Transcript Forces and COM

Week 11 – Linear Kinetics –
Relationship between force and motion
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Read Chapter 12 in text
Classification of forces
Types of forces encountered by humans
Force and motion relationships
– Instantaneous effect – Newton’s law of acceleration (F=ma)
– Force applied through time (Impulse-momentum)
• Conservation of Momentum
– Force applied through distance (work-energy)
• Conservation of Energy
• Problems
– Introductory problems, p 411: 1,3,5,7,8,10
– Additional problems, p 412: 6,8,9
Classification of Forces
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Action vs reaction
Internal vs external
Motive vs resistive
Force resolution – horizontal and vertical
components
• Simultaneous application of forces – determining
the net force through vector summation
Types of external forces encountered by
humans
• Gravitational force (weight = mg)
• Ground Reaction Force (GRF)(Figure 12-4, p 386)
– Vertical
– Horizontal (frictional)
• Frictional force (coefficient of friction) (pp 389-395)
• Elastic force (coefficient of restitution) (pp 399-402)
• Free body diagram - force graph (p 63)
Force Plates –
Measurement of ground
reaction forces
While walking
Cfr = Frf /Nof
Sample Prob
# 2, p 392
Coefficient of restitution: Sample problem #5, p 402
Free body diagrams:
Instantaneous Effect of Force on
an Object
• Remember the concept of net force?
• Need to combine, or add forces, to
determine net force
• Newton’s third law of motion (F = ma)
• Inverse dynamics – estimating net forces
from the acceleration of an object
• Illustrations from Kreighbaum: Figures F.4,
F.5, and F.6 (pp 283-284)
Force Applied Through a Time: ImpulseMomentum Relationship (pp 295-399)
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Force applied through a time
Impulse - the area under the force-time curve
Momentum - total amount of movement (mass x velocity)
An impulse applied to an object will cause a change in its
momentum (Ft = mv)
• Conservation of momentum (collisions, or impacts)
– in a closed system, momentum will not change
– what is a closed system?
Impulse: area
under forcetime curve
Impulse produces
a change in
momentum (mV)
Sample problem
#4, p 397
Vertical
impulse
While
Running:
Area under
Force-time
curve
Anterioposterior
(frictional)
component
of GRF: impulse
Is area under
Force-time curve
Positive and
Negative impulse
Are equal if
Horizontal comp
Of velocity is
constant
Conservation of momentum: when net impulse is zero
(i.e. the system is closed), momentum does not change
Conservation of momentum: is this a closed system?
Sample prob
#3, p 396
Force Applied Through a Distance: Work,
Power, Energy (pp 403-409)
• Work - force X distance (Newton-meters, or Joules)
– On a bicycle: Work = F (2r X N)
– On a treadmill: Work = Weightd X per cent grade
• Power - work rate, or combination of strength and
speed (Newton-meters/second, or watts)
– On a treadmill: P = Weightd X per cent grade/ time
– On a bicycle: P = F (2r X N) / time
• What about kilogram-meters/min?
• Energy - capacity to do work
– kinetic, the energy by virtue of movement (KE = 1/2 mv2 )
– gravitational potential, energy of position (PE = Weight x
height)
– elastic potential, or strain, energy of condition (PE = Fd)
Work while pedaling on bicycle:
From McArdle and Katch.
Exercise Physiology
Work while running on treadmill:
From McArdle and Katch. Exercise Physiology
Note that %grade = tan θ X 100,
and tan θ and sin θ are very
similar below 20% grade
Homework: Calculating Power
on a Treadmill
• Problem: What is workload (power) of a 100 kg
man running on a treadmill at 10% grade at 4 m/s?
• Solution:
– Power = force x velocity
– Force is simply body weight, or 100 x 9.8 = 980 N
– Velocity is vertical velocity, or rate of climbing
• Rate of climbing = treadmill speed x percent grade = 4 m/s x .1 = .4 m/s
– Workload, workrate, or power = 980N X .4 m/s = 392 Watts
• Note: 4 m/s = 9 mph, or a 6 min, 40 sec mile
• Calculate your workload if you are running on a treadmill
set at 5% grade and 5 m/s.
– Answer for 200 lb wt is: 223 Watts
Power running up stairs:
Work rate = (weight X vertical dist) ÷ time
Sample prob
#6, p 405
Conservation of Energy
• In some situations, total amount of mechanical energy
(potential + kinetic) does not change
– Stored elastic energy converted to kinetic energy
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diving board
bow (archery)
bending of pole in pole vault
landing on an elastic object (trampoline)
– Gravitational potential energy converted to kinetic energy
• Falling objects
• Videodisk on pole vault
Energy conservation – Case I : elastic potential (strain) and kinetic
Potential energy (FD) +
Kinetic energy (1/2mv2)
remains constant
Energy conservation – Case II : gravitational potential and kinetic
Potential energy
(Wh) + kinetic
energy (1/2mv2)
remains constant
Linear Kinetics Formulae