Unit 1: Fundamentals of mechanics - Subjective Questions

Newton's Laws of Motion form the foundation of biomechanics:

1. First Law (Law of Inertia):

• A body at rest remains at rest, and a body in motion continues in uniform motion in a straight line, unless acted upon by an external force.
• Biomechanical example: A sprinter's body tends to stay at rest in the starting blocks until muscular force overcomes inertia.

2. Second Law (Law of Acceleration):

• The acceleration of a body is directly proportional to the net force acting on it and inversely proportional to its mass.
• Mathematically:
• Biomechanical example: A heavier athlete requires greater force to achieve the same acceleration as a lighter athlete.

3. Third Law (Law of Action-Reaction):

• For every action, there is an equal and opposite reaction.
• Biomechanical example: When a runner pushes backward on the ground, the ground pushes the runner forward (ground reaction force).

These laws govern how forces produce movement in the human body and are essential for analyzing sport and rehabilitation mechanics.

Force:

• A push or pull that tends to change the state of motion or shape of a body.
• SI unit: Newton (N).
• Vector quantity having both magnitude and direction.

Moment:

• The turning effect produced by a force about a point or axis.
• Also called moment of force.

Torque:

• The rotational equivalent of force; the tendency of a force to rotate a body about an axis.
• Formula:
  where = applied force, = perpendicular distance (moment arm) from the axis to the line of action of the force.
• SI unit: Newton-metre (N·m).

Significance in human movement:

• Muscles produce torque at joints to create rotational motion.
• The moment arm of a muscle determines its mechanical advantage.
• Larger moment arms produce greater torque for the same muscle force.
• Understanding torque helps in analyzing lifting, throwing, and joint loading.

Work:

• Work is done when a force moves a body through a distance in the direction of the force.
• 
  where is the angle between force and displacement.
• SI unit: Joule (J).

Energy:

• The capacity to do work. Two main mechanical forms:
  • Kinetic Energy (KE): energy of motion,
  • Potential Energy (PE): energy of position,
• SI unit: Joule (J).

Power:

• The rate of doing work or expending energy.
• SI unit: Watt (W) = J/s.

Relationship:

• Work-Energy Theorem: The work done on a body equals the change in its kinetic energy:
• Power connects work and time, indicating how quickly work is performed.
• In sport, a powerful athlete performs a given amount of work in less time (e.g., explosive jumps).

When two bodies are in contact, several mechanical interactions occur:

Normal Reaction (N):

• The force perpendicular to the contact surface that supports the body against it.
• Equal and opposite to the component of weight pressing into the surface.

Friction:

• The force resisting relative motion between surfaces in contact.
• Acts parallel to the contact surface.

Types of Friction:

• Static friction: prevents motion until a threshold is reached.
• Kinetic (dynamic) friction: opposes motion once sliding begins.

Laws of Friction:

• Frictional force is proportional to the normal reaction:
  where = coefficient of friction.
• Independent of the apparent area of contact.
• Kinetic friction is generally less than maximum static friction.

Biomechanical relevance:

• Friction between shoes and ground enables walking and running.
• Insufficient friction causes slipping; excessive friction can cause injuries.
• Joint surfaces have very low friction due to synovial fluid lubrication.

Equilibrium:

• A state in which a body is at rest or moving with constant velocity, with no net force or net torque acting on it.

Conditions of Equilibrium:

1. Translational Equilibrium (First Condition):

• The vector sum of all forces acting on the body must be zero.
• In components:

2. Rotational Equilibrium (Second Condition):

• The sum of all moments (torques) about any point must be zero.

Types of Equilibrium:

• Stable equilibrium: body returns to original position after slight displacement.
• Unstable equilibrium: body moves further away after displacement.
• Neutral equilibrium: body stays in new position after displacement.

Biomechanical relevance:

• Maintaining balance during standing or gymnastics requires equilibrium.
• The body constantly adjusts muscle forces to keep torques balanced.

Free Body Diagram (FBD) Analysis is a systematic method to solve equilibrium problems.

Steps:

1. Isolate the body or segment of interest.
2. Identify all forces acting on it (weight, reactions, muscle forces, external loads).
3. Draw the FBD with force vectors, magnitudes, directions and points of application.
4. Establish a coordinate system (x and y axes).
5. Apply equilibrium equations:
6. Solve for the unknown forces or moments.

Example — Forearm holding a weight:

• Consider the forearm as a lever with the elbow as the axis.
• Forces: biceps muscle force (), weight of forearm (), external load (), joint reaction ().
• Taking moments about the elbow:
• Solving gives the muscle force required to hold the load in equilibrium.

This technique is fundamental for calculating internal joint and muscle forces.

Center of Gravity (COG):

• The point at which the entire weight of a body may be considered to be concentrated.
• The point through which the resultant force of gravity acts.
• Also referred to as the center of mass in a uniform gravitational field.

Location in the human body:

• In the standard anatomical position, the COG lies approximately at the level of the second sacral vertebra (S2), slightly anterior to it.
• It is around 55–57% of standing height in adults.

Factors affecting COG location:

• Body position/posture: raising arms shifts COG upward.
• Distribution of body mass: heavier lower body lowers COG.
• Addition of external loads: carrying weight shifts COG toward the load.
• Gender: females tend to have a slightly lower COG due to wider pelvis.
• Age: children have relatively higher COG due to larger head-to-body ratio.
• Segment movements: movement of any body segment changes the overall COG.

Significance:

• COG determines stability and balance.
• Athletes manipulate COG for performance (e.g., high jump Fosbury flop).

Balance:

• The ability to maintain the body's center of gravity over its base of support.
• Can be static (maintaining a position) or dynamic (maintaining control during movement).

Stability:

• The resistance of a body to disturbance of its equilibrium.
• A more stable body is harder to topple.

Factors influencing stability:

• Base of support (BOS): larger base → greater stability.
• Height of center of gravity: lower COG → greater stability.
• Position of the line of gravity: stability increases when the line of gravity falls near the center of the base.
• Body mass: greater mass → greater stability (more inertia).
• Friction: higher friction between body and surface increases stability.
• Segmentation and vision: proprioception, vision, and muscular control aid balance.

Biomechanical applications:

• Wrestlers widen their stance and lower their COG for stability.
• Sprinters raise their COG and reduce stability for quick forward movement.

Skeletal Joints (Articulations):

• Points where two or more bones meet, allowing movement and providing mechanical support.

Classification based on movement (functional):

1. Synarthroses (Immovable joints):

• No movement allowed.
• Example: sutures of the skull.

2. Amphiarthroses (Slightly movable joints):

• Limited movement permitted.
• Example: intervertebral discs, pubic symphysis.

3. Diarthroses (Freely movable / synovial joints):

• Wide range of movement; contain synovial fluid.
• Types include:
  • Hinge joint – elbow, knee (flexion/extension).
  • Ball and socket joint – shoulder, hip (multi-axial movement).
  • Pivot joint – atlanto-axial joint (rotation).
  • Gliding (plane) joint – intercarpal joints.
  • Saddle joint – thumb carpometacarpal joint.
  • Condyloid joint – wrist joint.

Mechanical relevance:

• Joint type determines the axes and range of motion available.
• Synovial fluid reduces friction and allows smooth movement.

Skeletal Muscle Structure:

• Composed of bundles of muscle fibers (fascicles).
• Each fiber contains myofibrils made of contractile units called sarcomeres.
• Sarcomeres contain overlapping protein filaments: actin (thin) and myosin (thick).

Force production (Sliding Filament Theory):

• Nerve impulse triggers release of calcium ions.
• Myosin cross-bridges attach to actin and pull the filaments, shortening the sarcomere.
• This produces muscle tension and force.

Types of muscle contraction:

• Concentric: muscle shortens while producing force.
• Eccentric: muscle lengthens under tension.
• Isometric: muscle produces force without changing length.

Mechanical properties:

• Contractility: ability to shorten and produce force.
• Extensibility: ability to stretch.
• Elasticity: ability to return to original length.
• Irritability: ability to respond to stimuli.

Force factors:

• Length-tension relationship: optimal overlap produces maximum force.
• Force-velocity relationship: force decreases as shortening velocity increases.
• Cross-sectional area: larger area produces greater force.

Mechanics of the Elbow Joint:

• The elbow is primarily a hinge joint allowing flexion and extension.
• Main flexor: biceps brachii; main extensor: triceps brachii.

Lever System:

• The elbow acts as a third-class lever during flexion.
  • Fulcrum (axis): elbow joint.
  • Effort: biceps muscle force, applied between fulcrum and load.
  • Load (resistance): weight in the hand.
• Because the effort arm is shorter than the load arm, muscle force must exceed the load — favoring speed and range of motion over force.

Force Analysis (holding a weight):

• Taking moments about the elbow:
  
  where:
  • = biceps force, = muscle moment arm.
  • = forearm weight, = its moment arm.
  • = load, = load moment arm.
• The small moment arm of the biceps means large muscle forces are required.

Joint Reaction Force:

• The elbow joint experiences a large compressive reaction force to maintain equilibrium.

This explains why the elbow is well suited for rapid, wide-range movements but requires high muscle forces.

Mechanics of the Shoulder Joint:

• The shoulder (glenohumeral joint) is a ball-and-socket joint offering the greatest range of motion of any joint in the body.
• Movements: flexion, extension, abduction, adduction, internal/external rotation, and circumduction.

Structural features:

• The humeral head (ball) is large relative to the shallow glenoid cavity (socket).
• Stability relies mainly on soft tissues: rotator cuff muscles, glenoid labrum, ligaments, and joint capsule.

Mechanical analysis:

• The deltoid and rotator cuff work together; the rotator cuff stabilizes the humeral head while the deltoid abducts the arm.
• During abduction, the muscle forces create a force couple to rotate the humerus smoothly.
• Large moment arms are needed to lift the arm against gravity, producing high muscle and joint forces.

Reasons for instability/dislocation:

• Shallow glenoid cavity provides little bony support.
• Large range of motion trades stability for mobility.
• Dependence on soft tissue means weakness or injury of the rotator cuff increases dislocation risk.
• Excessive abduction and external rotation is the common mechanism of anterior dislocation.

Thus the shoulder sacrifices stability for exceptional mobility.

Mechanics of the Spinal Column:

• The spine consists of 33 vertebrae with intervertebral discs acting as shock absorbers.
• It has natural curves (cervical, thoracic, lumbar, sacral) that increase strength and absorb loads.
• The spine functions to support the body, protect the spinal cord, and allow flexibility.

Load-bearing:

• Intervertebral discs distribute compressive loads.
• The curves increase the spine's resistance to axial compression (strength proportional to curves).

Forces during lifting:

• When lifting a load with a forward-bent trunk, the lumbar spine acts as a class-one lever with the fulcrum at the disc.
• The erector spinae muscles have a very short moment arm compared to the long moment arm of the load and upper body weight.
• Taking moments about the lumbosacral disc (L5-S1):
  
• Because is small (~5 cm) and , are large, enormous muscle forces are required.
• This generates very high compressive forces on the disc, often several times body weight.

Injury prevention:

• Lifting with a straight back and bent knees reduces the load moment arm.
• Keeping loads close to the body lowers spinal compression.

Mechanics of the Hip Joint:

• The hip is a ball-and-socket joint between the femoral head and the acetabulum of the pelvis.
• It supports body weight and allows movement in all three planes.
• Deep socket provides good stability while permitting large range of motion.

Single-Leg Stance Analysis:

• During single-leg support (as in walking), the pelvis tends to tilt due to body weight acting on the unsupported side.
• The hip abductor muscles (gluteus medius and minimus) must contract to keep the pelvis level.
• This forms a lever system about the femoral head (fulcrum).

Force balance (moments about femoral head):

• = abductor muscle force, = its short moment arm.
• = body weight (minus stance leg), = larger moment arm.
• Since , the abductor force must be greater than body weight.

Joint Reaction Force:

• The hip joint must support both body weight and the large abductor muscle force.
• Total joint reaction force can be 2.5 to 3 times body weight during single-leg stance.

Clinical relevance:

• Weak abductors cause a Trendelenburg gait (pelvis drops on the swing side).
• Using a cane in the opposite hand reduces hip joint forces.

Mechanics of the Knee Joint:

• The knee is a modified hinge joint allowing mainly flexion and extension, with slight rotation.
• It comprises the tibiofemoral joint (femur-tibia) and the patellofemoral joint (patella-femur).
• Stability is provided by ligaments (ACL, PCL, MCL, LCL) and menisci.

Role of the Patella:

• The patella acts as an anatomical pulley.
• It increases the moment arm of the quadriceps tendon relative to the knee's axis.
• This enhances the mechanical advantage and torque produced by the quadriceps, improving extension efficiency.

Forces during Squatting:

• During squatting, the knee flexes and the quadriceps contract to control descent (eccentric) and rise (concentric).
• As knee flexion angle increases:
  • The quadriceps force required increases.
  • The patellofemoral compressive force rises significantly.
• The line of pull of the quadriceps and patellar tendon creates a compressive force pushing the patella against the femur.

Force relationship:

• Deep squats increase the load moment arm and thus muscle and joint forces.

Clinical relevance:

• Excessive patellofemoral forces in deep squats can cause knee pain.
• Proper technique limits injury risk.

Mechanics of the Ankle Joint:

• The ankle (talocrural joint) is a hinge joint between the tibia, fibula, and talus.
• Primary movements: dorsiflexion (toes up) and plantarflexion (toes down).
• The subtalar joint allows inversion and eversion.

Standing on Toes (Plantarflexion) Analysis:

• When rising onto the toes, the foot acts as a second-class lever.
  • Fulcrum: ball of the foot (metatarsophalangeal joints).
  • Load (resistance): body weight acting through the ankle joint.
  • Effort: the gastrocnemius and soleus muscles pulling via the Achilles tendon.
• In a second-class lever, the load is between the fulcrum and effort, giving a mechanical advantage (effort arm > load arm).

Force balance (moments about the ball of the foot):

• The calf muscles produce force to lift the entire body weight.

Joint Reaction Force:

• The ankle joint must support the sum of body weight and Achilles tendon force, resulting in high compressive forces.

Biomechanical relevance:

• The second-class lever arrangement makes plantarflexion efficient for propulsion in walking, running, and jumping.
• Achilles tendon injuries impair push-off ability.

A lever is a rigid bar that rotates about a fixed point (fulcrum). In the body, bones are levers, joints are fulcrums, and muscles provide effort.

Components: Fulcrum (F), Effort (E), Load/Resistance (R).

1. First-Class Lever (E–F–R):

• Fulcrum lies between effort and load.
• Can favor force or speed depending on arm lengths.
• Example: The atlanto-occipital joint (head balancing on the neck) — neck muscles (effort), joint (fulcrum), head weight (load).

2. Second-Class Lever (F–R–E):

• Load lies between fulcrum and effort.
• Always provides mechanical advantage (favors force).
• Example: Rising on the toes — ball of foot (fulcrum), body weight (load), calf muscles (effort).

3. Third-Class Lever (F–E–R):

• Effort lies between fulcrum and load.
• Favors speed and range of motion, requires greater muscle force.
• Most common lever in the body.
• Example: Elbow flexion — elbow (fulcrum), biceps (effort), hand weight (load).

Summary Table:

Work-Energy Theorem states that the net work done on a body equals the change in its kinetic energy.

Derivation:

• Consider a body of mass acted on by a constant net force , moving through displacement .
• By Newton's second law:
• Work done:
• Using the kinematic equation , we get:
• Substituting:
• Therefore:

Thus, net work = change in kinetic energy.

Application in jumping:

• During a vertical jump, muscles do positive work on the body, increasing its kinetic energy at take-off.
• At the highest point, kinetic energy converts to potential energy:
• This relates take-off velocity to jump height:
• On landing, negative (eccentric) muscle work absorbs kinetic energy to decelerate the body safely.

Significance:

• Explains how muscular work translates into performance.
• Guides training for explosive power and safe landing techniques.

Equilibrium occurs when the net force and net torque acting on a body are zero.

Static Equilibrium:

• The body is completely at rest with no motion.
• Both linear and angular velocities are zero.
• Conditions:
• Examples:
  • Standing still in anatomical position.
  • Holding a static gymnastic pose (e.g., an iron cross on the rings).
  • Maintaining a bridge or plank hold.

Dynamic Equilibrium:

• The body is moving with constant velocity (no acceleration), so net force is still zero.
• Motion continues uniformly.
• Conditions:
• Examples:
  • Skating at constant velocity in a straight line.
  • A parachutist descending at terminal velocity.
  • Cycling at steady speed on level ground.

Key differences:

Common feature: In both, there is no acceleration, so Newton's first law and equilibrium conditions apply.

Balance depends on the interaction of three key concepts:

1. Center of Gravity (COG):

• The point where the body's total weight is concentrated.
• Located approximately at the S2 vertebra in standard standing posture.

2. Line of Gravity (LOG):

• An imaginary vertical line passing downward from the COG toward the ground.
• Represents the direction of gravitational pull.

3. Base of Support (BOS):

• The area beneath and between all points of contact with the supporting surface.
• For standing, it is the region between and under the feet.

Interaction determining balance:

• A body is balanced when its line of gravity falls within the base of support.
• When the LOG moves toward the edge of the BOS, stability decreases.
• When the LOG falls outside the BOS, the body topples (loss of balance) unless corrective action is taken.

Principles for improving stability:

• Enlarge the base of support (wider stance).
• Lower the center of gravity (bend knees).
• Keep the line of gravity centered over the base.

Practical examples:

• A sumo wrestler widens stance and lowers COG for maximum stability.
• A tightrope walker uses a long pole to keep the LOG over the narrow base.
• Leaning to catch a ball shifts the LOG; stepping widens the BOS to prevent falling.

These principles are fundamental to posture, sport performance, and fall prevention.