biomechanics linear kinematics

Chapter 12
Linear Kinetics of
Human Movement
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
© 2012 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

12-2
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.

12-3
Newton’s Laws
A skater has a tendency to continue gliding with
constant speed and direction because of inertia.

12-4
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

12-5
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.

12-6
Newton’s Laws
wt
R
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.

12-7
Newton’s Laws
In accordance with Newton’s third law of motion, ground
reaction forces are sustained with every footfall during
running.

12-8
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

12-9
Contact
Static
Fm = sR
Dynamic
Fk = kR
Applied external force
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.

12-10
Contact
Is it easier to
push or pull
a desk
across a
room?
Pushing a desk
Pulling a desk
R = wt + Pv
R = wt - Pv
wt
wt
P P
P P
Pv
Pv
PH
PH

12-11
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

12-12
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

12-13
Contact
What causes momentum?
impulse: the product of a force and the
time interval over which the force
acts
Ft

12-14
Contact
What is the relationship between impulse
and momentum?
Ft = M
Ft = (mv)2 - (mv)1

12-15
Contact
Force-time graphs from a force platform for high (A) and low
(B) vertical jumps by the same performer.
Force(BodyWeight)
3
2
1
Time (ms)
50 100 150 200 250
A
Time (ms)
3
2
1
50 100 150 200 250
B
What does the area under the curve represent?

12-16
Contact
What is impact?
a collision characterized by:
• the exchange of a large force
• during a small time interval

12-17
Contact
What happens following an impact?
This depends on:
• the momentum present in the system
• the nature of the impact

12-18
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.

12-19
Contact
What does the coefficient of restitution (e)
describe?
relative velocity after impact
-e = relative velocity before impact
v1 - v2
-e = u1 - u2

12-20
Contact
Ball velocities before impact
Ball velocities after impact
u1 u2
v1 v2
v1 - v2 = -e ( u1 - u2)
The differences in
two balls’ velocities
before impact is
proportional to the
difference in their
velocities after
impact. The factor of
proportionality is the
coefficient of
restitution.

12-21
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.)

12-22
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)

12-23
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)

12-24
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

12-25
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)

12-26
Relationships
During the pole vault, the bent pole stores potential energy for
subsequent release as kinetic energy and thermal energy.

12-27
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)

12-28
Relationships
29.4
24.5
19.6
14.7
9.8
0
3.1
4.4
5.4
6.3
0
4.9
9.8
14.7
19.6
3.0
2.5
2.0
1.5
1.0
Ht(m) PE(J) V(m/s) KE(J)
Time
Height,
velocity,
potential
energy, and
kinetic energy
changes for a
tossed ball.
Note:
PE + KE = C

12-29
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)

biomechanics linear kinematics

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