Download Work, Power, and Energy

Work, Power, and Energy
Explaining the Causes of Motion
Without Newton
Objectives
• Define mechanical work
• Distinguish the differences between
positive and negative work
• Define energy
• Define kinetic energy
Objectives
• Define gravitational potential energy
• Define strain energy
• Explain the relationship between
mechanical work and energy
• Define power
Introduction
• 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
power
• Some analyses and explanations are
easier if based on work and energy
relationships rather than Newtonian
mechanics
Work
• 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
Work
• 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
Work
•
To determine the amount of work done
on an object we need to know three
things:
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
Work
• 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?
Work
• 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?
Work
• 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—
Examples?
Work
• 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?
Work
• Muscles can also do mechanical work
• When a muscle contracts it pulls on points of
attachment
• 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)
Energy
• Capacity to do work
• Many forms (e.g. heat, light, sound,
chemical)
• 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
object
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
object
• Changing velocity means changing kinetic
energy
• 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
Power
• 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
Power
• 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
• 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)
Power
• 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)
Power
• 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
Summary
• 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