Download LINEAR KINETICS (PART 2): WORK, ENERGY, AND POWER

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LINEAR KINETICS (PART 2):
WORK, ENERGY, AND POWER
Readings: McGinnis Chapter 4
WORK: Another way of expressing the effect of a
force. Mechanically, work is done on an object
when a force causes a change in position.
The work done on a body by a force is equal
to the product of its magnitude and the
distance the body moves in the direction of
the force while the force is being applied to it.
[so d actually stands for the component of
displacement parallel to the force.]
Units of measurement: N⋅m
1 N⋅m of work = 1 joule (J)
Simple examples:
1. Weight lifting: Lifting a 750 N barbell 0.4 m
from the floor...
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Average force applied to the barbell?
Will the force be constant?
Distance through which the force is
applied?
W = (750 N)(0.4 m) = ______ = ______
2. Walking up a flight of stairs...
Effectively raising body weight some
vertical distance d represented by the
height of the stairs.
e.g., A person weighing 700 N climbs a
flight of stairs containing twenty (20) 25
cm steps. Average force needed to raise
body weight?
Total vertical distance?
d = (20)(25 cm) = ______ = _____
W = (700 N)(5 m) = _______= ______
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3. An aerobic step routine...
550 N aerobics instructor
15 cm steps (6 inches or 0.15 m)
600 steps (e.g., 60 steps per minute for 10
minutes)
Total distance body cg raised = (600
steps)(0.15 m/step) = ______
W=
We’ve focused on the positive work (lifting
the body). What about lowering the body?
Is there work done moving down?
Yes, gravity does work on the body as
the muscles resist the effort (i.e.,
eccentric muscle activity). During
eccentric activities, muscles are doing
“negative work.”
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From a human performance
perspective, negative work by muscles
is important:
a) it costs energy to do negative work
b) eccentric muscle activity is a major
contributor to ______________
4. Isometric muscle activity:
e.g., weightlifter applies 800 N force to barbell
but is unsuccessful in lifting it...
How much work is done?
Must be displacement in the direction
of the force in order for there to be
measurable work done by the force.
Thus far, no mention of time required for work to
be done...
e.g., previous stair climbing example:
700 N person, vertical rise = 5 m
Slowly (e.g., 20 s) vs. rapidly (e.g., 5 s)?
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Work done in each case?
W = (700 N)(5 m) = 3500 J
Same for both regardless of time (i.e.,
regardless of task intensity).
The rate at which work is being done (i.e., an
indicator of task intensity) = Power.
POWER (or power output): _________________:
P = W / (∆t)
Power—best mechanical indicator of the intensity
of physical task.
Analogous to VO2 from physiology.
Metric unit for power: watt (W)
U.S. or English unit: horsepower (hp)
1 hp = 746 W
Previous stair climbing example...
W = 3500 J Case 1: ∆t = 20 s,
Case 2: ∆t = 5 s
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Average Power?
Case 1:
P = (3500 J)/(20 s)
= _______ = ______
Case 2:
P = (3500 J)/(5 s)
= ______ = ______
Realistic power output values for the human
body?
Power capabilities of the human body?
Wingate anaerobic power task?
Well-trained distance cyclist?
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Ability to sustain power varies dramatically with
the duration of the task...
2.0
Power
(hp) 1.5
(1492 W)
(746 W)
Sprinting:
~1.5-2.0 hp
Distance running:
~0.5 hp
1.0
0.5
0
10
20
30
40
50
60
Duration of run (min)
Other engines:
75 cc motorcycle: 5 hp
250 cc motor: 20-35 hp
kitchen mixer: 0.1 hp
Human body...
not a “powerful” machine, but versatile.
Power can be applied in many ways for many
tasks.
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Components of human power production:
Strength (force producing ability combined
with speed (or velocity)...
P = W /(∆t) = (F·d)/(∆t)
since d/(∆t) = avg. velocity
P = F·v (average power)
P = F·v (instantaneous power)
“Powerful”
e.g., Automobile - main advantage of high hp
engine is not so much in producing a high
top speed but rather in generating high
acceleration (e.g., 0-60 mph in short time)
e.g., Human sprinter - high power output
capability is especially important to
success...Tied to ability to accelerate to
top speed. Capability of producing high
muscle forces with relatively high speeds
of muscle shortening
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Link to metabolic energy cost...
Stair climbing: Twenty 25 cm steps in 20
seconds by a 700 N person...
W = (700 N) (20)(25 cm) = (700 N)(5 m)
= ________
P = 3500 J / (20 s) = ______ = ______
This represents a low to moderate intensity
for a physically active, young adult.
Since 1 calorie (i.e., 0.001 Kcal) = 4.187 J
(or 1 J = 0.239 cal), the power output of the
stepping task can be converted to other units
of measurement:
P = (175 J/s)(.239 cal/J) =
=
=
=
41.8 cal/s
0.0418 Kcal/s
2.51 Kcal/min
150.5 Kcal/hr
Remember, this is the mechanical power
output.
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If the body is 25% efficient in converting
metabolic energy to mechanical energy, the
metabolic energy cost of the task would be 4
times greater than the mechanical power
generated...
(150.5 Kcal/hr) (4) = 602 Kcal/hr
This is our estimate of the rate of
metabolic energy consumption.
Stated differently, if a candy bar contains
300 Kcal, it would require about 30
minutes to burn off that candy bar, or
almost 6 hours to expend 3500 Kcal (1
lb. of fat).
Challenge of the day: Estimate the rate of
energy consumption for the aerobics
instructor in example 3.
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ENERGY: Broadly defined as
“the capacity to do work.”
Three forms of mechanical energy...
An object has energy by virtue of its motion
(kinetic energy), position (potential energy),
and/or state of deformation (strain energy):
1. Kinetic energy (KE)—energy of ______...
KE = ½ mv2
i.e., any body in motion will possess kinetic
energy
e.g., a 60 kg sprinter traveling at 10 m/s
KE = (½)(60 kg)(10 m/s)2
= 3000 kg·m2/s2 = _______
2. Potential energy (PE)—energy associated
with an object's vertical position with respect
to some arbitrary reference height, usually the
ground...
PE = Wh = mgh
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where W is weight (which = mg) and h is
height.
e.g., the mechanical energy of a 1.3 N (0.13
kg) baseball thrown vertically at 10 m/s...
At instant of release (h=0),
PE =
=
KE =
=
At peak height (5 m),
PE =
=
KE =
=
Upon returning to release position,
PE =
=
KE =
=
Note the direct exchange between PE and KE
PE is greatest when ball is at its highest
vertical position, and when gravity is the only
external force acting on an object, its
mechanical energy is _______. (Gravity is
said to be a “Conservative Force”.)
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Work-Energy Theorem:
Because work and energy have the same
units (J), you would suspect that there is a
relationship between the two.
This relationship is very similar to Newton’s
Second Law (and derived from it).
The Work-Energy Theorem states that the
work done by the resultant force acting on a
body equals the change in ___________ of
the body.
Example:
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One final mechanical energy form of interest:
3. Strain energy (SE)...
Whenever an object has the ability to return to
its original shape after being deformed...
(e.g., tennis ball during impact, rubber
band being stretched)
it is said to possess strain energy when
deformed.
e.g., an archery bow has the capacity to do
work on an arrow (i.e., strain energy) when
deformed by drawing the string back.
A useful concept when considering
impacts/collisions...
e.g., a bouncing ball
During each impact, KE from ball’s fall is
converted to SE during deformation. SE
is then converted back to KE during
restitution (during return to original
shape). Because collisions are not
perfectly elastic, some mechanical
energy is lost as heat (bounce height
gradually decreases).