Work_ Power_ and Energy

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					Work, Power, and Energy

Explaining the Causes of Motion
        Without Newton
• Define mechanical work
• Distinguish the differences between
  positive and negative work
• Define energy
• Define kinetic energy
• Define gravitational potential energy
• Define strain energy
• Explain the relationship between
  mechanical work and energy
• Define power
• The explanations for the causes of motion
  described in this chapter do not rely on
  Newton's laws of motion but rather on the
  relationship between work, energy, and
• Some analyses and explanations are
  easier if based on work and energy
  relationships rather than Newtonian
• Product of force and the amount of
  displacement in the direction of that force
• Means by which energy is transferred from
  one object or system to another
• U = F(d)
  – U = work done on an object
  – F = average force applied to an object
  – d = displacement of an object along the line of
    action of the force
• Units for work are units of force time units
  of length (ft·lb or Nm)
• International units—joule (J) is the unit of
  measurement for work
• 1J = 1Nm
•   To determine the amount of work done
    on an object we need to know three
    1. Average force exerted on the object
    2. Direction of this force
    3. Displacement of the object along the line of
       action of the force during the time the force
       acts on the object
• Discus thrower exerts an average force of
  1000N against the discus while the discus
  moves through a displacement of .6m in
  the direction of this force
• How much work did the discus thrower do
  to the discus?
• A weightlifter bench-presses a 1000N barbell—
  Begins the lift with arms extended and the
  barbell 75cm above the chest—Lowers the
  barbell to 5cm above the chest—Lifts the barbell
  back to the starting position 75cm above the
  chest—Average force while lowering and lifting
  1000N upward
• How much work did the lifter do on the barbell
  from the start until the finish of the lift?
• How much work during the lowering?
• How much work during lifting?
• Work can be positive or negative
  – Positive work is done by a force acting on an
    object if the object is displaced in the same
    direction as the force—Examples?
  – Negative work is done by a force acting on an
    object when the object is displaced in the
    direction opposite the force acting on it—
• Sample Problem 4.1 (text p. 105)
• A therapist is stretching a patient—
  Therapist pushes on the patient’s foot with
  an average force of 200N—Patient resists
  the force and moves the foot 20cm toward
  the therapist
• How much work did the therapist do on the
  patient’s foot during this stretch?
• Muscles can also do mechanical work
• When a muscle contracts it pulls on points of
• Limbs move in the direction of the applied
  force—Concentric muscle action (positive work)
• Limbs move in the direction opposite the applied
  force—Eccentric muscle action (negative work)
• No movement—Isometric muscle action (no
  mechanical work)
• Capacity to do work
• Many forms (e.g. heat, light, sound,
• In sports primarily concerned with
  mechanical energy
  – Kinetic—energy due to motion
  – Potential—energy due to position
            Kinetic Energy
• Moving object has the capacity to do work
  due to its motion
• Mass and velocity of an object affects
  kinetic energy and the capacity to do work
• Kinetic energy is proportional to the
  square of the velocity
              Kinetic Energy
• KE = ½mv²
  – KE = kinetic energy
  – m = mass
  – v = velocity
• Units for kinetic energy are units of mass times
  velocity squared, or kg(m²/s²) or [kg(m/s²)]m or
  Nm or Joules
• Unit of measurement for kinetic energy is the
  same as the unit of measurement for work
            Kinetic Energy
• How much kinetic energy does a baseball
  thrown at 80mi/hr (35.8m/s) have? A
  baseball mass is 145g (.145kg).
• Determining the kinetic energy of an object
  is easier than determining the work done
  by a force, because we can measure
  mass and velocity more easily than we
  can measure force
           Potential Energy
• Energy an object has due to position
  – Gravitational—Energy due to an object’s
    position relative to the earth
  – Strain—Energy due to the deformation of an
 Gravitational Potential Energy
• Related to the object’s weight and its
  elevation or height above the ground or
  some reference point
• PE = Wh or PE = mgh
  – PE = gravitational potential energy
  – W = weight
  – m = mass
  – g = acceleration due to gravity
  – h = height
 Gravitational Potential Energy
• How much gravitational potential energy
  does a 700N ski jumper have at the top of
  a 90m jump?
• Bottom of the hill is the reference point
              Strain Energy
• Energy due to the deformation of an object
• Related to stiffness, material properties,
  and its deformation
• SE = ½kΔx²
  – SE = strain energy
  – k = stiffness or spring constant of material
  – Δx = change in length or deformation of the
    object from its undeformed position
             Strain Energy
• How much strain energy is stored in a
  tendon that is stretched .005m if the
  stiffness of the tendon is 10,000N/m?
• In human movement and sports, energy is
  possessed by athletes and objects due to
  their motion (kinetic energy), their position
  above the ground (potential energy), and
  their deformation (strain energy)
   Work—Energy Relationship
• Relationship exists between work and
  energy—Work done on an object can
  change total mechanical energy
• Discus example
  – What was the velocity of the discus at the end
    of the period of work?
   Work—Energy Relationship
• Work done = ΔKE + ΔPE +ΔSE
• Work done = ΔKE + 0 + 0
• Potential energy is zero because the
  displacement of the discus was horizontal
• m = 2kg
• U = 600J
• vi = 0m/s
• vf = ?
   Work—Energy Relationship
• The work done by the external forces
  (other than gravity) acting on an object
  causes a change in energy of the object
• U = ΔE
• U = ΔKE + ΔPE +ΔSE
Doing Work to Increase Energy
• In sports and human movement, we are often
  concerned with changing the velocity of an
• Changing velocity means changing kinetic
• Large change in kinetic energy (and thus a large
  change in velocity) requires that a large force be
  applied over a long displacement
  – Similar to impulse/momentum relationship
Doing Work to Increase Energy
• Rules for shot putting indicate that the put
  must be made from a 7ft diameter circle
• Size of the ring thus limits how much work
  the athlete can do to the shot by
  constraining the distance over which the
  putter can exert a force on the shot
• Early 20th century, shot-putters began their
  put from the rear of the ring
Doing Work to Increase Energy
• Technique has now evolved with
  shoulders turned toward rear of the circle
  in the initial stance—Allowed greater
  displacement of shot before release
• Work done on the shot increased—
  Greater height (potential energy) and
  velocity (kinetic energy) of the shot at
  release—Resulted in longer put
Doing Work to Increase Energy
• Sample Problem 4.2 (text p. 110)
• Pitcher exerts an average horizontal force of
  100N on a .15kg baseball during delivery of a
  pitch—Hand and ball move through a horizontal
  displacement of 1.5m during the period of force
  application—If the ball’s horizontal velocity was
  zero at the start of the delivery phase, how fast
  will the ball be going at the end of the delivery
  phase when the pitcher releases the ball?
Doing Work to Increase Energy
•   m = .15kg
•   F = 100N
•   d = 1.5m
•   vi = 0
•   vf = ?
•   U = ΔE
Doing Work to Decrease Energy
• When you catch a ball, its kinetic energy is
  reduced (or absorbed) by the negative work you
  do on it
• Your muscles do negative work on your limbs
  and absorb energy when you land from a jump
  or fall
• Average force you must exert to absorb energy
  in catching a ball or landing from a jump or fall
  depends on how much energy must be
  absorbed and the displacement over which the
  force is absorbed
Doing Work to Decrease Energy
• Safety and protective equipment used in many
  sports utilizes the work/energy principle to
  reduce potentially damaging impact forces
• Examples of shock absorbing or energy
  absorbing materials
  – Landing pads (gymnastics, high jumping, and pole
    vaulting) increase displacement of the athlete during
    the impact period
  – Sand (long jumper), water (diver), midsole material in
    shoes (runner)
Conservation of Mechanical Energy
• Total mechanical energy of an object is
  constant or conserved when no external
  forces (other than gravity) act on the
  object (e.g. projectile motion)
• Drop a 1kg ball from a height of 4.91m–
  Potential energy (PEi) of the ball just
  before letting go is the same as the kinetic
  energy (KEf) of the ball just before hitting
  the ground
Conservation of Mechanical Energy
• We can determine how fast the ball was
  going just before it hits the ground
• PEi = Kef
• mgh = ½mvf²
• We could also use the equation from
  Chapter 2
  – vf² = 2gy (p. 66)
Conservation of Mechanical Energy
• Pole vaulting
  – Total mechanical energy at the instant of
    takeoff should equal the total mechanical
    energy at bar clearance
  – Vaulters kinetic energy at takeoff is
    transformed into strain energy as the pole
    bends, and this strain energy is then
    transformed into potential energy
  – Height of a pole vault largely dependent on
    running speed
• Rate of doing work
• In sports, excelling requires not just the
  ability to do a large amount of work, but
  also the ability to do that work in a short
  amount of time
• Power can be thought of as how quickly or
  slowly work is done
• SI units for power are watts (W)
• 1W = 1J/s
• P = U/Δt
  – P = power
  – U = work done
  – Δt = time taken to do the work
• P = F(d)/Δt
• P = Fv
• Power can be defined as average force
  times average velocity along the line of
  action of that force
• Combination of force and velocity
  determines power output—What is the
  best tradeoff?
• Cycling—Higher gear (higher pedal forces
  and slower pedal rate) versus Lower gear
  (lower pedal forces and higher pedal rate)
• Characteristics of muscles determine the optimal
  tradeoff between force and velocity
• As a muscle’s velocity of contraction increases,
  its maximum force of contraction decreases
• If the muscle’s velocity of contraction is
  multiplied by its maximum force of contraction
  for that velocity, the muscle’s power output for
  each velocity can be determined
• Maximum power occurs at a velocity
  approximately one-half the muscle’s maximum
  contraction velocity (depending on specific
  movement and training status)
• Places a constraint on performance
• Duration of activity influences the power output
  that an individual can sustain
• Olympic weightlifter performing a clean and jerk
  (high force and high velocity) generates a VERY
  LARGE power output, but only for a brief interval
  of time
• Sprinter, middle distance runner, marathon
  runner—Power output progressively decreases
  as the length of the activity increases
• Work done by a force is the force times the
  displacement of the object along the line of
  action of the force acting on it
• Energy is the capacity to do work
• Energy can be divided into potential (position)
  and kinetic (motion)
• Potential energy can be divided into gravitational
  and strain
• The work done by a force (other than gravity)
  causes a change in energy of an object
• Power is defined as the rate of doing work