Force-types of contact forces

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					  Force-types of contact forces
• Forces exist in nature that affect the way
  humans move.
• A common classification is to describe
  these as contact and non-contact forces.
Non-contact and contact forces
• Non-contact
• Gravity is the major external force acting
  on the body.
• Contact
• Reaction force
• Muscle force
• Elastic force
• Friction
 Types of forces-contract and non-
• Forces cause predictable and measurable
  responses to the human body when
  objects interact with the human body.
  These responses are:
• Resistive counter-forces
• Deformations
• breakage
Non-contact-Gravitational force
• F= Gm1m2
• G = universal gravitational constant
• M1 = mass of one object
• M2 = mass of the other subject
• r = distance between mass centres of the
            Contact forces

• Reaction forces
• Example- A runner experiences the
  following ground reaction force
  components at one point in time during the
  stance phase.
• Anterior-posterior (Fx) – 250 N (positive
• Vertical (Fy) = 800 N (positive upward)
• Medio-lateral (Fz) 60 N (positive lateral)
An example of the vertical ground reaction
      force from a force platform


     Vector components of ground
             reaction force
•   Check the components to draw:
•   X-component
•   Y-component
•   Z-component
•   xy Resultant of the horizontal components
•   xyz Resultant of all three components
      Ground reaction force
• FX-component of the ground reaction
• FY-component of the ground reaction
• FZ-component of the ground reaction
• Fxy Horizontal component of the ground
  reaction force
• Fxyz Resultant ground reaction force

• There will be a change in shape or size, of a structure that is
  composed of a deformable material.
• Strain is a measure of deformation and is an unit change in
  the shape or size of the material.
• There two types of strain:
• Normal or longitudinal strain - measure of elongation or
  contraction of material.
• Shear strain.- a measure of the relative rotation of the two
  materials from their original perpendicular location.
• Normal or longitudinal strain
  Shear strain =    change in angle between two elements
•                   that were originally at right angles
• Normal strain = change in length
                    Original length
             Tension                   bending

Shear         Torsion

• Mechanical properties provide a measure
  of a material’s ability to resist deformation
  when subjected to externally applied
• These properties can be determined
         Structural properties
• Structural properties:
• energy absorbed,
• stiffness,
• ultimate load and ultimate elongation.
• These structural properties are dependant on a
  number of parameters,
• the material properties of the tissue substance,
  the geometry of the tissue (cross sectional area,
  length and shape)
• and the properties of the bone-substance and
  muscle-substance junctions.
• Stress
• An applied force is known as stress.
• Normal stress = force
  Cross sectional area over which force acts
• SI units are 1 Nm-2 = 1 Pascal
        Stress-strain curve plotted by converting measures of force and
           deformation appropriately to represent material behavior.

Stress N/mm                               True stress strain
Ultimate strength
                                         Engineering stress strain
Yield    Yield point
strength                                       fracture

         Elastic region
                                Plastic region

         2%                    Elongation at failure
         Strain offset Strain mm/mm
   Strain-stress properties of body
• Bone
• Demonstrates a linearly elastic response from
  the onset of loading. Substantial plastic
  deformation occurs when bone is loaded in
  either tension or compression. Strength and
  elastic modulus of bone tissue are higher when
  loaded at high strain rates, with less energy
  absorbed than at lower strain rates.
          Articular cartilage
• Articular cartilage exhibits viscoelastic
  behavior in tension, appearing stiffer with
  increasing strain. Cartilage behaves
  elastically when subjected to sufficiently
  fast load application.
• Ligaments pulled in tension demonstrates a
  force –elongation curve shown by small
  nonlinear toe region, a relatively large linear
  region and often a second nonlinear region that
  may plateau. The toe region corresponds to low
  forces associated with everyday PA. Ligaments
  strain-stress is associated with their structure
  and material as they attach directly into bone.
• Tendon similar force –elongation curve as
  ligaments shown by very small (0-3%) nonlinear
  toe region (due to straightening of crimped
  collagen fibrils), a relatively large linear region
  up to 4% and often a second nonlinear region
  that may fail up to 8-10% - elongate or break.
  Tendons efficiently transmit force without
  dissipating much energy during activity (90-
• Discuss the torsion stress on bone in two
  cross sections of a tibia –the distal and
  proximal ends.
                                 Elastic force
•    Elasticity:
•    When a force is applied to a material, the material undergoes a change
     in its length, so F = k∆
•    A measure of the ability to reform after being deformed.
•    Newton’s Law of Coefficient of elasticity or restitution:
•    “A degree of reformation or restitution of a deformed body that occurs
     after impact. The material when deformed stores energy known as
     strain energy.”
•    Velocities of two materials before u1 and after u2
•    Velocities of two materials after impact v1 and v2
•    Velocities after impact v1 -v2 = -e (u1-u2)
•    In the case of a rigid body i.e.the floor u2 and v2 are zero
•    the coefficient of restitution e = - v1
or     e = v1 -v2
It can also be written e =  h rebound height
                              H start height
        Force applied to a spring
• Stiffness is defined as the amount of force
  necessary to extend the body one unit of
  length (N/m).

          Force N   10
                         2 4 6 8 10 12
                            Length mm
• Work done to stretch the spring 1 mm is
  greater at longer lengths.
Force can be internal relative to a
• Internal force
• Muscle force is a major internal force creating
  movements of body segments.
• Ligaments and tendons also apply forces to
  create and restrict limb movements.
• The body has the ability to also use viscoelastic
  properties to create force.
• These forces are not easily measurable in the
  human body.
• Mineral crystals within bone tissue
  transmit large forces without significant
  dissipation of energy; deformation is small
  and primarily elastic. Bone gives structural
  rigidity to the body.
• Tendon (viscoelastic) composition and tensile
  stiffness reflect their role in generating motion by
  efficiently transmitting muscle contraction forces
  across joints.
• Tendons are stronger enough to sustain high
  tensile forces that result from muscle contraction
  during joint motion, yet are flexible enough to
  angle around bone to change the final direction
  of muscle pull.
Ligament and articular cartilage
• Ligaments and articular cartilage
  experience relatively large deformations,
  dissipating energy through viscoelastic
  and poroelastic processes.
• The ligaments are pliant and flexible,
  allowing movement of bones, but are
  strong and inextensible offering suitable
  resistance to applied forces.
• There are 430 muscles in the body
• The most vigorous movements are
  conducted by only 80 pairs.
• Muscles provide strength and protection to
  the skeleton by distributing loads and
  absorbing shock; they enable bones to
  move at joints and provide body posture
  against force.
• Maximal tension is produced when the
  muscle fibre is at resting length (slack).
• If the muscle is shorter, tension falls of
  gradually at first, then rapidly, and if the
  muscle is longer than resting length
  tension progressively decreases.
            Muscle force
      Motive and resistive force
• One body segment can exert a force on another,
  causing movement in that segment that is not
  due to muscle action.
• Joint forces account for inertial forces and
  gravity, they do not represent internal contact
• The bone on bone (contact) forces depend on
  the level of muscle activity.
• The bone on bone and joint forces may act in
  different directions.
Joint reaction force of the knee with
     its shear and compressive
Muscle force vector, angle of pull
 and its vertical and horizontal



     Biceps brachii muscle force vector
             Net muscle force
                   b)                  c)
a)                   Fmc                           Fms
                           0.55 rad
           Fmc             0.35 rad               Fm

     Fms             Fms

     Geometric composition of the resultant muscle Fm
     Due to activation of both clavicular Fmc and sternal
     Fms components of the pectoralis major muscle.
     a) orientation of the two vectors b) graphic addition
     c) Calculation of the resultant vector.
                    Friction force
• Friction: Ffr = μ N
• Fr = Friction force = μ = coefficient of friction and N =
  normal force

• A force exerted between two contacting surfaces that
  slide past each other.
• Factors that effect friction:

      • Texture of surfaces
      • Force or pressure between the two surfaces (normal or
        perpendicular force)
      • Actual contact area
      • Other conditions – wet or dry surface
        Quantifying friction force
     • A force acting at a point can be
       resolved into a normal and tangential
     • Normal force
     • Coefficient of friction
     • μ = Ffr/N
• The direction of the kinetic frictional force
  is opposite the direction of motion of the
  object it acts on.
           Coefficient of friction
• The coefficient of friction
  is the ratio of the friction
  force to the normal force.

• μ = Ffr
•        Fn                          F fr Tangential force
• μ is the coefficient of
  static friction, Ffr is the    F                      Fn
  maximum static friction                     θ
  force and Fn is the
  perpendicular force
  pressing the two surfaces
    Two types of coefficients of
      • Coefficient of static friction – amount of
        force that is required before an object will
        begin to move.
      • Coefficient of kinetic friction – amount of
        force required to keep an object moving.
•       Coefficient of kinetic friction
       < coefficient of static friction
                Rolling friction
• Rolling friction designates the
  ratio of the horizontal force
  necessary to induce the wheel
  rotation to the weight (vertical
  or normal force) that acts on
  the wheel. F hoz
                                           F hoz
• Discuss – what you see.
        F ver   E    R         F ver        R
• A 12 kg mass is pushed across a horizontal
  surface by a force of 80 N inclined at an angle of
  30° with the horizontal. The coefficient of sliding
  friction is 0.35.
  a. Make a free body diagram of the mass and
  find the normal force acting on the mass.
  b. Find the force of friction acting on the mass.
  c. Find the acceleration of the mass as it moves
  across the surface.