Kinesiology II

 Physics of Motion

I.  Force

A.  Definition

1.  Force = mass * acceleration

2.  Mass is a fundamental dimension, units g, kg

3.  Acceleration is change in velocity, units m/sec/sec or m/s2

4.  “Weight” is a force, units pounds or Newtons

- Pounds = mass * acceleration of gravity

- Why your weight, but not your mass, is different on the moon

- Gravity on Earth = 9.8 m/sec2

5.  Example:  A person with a mass of 70 kg weighs:

                        70*9.8 = 686 kg*m/sec2 or 686 N

 

B.  Aspects

1.  Force has a point of application or origin

Example:  location where muscle attaches to bone

2.  Force has a line of application

Follows the tendon

3.  A rotational force is called torque

4.  Force has direction

Can be indicated in two (x,y) or three (x,y,z) dimensional space

5.  Force has magnitude

Magnitude is measured in Newtons

 

II.  Rotational Force

1.  Force (mass*acceleration) may cause rotation about an axis

2.  Moment of force (=Torque) is equal to the force times the lever arm – the perpendicular, straight line distance between the axis of rotation and the force

3.  Moment of force (torque) = force* perpendicular distance

Units:  N*m

4.  Sign convention: 

Clockwise moment = negative

Counterclockwise moment = positive

 

III.  Levers – Location of effort force, load or resistance force, and rotational axis

A.  Three types of levers

1.  First class

2.  Second class

3.  Third class

4.  Differences between the three have to do with the relative locations of the effort, load, and the axis of rotation

 

B.  First Class Lever

1.  “EOR”

O = axis or pivot point

E = effort force (as applied by muscle/tendon)

R = resistance (load) force (outside force such as barbell)

2.  The effort force and the load force are located on opposite sides of the axis of rotation

3.  Example:  seesaw

4.  Anatomical example:  Triceps muscle – elbow extensor

Insertion:  Olecranon process of ulna

5.  First class levers are rare in human body

 

C.  Second Class Lever

1.  “ORE”

2.  The resistance (load) force and the effort force are on the same side of the axis of rotation

3.  The effort lever arm is GREATER than the resistance lever arm

4.  Example:  wheel barrow

5.  Anatomical example:  brachioradialis – elbow flexor

Insertion:  Styloid process of radius (distal – past the center of mass)

6.  Second class levers are rare in the human body

 

D.  Third Class Lever

1.  “OER”

2.  Effort and resistance (load) forces are on the same side of the axis of rotation

3.  The effort lever arm is SMALLER than the resistance lever arm

4.  Anatomical example:  Biceps brachii – elbow flexor

Insertion:  Tuberosity of radius (proximal)

5.  Anatomical example 2:  Quadriceps group – knee extensors

Insertion:  Patella, tibia

6.  Third class levers are common in the human body

 

IV.  Mechanical Advantage

     A.  Mechanical Advantage defined as:

Effort Lever Arm/Resistance Lever Arm

1.  A second class lever will always have a mechanical advantage greater than one because the effort lever arm is always GREATER than the resistance lever arm

2.  A third class lever will always have a mechanical advantage less than one because the effort lever arm is always LESS than the resistance lever arm

3.  A first class lever can have a mechanical advantage less than, equal to, OR greater than one, depending on the locations of the effort force and resistance force versus the axis of rotation

 

B.  Mechanical Advantage VS. Speed

1.  The mechanical advantage of a third class lever – common in the body – is poor – always less than one

2.  However, the SPEED of rotation created by a third class lever is high

 

3.  Because the origin of the resistance force is located farther from the axis than the origin of the effort force, it must travel a greater distance in the same time

4.  Greater distance per unit time = greater speed

5.  Good for throwing objects, kicking, etc.

6.  Opposite would be true of second class lever

 

V.  Equilibrium – Balance of Forces

1.  Equilibrium means that opposing forces or moments are balanced

2.  Put another way, the sum of all forces or moments is ZERO

3.  Static equilibrium:  There is NO movement

4.  Dynamic equilibrium:  There is NO change in velocity (I.e., no acceleration or deceleration) and NO change in direction of movement

5.  If forces or moments are not balanced (I.e., do not sum to zero), there will be acceleration

6.  From static to moving (zero to some velocity) or a change in velocity (accel/decel)

7.  To move a static object or change velocity, the effort force or moment must overcome the inertia

8.  The greater the mass of the object, the greater its inertia

9.  For example, to LIFT an object off the ground, the effort force must exceed the object’s weight:

Effort Force > mass * acceleration of gravity

Newton’s Laws (in book)

Ø  Law of Inertia:  An object at rest will remain at rest unless it is acted upon by an external force; an object in motion will remain at a constant velocity unless acted upon by an external force;  the greater the mass, the greater the inertia

Ø  Law of Acceleration:  An object’s velocity will change in magnitude and/or direction when an external force is applied, the greater the force, the greater the change

Ø  Law of Action-Reaction:  For every external force, there is an equal but opposite reciprocal force

 

VI.  Unbalanced Moments – Movement at a hinge joint

1.  Movement will occur if the effort moment and the resistance moment are not equal:

                                    EF*ELA is not = RF*RLA

            EF = effort force

            ELA = effort lever arm (distance)

            RF = resistance force

            RLA = resistance lever arm

2.  The force required to move the object:

                                    EF = RF*RLA/ELA

Note:  the longer the effort lever arm, the less the force required – why you use a spoon to pry open a can, why a mole has a very long olecranon process, why you would never carry a heavy box with straight arms

 

VII.  Muscle – Produces Effort Force

    A.  Overview

1.  Muscles produce the effort force needed to overcome resistance forces

2.  Muscles are attached to the bones via tendons

3.  Muscles have properties that affect the force produced and the speed at which that force is produced

 

B.  Determinants of Muscle Force

1.  The amount of force generated in a single muscle fiber is determined by the number of x-bridge formations

2.  The amount of force exerted during muscle contraction of a group of muscles is dependent upon:

a.  Number (cross sectional area) of fibers recruited

b.  Type of fibers recruited (I, IIa, IIb)

c.  Length of muscle fiber

d.  Velocity of shortening

e.  Nature of the neural stimulation of motor units

 

C.  Muscle Shape

1.  Muscle shape can affect the number of fibers recruited & the force produced

2.  Two basic categories:  Longitudinal and Pennate

3.  Longitudinal includes:

Spindle or fusiform – fibers are in line with the direction of tension, example:  biceps

Fan shape – fibers are almost in line with the direction of tension (fan orientation), example:  pectoralis major with an origin along the clavicle and sternum and insertion on the humerus

4.  Relatively lower force with greater length change (longer fibers but fewer of them)

5.  Pennate (like a feather) includes:

Unipennate – fibers are diagonal to the direction of pull in one direction, example flexor pollicus longus

Bipennate – fibers are diagonal to the direction of pull in two directions – muscles with a central tendon, example – rectus femoris

6.  Relatively high force production (more fibers packed in)  but less length change (shorter fibers)

 

D.  Muscle – Length-Tension Curve

1.  Muscles have an optimal length for force generation (sometimes close to the resting length)

2.  Optimal length is the length at which the overlap of actin and myosin yields a high number of cross-bridges but also allows further contraction

3.  Above the optimal length, the number of cross-bridges, and therefore force, falls

4.  Below the optimal length, the overlap becomes too great, fewer cross-bridges are formed

 

E.  Muscle Force-Velocity Curve

1.  The greater the velocity of contraction, the lower the maximum force that can be produced

- True for both slow and fast-twitch fibers

2.  The lower the velocity of contraction, the greater the maximum force that can be produced

–    True for both slow and fast-twitch fibers

3.  At any absolute force, the speed of movement is greater in muscle with a higher percent of fast-twitch fibers

 

F.  Summary

1.  The shape, size, length, fiber type composition, and velocity of contraction of a muscle affects the force it can produce

2. In general, muscles are adapted for the job each does – as this varies in different mammals, so do the muscles

Vary in shape

Vary in size & length

Vary in fiber type composition

Vary in max velocity