CHAPTER 12:PART 1CHAPTER 12:PART 1THE CONDITIONS OF THE CONDITIONS OF

LINEAR MOTIONLINEAR MOTION

CHAPTER 12:PART 1CHAPTER 12:PART 1THE CONDITIONS OF THE CONDITIONS OF

LINEAR MOTIONLINEAR MOTION

KINESIOLOGYScientific Basis of Human Motion, 12th edition

Hamilton, Weimar & Luttgens

Presentation Created by

TK Koesterer, Ph.D., ATC

Humboldt State University

Revised by Hamilton & Weimar

Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

12A-2

ObjectivesObjectives1. Name, define, and use the terms of linear motion.

2. Define magnitude, direction, and point of application of force and use terms properly.

3. Explain the effect of changes in magnitude, direction, and point of application of force have on the motion state of a body.

4. Define and give examples of linear forces, concurrent forces, and parallel forces.

5. Determine magnitude, direction, and point of application of muscle forces.

6. State Newton’s laws as they apply to linear motion.

12A-3

ObjectivesObjectives7. Explain cause and effect relationship between

forces causing linear motion and the objects in motion.

8. Name & define basic external forces that modify motion.

9. Draw and analyze a 2D free-body diagram.

10. Explain the work-energy relationship applied to a body experiencing linear motion.

11. Define and use properly the terms work, power, kinetic energy, and potential energy.

12. Perform a mechanical analysis of a motor skill.

12A-4

The Nature of ForceThe Nature of Force

Force is that which pushes or pulls through direct mechanical contact or through the force of gravity to alter the motion of an object.

Internal forces are muscle forces that act on various structures of the body.

External forces are those outside the body:Weight, gravity, air or water resistance, friction,

or forces of other objects acting on the body.

12A-5

Aspects of Force Aspects of Force

Force is a vector quantity:Magnitude and directionAlso has a point of application

All three characteristics must be identified. For a weight lifter to lift a 250 N barbell:

Lifter must apply a force greater than 250 N, in an upward direction, through the center of gravity of the barbell.

12A-6

MagnitudeMagnitude

Amount of force being applied.Force exerted by the barbell had a magnitude of

250 N.This force was the result of gravity acting on the

mass of the barbell.

In this case, the force is referred to as weight.

Weight is mass times acceleration due to gravity:

w = mg

12A-7

Magnitude of Muscular ForceMagnitude of Muscular Force

In direct proportion to the number & size of fibers contracting in a muscle.

Muscles normally act in groups whose force or strength is measured collectively.

Maximum muscular strength is measured by a dynamometer.Measures force applied by a group of

muscle through an anatomical lever.

12A-8

Point of ApplicationPoint of Application

Point at which force is applied to an object.

Where gravity is concerned this point is always through the center of gravity.

For muscular force, this point is assumed to be the muscle’s attachment to a bony lever.The point of intersection of the line of

force and the mechanical axis of the bone.

12A-9

Mechanical AxisMechanical Axis

Fig. 12.3

• The mechanical axis of a bone is a straight line that connects the midpoint of the joints at either end of the bone.• Not necessarily the long axis of the bone.

12A-10

DirectionDirection

Direction of a force is along its action line.Gravity is a downward-directed

vector through the center of gravity of the object.

Direction of a muscular force vector is the direction of line of pull of the muscle.

12A-11

Direction of Muscular Force VectorDirection of Muscular Force Vector Muscle angle of pull: the angle between

the line of pull and the mechanical axis of the bone.

Fig 12.1

12A-12

Resolution of ForcesResolution of Forces

Fig 12.2

Magnitude

Point of Application is at point B.

Direction is represented by the arrowhead and the angle

12A-13

Angle of PullAngle of PullForce may be resolved into x (horizontal)

and y (vertical) components. The x-axis is always the mechanical axis of the bone. The y-axis is always perpendicular to the mechanical axis

of the bone.

Size of each depends on angle of pull.

Since a muscle’s angle of pull changes with every degree of joint motion, so do the x & y components .

The larger the angle (0º - 90º), the greater the y and less the x component.

12A-14

Angle of PullAngle of Pull

The y component is perpendicular to the lever, called rotary component.

The x component is parallel to the lever and is the non-rotary component.

Most resting muscles have an angle of pull < 90º.

Fig 12.1a

Rotary component

Nonrotary component

12A-15

Rotary vs. Non-rotary ComponentsRotary vs. Non-rotary ComponentsAngle of pull < 90º

Non-rotary force is directed toward fulcrum.

Helps maintain integrity of the joint (stabilizes).

Fig 12.1a

Rotary component

Non-rotary component

12A-16

Rotary vs. Non-rotary ComponentsRotary vs. Non-rotary ComponentsAngle of pull > 90º

Dislocating force is directed away fulcrum.

Does not occur often.

Muscle is at limit of shortening range and not exerting much force.

Fig 12.1c

12A-17

Rotary vs. Non-rotary ComponentsRotary vs. Non-rotary ComponentsAngle of pull = 90º

Force is all rotary.

Angle of pull = 45º

Rotary & non-rotary components are equal.

Muscular force functions:

Movement

Stabilization Fig 12.1b

12A-18

Anatomical PulleyAnatomical Pulley

Changes the angle of pull of the muscle providing the force.

This increase in angle of pull increases the rotary component.e.g. Patella for the

quadriceps.Fig 12.4

Rotary force in red

12A-19

Resolution of External ForcesResolution of External ForcesAccomplished in the

same manner as muscular forces applied at an oblique angle.

Only horizontal force will move the table.

Vertical force serves to increase friction.

Fig 12.7

12A-20

Composite Effects of Two or More ForcesComposite Effects of Two or More Forces

Two or more forces can be applied to objects.A punted ball’s path is the result of force of

the kick, force of gravity, and force of wind.Muscles work in groups, e.g. the 3 hamstrings.

Composite forces on the body may be classified according to their direction and application as linear, concurrent, or parallel.

12A-21

For forces applied in the same direction, the resultant is the sum of the forces:a + b = c

For forces applied in the opposite directions, the resultant is the sum of the forces:

a + (-b) = c

Linear ForcesLinear Forces

=+a b c

=+a b c

12A-22

Concurrent ForcesConcurrent Forces

Act at the same point of application at different angles.

Resultant of two or more concurrent forces depends on both the magnitude of each force and the angle of application. Fig 12.8

12A-23

Parallel ForcesParallel Forces

Forces not in the same action line, but parallel to each other.

Three parallel forces:two upwardone downward

Fig 12.9

12A-24

Parallel ForcesParallel Forces

10 N weight at 90º.

Gravity acts at points B & C.

A is the force of biceps.

Effect of parallel forces on an object depends on magnitude, direction & application point of each force. Fig 12.9

12A-25

Newtons’ Laws of MotionNewtons’ Laws of Motion

A body continues in its state of rest or of uniform motion unless an unbalanced force acts on it.An object at rest remains at rest.An object in motion remains in same motionUnless acted upon by an outside force.

Friction & air resistance effect objects in motion.

F ≠ 0

1. Law of Inertia1. Law of Inertia

12A-26

Law of Inertia Law of Inertia

A body continues in its state of rest or of uniform motion unless an outside, unbalanced force acts on it.

Fig 12.11

Gravity

Vy

Vx

12A-27

2. Law of Acceleration2. Law of AccelerationThe acceleration of an object is directly

proportional to the force causing it and inversely proportional to the mass of the object.

What is the force needed to produce a given linear acceleration?

Since m = w/g, F = (w/g) x a

Force to accelerate a 300 N object 2 m/sec2

F = (300 N / 9.8m/s2) x 2 m/s2 = 61 NF = ma

12A-28

Impulse Impulse

The product of force and the time it is applied.F = ma

Substitute (vf – vi) / t for a:F= m (vf – vi) / t

Multiply both sides by time:Ft = m (vf – vi)

Fig 12.12

Ft = m(vf – vi)

12A-29

Momentum Momentum

The product of mass and velocity

20 N force applied for 5 sec has equal momentum to a 100 N force falling for 1 sec. Why?

Any change in momentum is equal to the impulse that produces it.

Force applied in direction of motion will increase momentum.

Force applied opposite to direction of motion will decrease momentum.

Ft = mvf - mvi

12A-30

3. Law of Reaction3. Law of Reaction

For every action there is an equal and opposite reaction.

Fig 12.13 & 12.14

F = -F

12A-31

Conservation of MomentumConservation of Momentum

In any system where forces act on each other the momentum is constant.

An equal and opposite momentum change must occur to object producing reaction force.

Therefore:

m1vf1 – m1vi1 = m2vf2 – m2vi2

Fig 12.15

12A-32

Summation of ForcesSummation of ForcesForce generated by muscle may be summated

from one segment to another.

Typical throwing pattern:

Force from legs is transferred to the trunk.

Further muscular force increases momentum and is transferred to upper arm.Mainly as an increase velocity because mass is

smaller.

Sequential transfer of momentum continues with mass decreasing and velocity increasing.

Finally, momentum is transferred to thrown ball.