Transcript Forces and COM

Force and Motion Relationships
• Instantaneous Effect of force on motion is
to accelerate the object: F=ma
• Force applied through a distance: workenergy relationship
• Force applied through a time: impulsemomentum relationship
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:
Impulse-Momentum Relationship
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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)
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?
Force Applied Through a Distance: Work,
Power, Energy
• 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
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
• Homework:
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
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
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
Vector Resolution Problems
• Projectile motion situations
– Find horizontal velocity
– Find vertical velocity
• Friction problems
– Find horizontal force component (Friction)
– Find vertical component (Normal)
• First step in adding, or combining vectors
– When more than one force is acting on an object
– When adding velocity vectors
Vector resolution:
Vert comp = F•sin•Θ
Horiz comp = F•cos•Θ
Θ
Θ
Vert comp = F•sinΘ
Horiz comp = F•cosΘ
Θ
Θ
d
Θ
Turning comp = F•d•sinΘ
Radial comp = F•d•cosΘ
(d = d•sinθ)
Vector Addition Problems
• Combining forces
– Net effect of two forces applied to any object
– What is maximum safe speed for a curve?
• Centrifugal force, frictional force, & gravity
– What makes a spitball work?
• Wind force and weight
• Combining velocities
– In crossing a river, what direction is best?
• Velocity of water and swimmer
– In aviation, correcting for wind
• air speed and ground speed
Sum of two forces:
Sum of two velocities:
(May be deleted if your calculator provides
resultant angle in a 0-360 deg system)
COM Questions
• What is COM (or COG) and why is it important?
• How is COM location different for infants and how does
this affect their movement?
• Is COM location different for men vs women?
• How is COM different if you lose an arm and how does
this affect movement?
• How does COM relate to stability?
• Why do you lean to one side when carrying a load with
one arm?
• Can Vince Carter, or any athlete really hang in the air?
COM/COG Concept and Calculation
Method (Adrian pp 33-41)
• Center of Mass (COM)
• Concept of balancing segmental torques
• Segmental Calculation of COM
– General calculation method
– Information needed
• Proportionate mass of each segment
• location of COM of each segment
Segmental concept of center of mass
Segmental concept of center of mass