1. Linear Kinetics of Human Movement
Chapter 12
Linear Kinetics of Human Movement
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.
© 2014 The McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/Irwin

2. Basic Biomechanics, 7th edition
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, 7th edition
By Susan J. Hall, Ph.D.

3. Basic Biomechanics, 7th edition
Newton’s Laws
For example, a skater has a tendency to continue gliding with constant speed and direction because of inertia.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

4. Basic Biomechanics, 7th edition
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, 7th edition
By Susan J. Hall, Ph.D.

5. Basic Biomechanics, 7th edition
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, 7th edition
By Susan J. Hall, Ph.D.

6. Basic Biomechanics, 7th edition
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. wt R
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

7. Basic Biomechanics, 7th edition
Newton’s Laws
In accordance with Newton’s third law of motion, ground reaction forces are sustained with every footfall during running.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

8. Basic Biomechanics, 7th edition
Newton’s Laws FH FV F
Better sprinters are able to generate a forward-directed horizontal component (FH) of the total ground reaction force (F).
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

9. Basic Biomechanics, 7th edition
Newton’s Laws
Typical ground reaction force patterns for rearfoot-strikers and others. Runners may be classified as rearfoot-, midfoot-, or forefoot-strikers according to the portion of the shoe that usually contacts the ground first.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

10. Basic Biomechanics, 7th edition
Newton’s Laws
The vertical ground reaction force (GRFv) for a classic countermovement vertical jump illustrates peak force during the propulsive/pushoff phase (~1.4s) and peak force during the landing phase (~2.0s). The horizontal dashed line represents the magnitude of one body weight (~725N). The shaded area represents the impulse generated against the floor during takeoff. Graph courtesy of Dr. Todd Royer, University of Delaware.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

11. 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, 7th edition
By Susan J. Hall, Ph.D.

12. Mechanical Behavior of Bodies in Contact1 3 2 4
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

13. Mechanical Behavior of Bodies in Contact
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.
Static
Fm = sR
Dynamic
Fk = kR
Applied external force
Friction
(motion occurring)
(no motion)
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

14. Mechanical Behavior of Bodies in Contact
Pushing a desk
Pulling a desk
R = wt + Pv
R = wt - Pv wt P Pv PH
Is it easier to push or pull a desk across a room?
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

15. Mechanical Behavior of Bodies in Contact
The coefficient of friction between a dancer’s shoes and the floor must be small enough to allow freedom of motion but large enough to prevent slippage.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

16. 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, 7th edition
By Susan J. Hall, Ph.D.

17. 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, 7th edition
By Susan J. Hall, Ph.D.

18. 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, 7th edition
By Susan J. Hall, Ph.D.

19. Mechanical Behavior of Bodies in Contact
What is the relationship between impulse and momentum?
Ft = M
Ft = (mv)2 - (mv)1
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

20. Mechanical Behavior of Bodies in Contact
What does the area under the curve represent? 3 2 1
Time (ms) A B
Force (Body Weight)
Force-time graphs from a force platform for high (A) and low (B) vertical jumps by the same performer.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

21. 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, 7th edition
By Susan J. Hall, Ph.D.

22. 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, 7th edition
By Susan J. Hall, Ph.D.

23. 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, 7th edition
By Susan J. Hall, Ph.D.

24. 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, 7th edition
By Susan J. Hall, Ph.D.

25. Mechanical Behavior of Bodies in Contact
Ball velocities before impact
Ball velocities after impact
u u2
v 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.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

26. Mechanical Behavior of Bodies in Contact
In a “break” in billiards, the cue ball is struck to impart high velocity since the numbered balls are motionless, the idea being to disperse the numbered balls.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

27. 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)(superball bounce is close…)
Perfectly plastic impact - in which there is a total loss of system velocity;
(e = 0)(spaghetti hits a wall)
(Most impacts fall in between perfectly elastic and perfectly plastic.)
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

28. Mechanical Behavior of Bodies in Contact
Bounce heights of a basketball, golf ball, racquetball, and baseball dropped from a height of 1 m on two different surfaces. Note that the basketball bounces higher on the wood floor but the other balls bounce higher on concrete.
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

29. 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, 7th edition
By Susan J. Hall, Ph.D.

30. 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, 7th edition
By Susan J. Hall, Ph.D.

31. 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, 7th edition
By Susan J. Hall, Ph.D.

32. 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, 7th edition
By Susan J. Hall, Ph.D.

33. 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, 7th edition
By Susan J. Hall, Ph.D.

34. 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, 7th edition
By Susan J. Hall, Ph.D.

35. Work, Power, and Energy Relationships
29.4
24.5
19.7
14.7
9.8
3.1
4.4
5.4
7.3
4.9
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
Basic Biomechanics, 7th edition
By Susan J. Hall, Ph.D.

36. 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, 7th edition
By Susan J. Hall, Ph.D.