chapter 12 linear kinetics of human movement basic biomechanics, 7 th edition by susan j. hall,...

Chapter 12

Linear Kinetics of Human Movement

Basic Biomechanics, 7th editionBy Susan J. Hall, Ph.D.

© 2014 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


For example, 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

Newton’s Laws


Better sprinters are able to generate a forward-directed horizontal component (FH) of the total ground reaction force (F).

FH

FV

F

12-9

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.

12-10

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.

12-11

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


12-12



1

2

3

4

12-13


StaticFm = sR

DynamicFk = kR

Applied external force

Fric

tion

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.


(motion occurring)(no motion)

12-14


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

12-15


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.


12-16


What is momentum?

• Quantity of motion possessed by a body

• Measured as the product of a body’s mass and its velocity;

M = mv


12-17


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


12-18


What causes momentum?

Impulse: the product of a force and the time interval over which the force acts

Ft


12-19


What is the relationship between impulse and momentum?

Ft = M

Ft = (mv)2 - (mv)1


12-20


Force-time graphs from a force platform for high (A) and low (B) vertical jumps by the same performer.

For

ce (

Bod

y W

eigh

t) 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?


12-21


What is impact?

A collision characterized by:

• The exchange of a large force during a small time interval


12-22


What happens following an impact?

This depends on:

• The momentum present in the system

• The nature of the impact


12-23


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.


12-24


What does the coefficient of restitution (e) describe?

relative velocity after impact -e = relative velocity before impact

v1 - v2

-e = u1 - u2


12-25


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.


12-26


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.


12-27


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.)


12-28

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.



12-29

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)


12-30


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)


12-31


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


12-32


What is kinetic energy?

• Energy of motionKE = ½mv2

What is potential energy?

• Energy by virtue of a body’s position or configuration

PE = (wt)(ht)


12-33



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

12-34


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)


12-35


29.4

24.5

19.7

14.7

9.8

0

3.1

4.4

5.4

7.3

0

4.9

9.8

14.7

19.7

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


12-36


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)


chapter 12 linear kinetics of human movement basic biomechanics, 7 th edition by susan j. hall,...

Documents

th edition

r basic biomechanics

contact basic biomechanics

ma basic biomechanics

peak force

total ground reaction

law of reaction

external force