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- contact • 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 r2 • G = universal gravitational constant • M1 = mass of one object • M2 = mass of the other subject • r = distance between mass centres of the objects 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 =forward • 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 Fz Fx Fy 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 force • FY-component of the ground reaction force • FZ-component of the ground reaction force • Fxy Horizontal component of the ground reaction force • Fxyz Resultant ground reaction force Deformation-strain • 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 Unloaded Tension bending Compression Shear Torsion Combined Deformation • Mechanical properties provide a measure of a material’s ability to resist deformation when subjected to externally applied forces. • These properties can be determined experimentally. 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 • 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 tissue • 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 • 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. Tendons • 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- 96%). Question • 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 u1 or e = v1 -v2 u1-u2 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). 15 Force N 10 5 0 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 system. • 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. Bone • 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 • 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. Muscles • 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. Muscles • 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 forces. • 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 components Muscle force vector, angle of pull and its vertical and horizontal components Fy θ Fx Biceps brachii muscle force vector Net muscle force b) c) a) Fmc Fms Fmc 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 components. • 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 together. Two types of coefficients of friction • 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. E F ver E R F ver R Question • 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.