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```Chapter 12
Linear Kinetics of
Human Movement
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
McGraw-Hill/Irwin
Newton’s Laws
What is the law of inertia?
A body will maintain a state of rest or
constant velocity unless acted
on by an external force that
changes the state.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-2
Newton’s Laws
A skater has a tendency to continue gliding with
constant speed and direction because of inertia.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-3
Newton’s Laws
What is the law of acceleration?
A force applied to a body causes
acceleration of that body
• of a magnitude proportional to the
force
• in the direction of the force
• and inversely proportional to the
body’s mass
F = ma
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-4
Newton’s Laws
What is the law of reaction?
• For every action, there is an equal
and opposite reaction.
• When one body exerts a force on a
second, the second body exerts a
reaction force that is equal in
magnitude and opposite in
direction on the first body.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-5
Newton’s Laws
In accordance with the
law of reaction, the weight
of a box sitting on a table
generates a reaction force
by the table that is equal
in magnitude and
opposite in direction to the
weight.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
wt
R
12-6
Newton’s Laws
In accordance with Newton’s third law of motion, ground
reaction forces are sustained with every footfall during
running.
Basic Biomechanics, 6 edition
th
By Susan J. Hall, Ph.D.
12-7
Mechanical Behavior of Bodies in
Contact
What is friction?
A force acting over the area of contact
between two surfaces
• direction is opposite of motion or
motion tendency
• magnitude is the product of the
coefficient of friction () and the
normal reaction force (R)
F = R
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-8
Mechanical Behavior of Bodies in
Contact
Static
Fm = sR
Dynamic
Fk = kR
Friction
For static (motionless)
bodies, friction is
equal to the applied
force. For dynamic
bodies (in motion),
friction is constant
and less than
maximum static
friction.
Applied external force
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-9
Mechanical Behavior of Bodies in
Contact
P
P
PH
Pv
Is it easier to
push or pull
a desk
across a
room?
wt
Pushing a desk
R = wt + Pv
P
P
Pv
wt
PH
Pulling a desk
6th
Basic Biomechanics,
edition
By Susan J. Hall, Ph.D.
R = wt - Pv
12-10
Mechanical Behavior of Bodies in
Contact
What is momentum?
• quantity of motion possessed by a
body
• measured as the product of a body’s
mass and its velocity;
M = mv
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-11
Mechanical Behavior of Bodies in
Contact
What is the principle of conservation of
momentum?
In the absence of external forces, the
total momentum of a given system
remains constant.
M1 = M2
(mv)1 = (mv)2
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-12
Mechanical Behavior of Bodies in
Contact
What causes momentum?
impulse: the product of a force and the
time interval over which the force
acts
Ft
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-13
Mechanical Behavior of Bodies in
Contact
What is the relationship between impulse
and momentum?
Ft = M
Ft = (mv)2 - (mv)1
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-14
Mechanical Behavior of Bodies in
Contact
Force (Body Weight)
What does the area under the curve represent?
3
3
B
A
2
2
1
1
50
100
150 200 250
50
Time (ms)
100
150 200 250
Time (ms)
Force-time graphs from a force platform for high (A) and low
(B) vertical jumps by the same performer.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-15
Mechanical Behavior of Bodies in
Contact
What is impact?
a collision characterized by:
• the exchange of a large force
• during a small time interval
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-16
Mechanical Behavior of Bodies in
Contact
What happens following an impact?
This depends on:
• the momentum present in the system
• the nature of the impact
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-17
Mechanical Behavior of Bodies in
Contact
What happens during impact?
This is described by the coefficient of
restitution, a number that serves
as an index of elasticity for
colliding bodies; represented as
e.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-18
Mechanical Behavior of Bodies in
Contact
What does the coefficient of restitution (e)
describe?
relative velocity after impact
-e = relative velocity before impact
v1 - v2
-e = u1 - u2
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-19
Mechanical Behavior of Bodies in
Contact
The differences in Ball velocities before impact
u1
u2
two balls’ velocities
before impact is
proportional to the
difference in their
velocities after
impact. The factor of
v1
v2
proportionality is the
coefficient of
Ball velocities after impact
restitution.
v1 - v2 = -e ( u1 - u2)
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-20
Mechanical Behavior of Bodies in
Contact
What kinds of impact are there?
• perfectly elastic impact - in which the
velocity of the system is conserved;
(e = 1)
• perfectly plastic impact - in which there
is a total loss of system velocity;
(e = 0)
• (Most impacts fall in between perfectly
elastic and perfectly plastic.)
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-21
Work, Power, and Energy
Relationships
What is mechanical work?
• the product of a force applied against a
resistance and the displacement of
the resistance in the direction of the
force
W = Fd
• units of work are Joules (J)
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-22
Work, Power, and Energy
Relationships
What is mechanical power?
• the rate of work production
• calculated as work divided by the time
over which the work was done
W
P= t
• units of work are Watts (W)
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-23
Work, Power, and Energy
Relationships
What is mechanical energy?
• the capacity to do work
• units of energy are Joules (J)
• there are three forms energy:
• kinetic energy
• potential energy
• thermal energy
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-24
Work, Power, and Energy
Relationships
What is kinetic energy?
• energy of motion
KE = ½mv2
What is potential energy?
• energy by virtue of a body’s position or
configuration
PE = (wt)(ht)
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-25
Work, Power, and Energy
Relationships
During the pole vault, the bent pole stores potential energy for
subsequent release as kinetic energy and thermal energy.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-26
Work, Power, and Energy
Relationships
What is the law of conservation of
mechanical energy?
When gravity is the only acting external
force, a body’s mechanical energy
remains constant.
KE + PE = C
(where C is a constant - a number that
remains unchanged)
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-27
Work, Power, and Energy
Relationships
Ht(m) PE(J)
Height,
velocity,
potential
energy, and
kinetic energy
changes for a
tossed ball.
Note:
PE + KE = C
V(m/s) KE(J)
3.0
29.4
0
0
2.5
24.5
3.1
4.9
2.0
19.6
4.4
9.8
1.5
14.7
5.4
14.7
1.0
9.8
6.3
19.6
Time
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-28
Work, Power, and Energy
Relationships
What is the principle of work and energy?
The work of a force is equal to the
change in energy that it produces in
the object acted upon.
W = KE + PE + TE
(where TE is thermal energy)
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
12-29
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