • a s = vi^2 =vi^2 + 2as →
  • Vf^2 = vi^2 / 2 = as →
  • W = m (vi^2 - vi^2 / 2)
  • W = ½ mvi^2 - ½ mvi^2
• Work-Energy Example: Landing

  • At point A
  • EP1 = mgh
  • EK1 = ½ mv1^2
  • TMEA = EP1 + EK1
  • At point B
  • E21 = mgh
  • EK2 = ½ mv2^2
  • TMEB = EP2 + EK2
  • At point C
  • EP3 = mgh
  • EK3 = ½ mv3^2 = 0 (bc/ v = 0)
  • TMEC = EP3 + EK3
• Work-Energy Example: Landing

  • Work changes the energy of the system
  • bw/ A & B
  • mg is the only force
  • Ep is transferred to Ek
  • Is there work done?
  • Hint: Remember the rule about conservation of energy
  • TMEA = TMEB
• Work-Energy Example: Landing

  • bw/ A & C
  • External Ground Force acts on the body
  • Is there work done?
  • TMEC ≠ TMEA
  • Work = ΔEK
  • W = TMEC = TMEA
  • Work = (mgh3 + ½ mv3^2) = (mgh1 + ½ mv1^2)
  • or
  • Work = mgh3 - (mgh1 + ½ mv1^2)
• Work-Energy Example: Landing

  • Work landing = mgh3 - (mgh1 + ½ mv1^2)
  • What does this equation tell us about landing?
  • A large amount of work needs to be done on a body at landing when:
  • The body takes off from a high position
  • To body lands at a low position
  • The body has a large velocity at take-off
  • The weight (mass) of the body is large
• Injury of Hamstrings:

  • Hamstring is doing work on the shank to change the kinetic energy of the knee
  • Hamstring acts as damper to absorb energy out of shank to protect knee (hamstring doing work = F * d (Work) = contraction of muscle (F) change in length of hamstring (d) = elongates)
  • If can't control velocity injury as it elongated, too much energy cause it to snap - hip flexors to strong
  • Too much for hamstrings to absorb/control
• Why is walking more efficient than running? Walking vs running:

  • Running cost more energy
  • bc/ have to propel/move CoM
  • Walking CoM
  • Mid swing mass highest, lower at toe off (when providing most kinetic energy)
  • Conservation of energy more in walking (transfer bw/ potential & kinetic)
  • When you run:
  • CoM at lowest during heel strike, at toe off = highest point of CoM (no trade off bw them, almost mirror each other)
  • More energy bc/ less benefit from trade off bc/ work at same time so have to do more work to move CoM
• Why is walking more efficient than running? Walking vs running:

  • Main difference is that running has a flight phase (is conserved), have to propel so both energies used to get that flight
  • Similar to tramp
  • Work together at toe off more mechanical & physiological work
  • Running overloads system to stimulate metabolic response