Static Forces and Equilibrium

• Introduction to static forces concerns definitions of static forces and equilibrium
• Conditions for static equilibrium require that the sum of forces and torques equals zero, ΣF = 0, Στ = 0
• Levers are a key concept
• Medical applications include how muscles and bones maintain posture and stability of medical implants and prosthetics
• An example considers how the spine supports the body while standing
• Equilibrium can be neutral, stable, or unstable

Definition of Static Forces and Equilibrium

• Static forces are forces acting on an object at rest or moving at a constant velocity
• These forces are balanced, meaning their vector sum equals zero, so they do not cause acceleration
• Common examples include gravitational force, normal force, tension, and friction in stationary systems
• Equilibrium occurs when the net force and net torque acting on an object are zero
• Translational equilibrium means the sum of all forces acting on the object is zero
• Translational equilibrium ensures the object remains at rest or moves uniformly, ΣF = 0, ΣFy = 0, ∑ Fz = 0
• Rotational equilibrium means the sum of all torques about any axis is zero
• Rotational equilibrium prevents rotational acceleration, Στ= 0

Key Factors Affecting Equilibrium in the Human Body

• Center of Gravity (CoG) is the point where the body's mass is evenly distributed
• Lowering the CoG increases stability
• Base of Support (BoS) is the area beneath the body that supports its weight
• A wider BoS enhances stability
• Line of Gravity is an imaginary vertical line extending from the CoG toward the ground
• Stability is maximized when this line falls within the BoS
• Muscle Strength and Joint Stability: Proper muscle engagement and joint positioning help maintain equilibrium
• Strong muscles generate the necessary force to counteract gravity and external forces to ensure balance
• Core muscles, abdominals, back, and pelvis, stabilize the spine and trunk, serving as a central foundation for balance
• Lower limb muscles, such as the quadriceps, hamstrings, and calf muscles, support the body while standing or moving
• Upper body muscles help maintain posture and prevent imbalance, especially when lifting or carrying objects

Levers

• A lever is a simple mechanical device used to lift or move a load with the help of an applied force
• A lever consists of a rigid bar or beam that rotates around a fixed point called the fulcrum
• Levers work based on the principle of mechanical advantage, allowing a small effort to move a much larger load, or vice versa
• In the human body, levers are formed by bones, muscles, and joints working together to produce movement
• A lever consists of three key components: fulcrum (pivot), effort (force), and load (resistance)
• Fulcrum, is the fixed point around which the lever rotates, usually a joint
• Effort, is the force applied by muscles to move the lever
• Load, is the weight or resistance that the lever moves, such as a body part or external object
• In a First-Class Lever, the fulcrum is located between the effort and the load
• First-class levers can either increase force or speed, depending on the relative distances
• An example of a first-class lever is the neck during nodding
• In a Second-Class Lever, the load is located between the fulcrum and the effort
• Second-class levers always increases force but sacrifices speed and range of motion
• A second-class lever example is standing on tip-toe
• In a Third - Class Lever the effort is applied between the fulcrum and the load
• Third-class levers increases speed and range of motion but requires more effort
• A third-class lever, which is most common in the human body, is holding a weight in your hand, such as during a biceps curl

Elasticity

• Elasticity refers to the ability of a material or object to deform under stress and return to its original shape or position once the stress is removed
• Elasticity is a physical property that determines how much a material can stretch or bend without permanently altering its structure or integrity
• Elasticity is often quantified by parameters such as the modulus of elasticity or Young's modulus, which describe the material's resistance to deformation
• Understanding elasticity is crucial in fields such as materials science, engineering, and biomechanics for designing structures, predicting behavior, and ensuring performance and safety
• Biomaterials science is a multidisciplinary field including medicine, biology, chemistry, tissue engineering, and materials science
• A biomaterial is any matter or surface that interacts with biological systems
• Knowledge of biomaterials allows understanding of the regularities between the mechanical properties and composition of biomaterials, as well as modeling of the physical properties of materials
• Ceramics have very high strength and elastic modulus, but low deformability
• Metals have high strength, elastic modulus and deformability
• Polymers have low strength and elastic modulus, but high deformability

Hooke's Law

• An ideal spring has an equilibrium length
• An ideal spring abides by Hooke's Law
• Hooke's Law can be expressed as the following equation: F = - k * x
• Where F is the force in Newtons
• k is the spring constant
• x is the amount of extension, measured in meters
• Length of the spring (L) is proportional AL (length)
• The amount of AL (length) is proportional to 1 / Total Number of Springs
• F (Force) is proportional to L (length)
• (AL) is proportional to 1 / A (cross-sectional area)

Young's Modulus

• (AL) is proportional 1/A (cross-sectional area)
• F (Force) is proportional L (length)
• Length of the spring (L) is proportional AL (total length)
• A formula for Young's Modulus is E = Stress / Strain
• The Young's modulus (E) is a property of the material that tells us how easily it can stretch and deform

Elements of theory of elasticity

• Hookean Elastic behaviour is a linear stress-strain relationship
• Bone mineral is a ceramic material exhibiting normal behaviour
• Collagen is a polymer exhibiting a J-shaped stress-strain curve

Mechanical properties of bone

• Mechanical properties of bone depend on factors such as age, gender, location in the body, temperature, mineral content, amount of water present, and disease, e.g. osteoporosis
• Osteoporosis is a disease involving a marked decrease in bone mass
• As humans age, their bones typically become less dense and the strength of these bones decreases, meaning they are more susceptible to fracture
• Changes in mechanical properties of bones occur due to age-related factors like osteoporosis or changes in tissue composition
• Bones become more brittle and less dense with age, affecting the ability to withstand stress and strain
• This is a change in the biological material, not Young's modulus itself
• Bone can be thought of as a fibre composite consisting of collagen fibres and an inorganic matrix
• The longitudinal direction refers to the orientation that runs along the length of the bone and is typically aligned with the long axis
• When forces are applied along the longitudinal direction, they act along the length of the bone, such as compression or tension
• The transverse direction refers to the orientation that is perpendicular to the longitudinal axis of the bone
• Forces applied in the transverse direction act across the bone's cross-section, typically testing its strength against bending or shear forces