Newton's Laws of Motion

Newton's Laws of Motion

• Classical physics builds upon the three laws of motion formulated by Isaac Newton.
• Newton's First Law, also known as the law of inertia, states that an object remains at rest or in motion at a constant speed in a straight line unless acted upon by a net external force.

Newton's Second and Third Laws

• Newton's Second Law: force equals mass times acceleration (F=ma); the acceleration of a body is in the direction of, and proportional to, the force, but inversely proportional to the mass of the body.
• Newton's Third Law: for every action, there is an equal and opposite reaction; objects exert equal but opposite forces on one another.

Mass

• Mass is the amount of matter in an object.
• Ordinary objects possess mass, while electromagnetic radiation does not.
• Mass is the resistance of an object to acceleration; a push is needed to start, stop, or change an object's direction.

Velocity

• Average velocity is displacement divided by the time it takes to make the trip.
• Average velocity is measured over a finite time interval, without noting changes.
• Velocity differs from speed; speed is a scalar value without directional qualities.
• Speed measures distance, while velocity measures displacement.

Scalar vs. Vector Quantities

• Scalar quantities, e.g. distance, height, mass, and age, have magnitude only, so they are typically specified with scalar quantities.
• Vector quantities have both magnitude and direction and direction must be specified.
• Weight, velocity and the force applied to a syringe are examples of vectors.
• An ECG is a vector diagram; axis deviation estimates the summation of forces that shift from normal electrical flow in the heart.

Vector Addition

• Adding vectors requires accounting for magnitude and direction.
• The sum of two or more vectors is the resultant and is determined by the graphical or head-to-tail method.

Acceleration

• Acceleration is a vector describing the rate of change of velocity with time.
• Average acceleration = Change velocity / Change time
• The units for acceleration are meters per second squared (m/s²).
• Acceleration involves changing speed and/or direction.

Force

• The physical world is dominated by four fundamental forces: strong nuclear force, electromagnetic force, weak nuclear force, and gravitational force.
• Gravitational force pulls or accelerates all objects with a standard force of 9.81 m (or 32 feet) per second.
• Force is required to produce acceleration and can be a push or a pull.
• Newton's Second Law describes the relationship between force and mass.
• For a given mass, a larger force produces a greater acceleration.

Gravity and Weight

• Gravity is the universal attraction between objects with mass and is the weakest force.
• Weight is the gravitational force exerted on an object by a much larger object, such as the Earth.
• Near the Earth's surface, objects experience the Earth's gravitational field.
• The effect of air molecules interacting with falling objects often hides the force of equal attraction.

Units of Mass and Weight

• Mass is the amount of matter contained in an object.
• Weight is the gravitational force exerted on an object by a larger object.
• The standard unit of force is the newton (N).
• One newton of force accelerates 1 kg of mass by 1 m/s².
• 1 kg mass has a weight of 9.8 N (gravity).
• A dyne is the force required to move 1 g of weight 1 cm/sec.
• Dynes are used in calculating systemic (SVR) and pulmonary vascular resistance (PVR).
• 1 lb. = 4.45 N

Pressure: Definition and Modulation

• Pressure is the force per unit area.
• Pressure can be increased by increasing the applied force or decreasing the area over which the force is applied.
• Pressure can be decreased by decreasing the applied force or increasing the area over which the force is applied.

Units of Pressure

• Pressure is measured in pounds per square inch (psi) in the British system.
• The Sl unit of pressure is the pascal (Pa), which is the pressure exerted by the force of 1 newton over 1 square meter of area.
• Other units in the measurement of pressure are torr, inches of mercury, atmospheres and bar.
• Atmosphere (atm) is the pressure necessary to support a column of mercury 760 mm in height.
• One bar is equivalent to 100 kPa.

Atmospheric Pressure

• Air pressure comes from gravity pulling on the atmosphere, spreading the force over Earth's surface.
• Normal air pressure around 14.7 psi estimates the total weight of the atmosphere.
• 1 atm = 760 mmHg = 14.7 psi; 1 atm = 1 bar = 100 kPa = 1020 cm H2O.
• 1 psi = 54 mmHg; 1 torr = 1 mm Hg.
• 1 kPa = 10.2 cm H2O = 7.5 mm Hg.

Measuring Pressure: Barometers

• A simple mercury barometer consists of a tube closed at one end and open at the other.
• The tube is filled with mercury and inverted into a larger mercury reservoir that is open to the atmosphere.
• This creates a vacuum at the top of the glass tube as mercury runs through it.
• Atmospheric pressure pushes down on the mercury reservoir surface.
• The top of the inverted tube has virtually no pressure causing atmospheric pressure to support column of mercury to a height h.
• Calculation: Patmosphere = pgh, where p is the fluid density, g is the acceleration due to gravity, and h is the height of the column in meters.
• 1 atm of pressure supports a column of mercury 760 mm tall.

Measuring Pressure: Manometers

• A U-shaped tube filled with a fluid of known density reads pressure.
• One end connects to the system to be measured, the other opens to the atmosphere.
• The pressure of the system is determined from ΔP = Psystem- Patmosphere.
• A positive ΔP shows the system exerts pressure higher than atmospheric.
• A negative ΔP shows pressure lower than atmospheric.

Measuring Pressure: Gauges

• Aneroid bellows gauges do not require liquid to operate.
• Aneroid bellows gauges rely on expansion or contraction of bellows as pressure changes.
• Gauges sealed with respect to measure changes in the absolute pressure of the atmosphere.
• Gauges open to the atmosphere and sample measure gauge pressure.
• Bourdon gauges are used on gas cylinders and are a type of aneroid gauge.
• Bourdon gauges measure the pressure difference between a gas in a cylinder & atmospheric pressure.
• Gas at a pressure above atmospheric enters a coiled tube, causing the pointer to move to calibrate.

Measuring Pressure: Gauge Pressure and Total Pressure

• It is vital to specify the type of pressure and how it was determined.
• Barometers measure actual or absolute pressure.
• Manometers and Bourdon gauges measure gauge pressure (pressure of a system "above or below" atmospheric pressure)
• Gauge pressure is relative to atmospheric pressure, not absolute.
• Total pressure includes the atmospheric pressure plus the gauge pressure

Measuring Pressure: Oscillometry

• Automated, noninvasive blood pressure (NIBP) measurement devices are the norm in hospitals, clinics, and medical offices.
• Oscillometry is a method that relies on the measurement of blood pressure oscillations.
• An effective method is to use the piezoelectric transducer that is distorted by pressure, resulting in an electrical signal (a voltage) that is proportional to the pressure change.
• Systolic and diastolic blood pressures are calculated based on the oscillatory pressure readings using computerized algorithms.

Fluids: A Definition

• A fluid is any material that can flow and fluids are defined by their response to stress.
• Stress is the distribution of force per unit area.
• Forces of distribution can be either tangential (shear stress) or perpendicular (normal force).
• Strain is the deformation caused by stress.
• Fluids change shape when subjected to shear stress, which act in one of two ways to perpendicular forces: resist compression (e.g., liquids) or become compressible and easily expandable (e.g., gases).

Fluids

• Liquids and gases are both considered fluids.
• Fluids flow (change shape) due to basic forces, such as gravity, friction, or pressure differences.
• Friction is resistance to flow from surface interaction and is proportional to viscosity.
• Viscosity relates shear stress to the rate of strain (honey vs water).
• Flow results from pressure in a fluid established by differences from one point to another, which creates a pressure gradient as well as is the inherent property of a fluid that resists flow.

Viscosity

• Viscosity is proportional to friction and increases with increasing intermolecular forces.
• Fluids with high viscosity, e.g. honey, do not flow readily.
• Fluids with low viscosity, e.g. water, flow more easily.
• The closer a fluid molecule is to a wall, the slower it moves (think about a river): Adjacent fluid regions will have varying speeds, the faster past the slower.
• Poiseuille's law is used to determine laminar flow based on viscosity and flow.

Hydrostatics

• Hydrostatics studies fluids at rest, while hydrodynamics studies fluids in motion.
• Consider the effects of pressure while thinking about a water beaker or ocean scenario: only the weight of atmosphere is pushing down on the top surface of the water, while atmosphere and the water are pushing down on the beaker bottom.

Hydrostatics: Pressure at the Same Depth

• Assume that a point particle suspended in a fluid with density p occupies no space or volume, then the fluid will act the same, exerting the same pressure in all directions.
• The pressure is independent of the container shape.

Hydrostatics: Pascal's Principle

• External pressure applied to a confined liquid transmits unchanged to every point.
• Pressure can be easily understood by examining the pressure v. depth equation.
• If we increase the pressure by 3 psi on the plunger of a syringe, the pressure will increase everywhere by the same amount, but only if the fluid doesn't move.

Hydrostatics: Buoyancy and Archimedes' Principle

• All fluids exert a buoyant on objects immersed them;
• If an object immersed either totally or partially in a fluid, it will experience a buoyant force equal to its weight.
• The fluid is displaced
• The density of immersed objects determine if they float: objects of greater densities sink, lower densities float.

Hydrostatics: Hydrometers

• Hydrometers measure the specific gravity of liquids such as urine or milk.
• The typical hydrometer has been calibrated and has a weighted end to keep it upright.
• A hydrometer will sink until displacing an amount of of liquid that is exactly equal to its weight.
• If a fluid is dense, a hydrometer will only displace a small amount; a less dense fluid will cause it to sink deeper.

Hydrodynamics: Flow Rate and Types of Fluids

• Flow rate is the volume of fluid passing a particular point per unit time.
• The given volume is expressed as units of volume divided by time, such as gallons per minute or liters per hour (gases LPM)
• The standard units are cubic meters per second (m³/s).
• In terms of speed and diameter: as tube diameter decreases, the speed of the fluid flowing through it increases

Equation of Continuity

• If there are no leaks in the system, the flow rate through a pipe that is narrower on one end must be the same everywhere throughout the area: Flow Rate = Area x Quantity
• Large pipe: larger area but smaller quantity.
• Small pipe: the inverse.

Types of Flow: Laminar Flow

• Laminar flow is smooth.
• In terminal bronchioles, the unchanging character of laminar flow will determine how fluids smoothly slide past each other.
• Molecules positioned in the tube center will encounter less adhesion, leading to a faster velocity.

Types of Flow: Turbulent and Transitional Flow

• Turbulent Flow is not smooth: often occurring bent or corrugated tubing.
• Turbulence is characterized by chaotic and abrupt changes.
• Transitional flow indicates an intermediate mixture of laminar flow at the tube walls mixed with a turbulent flow in the center.

Poiseuille's Law

• Poiseuille's law defines laminar flow for a fluid or gas moving through a tube.
• Flow is directly proportional to r4.
• Per the formula: F = (πr4ΔP/8ηl)
• F represents flow rate, r is radius, n is viscosity, and I is the length of tubing.

Anesthesia Implications of Poiseuille's Law

• This is used to understand the flow rate of air within the lungs, blood in vessels, or fluid in an IV line.
• Increasing the radius flows through a fluid will have the most effect on the rate of flow b/c r is to the power of 4; doubling r increases flow 16 times.
• Decreasing length increases rate of flow. 50% leads to double the rate.
• Decreasing viscosity increases flow.
• Larger diameter endotracheal tubes offer better gas flow.
• Syringes illustrate that doubling the barrel diameter will decrease pressure by a factor of 4.

Specific Examples of Poiseuille's Law

• IVs: a shorter, larger-bore IV increases flow rate.
• PRBCs: adding NS to a unit will both decrease its viscosity and increase flow rate.
• Raising the IV pole or pressure bag increases hydrostatic pressure.
• Albuterol: works to facilitate the diameter of bronchial tubes, enhancing flow.

Reynolds Number

• Reynolds number indicates if a given flow is laminar or turbulent.
• Derived from Poiseuille's law, Reynolds numbers also incorporate fluid density in calculation:

• 2300 is indicative of predominantly turbulent flow, while a value < 2300 indicates predominantly laminar flow.

• Helium serves as an additional example of Reynolds number: it is significantly less dense and functions to restore laminar flow through narrowed airways.
• Reynolds number is directly proportional to density, velocity of flow, tube diameter, and inversely proportional to viscosity

Bernoulli's Principle

• The flow increase applies during gas or fluid passage through a tube diameter narrows (constriction).
• Along with this comes a drop in pressure in the constriction area, relative to the conservation of energy law.
• When attaching a endotracheal tube with half cross-section area decreases speed, increases rate of flow.

Venturi Tube Flowmeter

• The Venturi tube's operation principle is the Bernoulli principle.
• Venturi tubes measure the fluid speed in a pipe, which consists of a middle section with a small diameter connected on both ends to larger diameter sections (allowing for smooth transitions to prevent turbulence).
• The u-tube, which contains a fluid of known density, connects the large and small diameter tubes, and functions like a manometer, determining pressure differential.

Venturi Effect

• The Venturi effects utilizes the Bernoulli effect to add and entrain air to a specific tubes.
• Entrainment, or decreases in pressure, will "pull" air.
• This technique is utilized by both jet ventilation and nebulization.

Coanda Effect

• Coanda effect indicates fluid or gas disposition and its affect on an emerging, curved path/constriction.
• The gas or fluids area tubes increases (x-sectional), the gas/fluid velocity and pressure decreases.
• Given its predisposition to receive the gas or fluid, the tube "tends," in which the pressure increases, to receive the gas or fluid.
• Airways: can cause increased airway occlusions with mucous plugs.

Surface Tension

• Greater intermolecular attractions create both high surface tensions and "skins" on the surface.
• Molecules in the liquid state are attracted to all neighboring molecules by intermolecular forces as well as can operate in all directions and cancel each other out (Deep Sample).
• Attractive Strength also indicates Surface Tension, and that has “no” attraction force from different substances (Surface).

Surface Tension and Water

• Cohesive forces between H20 create significant surface tensions and result in beading of water on a freshly waxed car.
• Higher contact angle: higher bead of water.
• Low contact angle: water spreads across the surface.
• The smaller the tube, the greater the rise.

Surfactants

• Surfactants improve a solvent's ability to be a sovlent.
• They, in general, contain both polar and nonpolar (hydrophobic) tails and tend to generate the "suds" or "bubbles," known as detergents and soaps form the surfactant molecules.
• By forming monolayers, nonpolar molecules will remain "stuck" and "non-water" based and will strive to remain greasy (tails).

Surfactants: Bilayers and Micelles

• Bilayers form when the tails form a double layer during cell membrane creation.
• Micelles are "my cells," where tails form spherical structures.

Laplace's Law

• Surface tension has a way of causing smaller bubbles to empty into larger ones.
• The tension is a force exerted along a straight line.
• Cylinders: T = Pr (vessels;left ventricle) Spheres: T = Pr/2 2T = PR (Pressure-Radius).

Laplace's Law and Alveoli

• Smaller bubbles will increase the smaller pressure.
• Alveoli will vary dramatically for opening.
• Surfactants both lower tension and are chemical and prevent Laplaces Law effects and are also concentrated in the pressure sensitive alveoli by extension.