University of Nicosia Medical School Lectures - Week 1 PDF

INTRODUCTION Dr Anastasia Hadjiconstanti Prof Vered Aharonson Aknowledgements: Dr C.Zervides WELCOME TO THE WORLD OF  Medicine and Physics List the Treatment Chief...

INTRODUCTION Dr Anastasia Hadjiconstanti Prof Vered Aharonson Aknowledgements: Dr C.Zervides WELCOME TO THE WORLD OF  Medicine and Physics List the Treatment Chief Obtain Examination and differential and complaint history tests diagnosis evaluation Use data Select further Final to narrow the tests diagnosis diagnosis More than one Only one likely likely  MEDICAL PHYSICS - DEFINITION Two major areas: 1. Application of physics principles to the understanding of the function of the human body in health and disease (PHYSICS OF PHYSIOLOGY). 2. Application of physics in the instrumentation used in diagnosis, monitoring and treatment (CLINICAL MEDICAL PHYSICS).  Topics covered in MED 101 WEEK TOPIC 1 Introduction, Motion and Statics of the body 2 Energy Kinematics, dynamics, and energetics of human 3 motion and human body collisions Elastic properties of the body and bone fractures 4 and Thermodynamics Fluid pressure, fluid flow in the body and motion 5 in fluids 6 Midterm 7 Lungs and breathing 8 Sound, speech and hearing 9 Light, eyes and vision 10 Electric properties of the body 12 Review  LECTURE LOB’S 1. DESCRIBE THE CONCEPT OF UNITS. 2. DESCRIBE THE CONCEPTS OF ACCURACY, UNCERTAINTY AND SIGNIFICANT FIGURES. 3. DESCRIBE THE CONCEPT OF KINEMATICS (TIME, DISTANCE, DISPLACEMENT, SPEED, VELOCITY & ACCELERATION) 4. UNDERSTAND THE RELATIONSHIPS BETWEEN TIME, DISPLACEMENT, VELOCITY, AND ACCELERATION. 5. UNDERSTAND THE DISTINCTION BETWEEN AVERAGE AND INSTANTANEOUS VELOCITY AND ACCELERATION.  UNITS I Physics is not mathematics, although a considerable amount of mathematics can be required when solving physics problems. Physics, like all sciences, is based on the verification of theories by experiments. Physics is about quantities and not about numbers. A distance of 5 m is different from a time of 5 s, even though the number 5 is used in both cases. This is why physicists insist on the use of units.  UNITS II A unit is a carefully defined amount of a quantity. The measurement of each physical quantity on its own units, by comparison with a standard. The unit is a unique name we assign to measures of that quantity – In example, meter (m) is the unit for the quantity length.  UNITS III Almost all measurable quantities in physics may be expressed in terms of a small number of fundamental types of quantity. These fundamental quantities are: LENGTH, TIME, MASS, ELECTRICAL CURRENT, TEMPERATURE, AMOUNT OF SUBSTANCE AND LUMINOSITY. Most properties of the physical world not included in this list, may be constructed as a combination of these fundamental properties, In example, speed is the ratio of a length to a time. This fact allows us to define systems of units.  UNITS IV A system of units is a convention which defines the standard amounts or units of a set of fundamental quantities. These are called base units. The system of units used almost exclusively in science is the SI system. The SI system of units is a metric system, i.e., a system based on the number 10. In this system the unit of length is the metre (m), the unit of time is the second (s) and the unit of mass is the kilogram (kg). The other base units in the SI system can be found in the Table that follows. Origin of the SI units UNITS V – TABLES FOR SI UNITS  UNITS VI There are many other units in use for quantities other than those described by the base SI units. The table in the previous slide had a short list of units for such quantities. Some of these quantities have their own named unit such as the unit of force, the newton. Such units are often named after famous scientist. All of these other units can, however, be expressed as a combination of the six base SI units. Some definitions, and medical terminology A common language is essential for a “Pericarditis“ meaningful communication prefix: peri- = “surrounding” root: cardi = “heart” Medical terms are international, suffix: -itis = “inflammation” derived from Greek and Latin = an inflammation of the area surrounding the heart construction of the medical terms: root (word base) “Phonocardiography“ prefixes phono = sound; suffixes cardi = heart; linking or combining vowels graph = write = graphic recording of heart sounds  UNITS VII - TERMINOLOGY This system of units also specifies a set of prefixes which are prepended to the unit to indicate quantity in powers of 10 : N X 10x {Unit} N: Numbers 10: Base x: Exponent Note: 10-x à 1/10x Each prefix has a specific name. Each prefix has a specific abbreviation. Nano-, micro-, milli-, centi-, …, kilo-, mega-, giga-, tera- 10-9 …………………………………………………………………………………………………………1012 These prefixes make it easier to refer to very large or very small numbers.  UNITS VIII – PREFIXES TABLE There are many more, but these are the ones which will be useful in this course. Symbol Name Multiplication p pico 1 x 10-12 n nano 1 x 10-9 μ micro 1 x 10-6 m milli 1 x 10-3 k kilo 1 x 103 M Mega 1 x 106 G Giga 1 x 109 T Tera 1 x 1012  UNITS IX – CHANGING UNITS We often need to change the units in which a physical quantity is expressed. We do so by a method called chain – link conversion. In this method, we multiply the original measurement by a conversion factor (a ratio of units that is equal to unity).  CLASS EXAMPLE I: Changing units Because 1 min and 60 s are identical time intervals, we have 1min 60 s =1 and =1 60s 1min Thus, the ratios can be used as conversion factors. This is NOT the same as writing or 1 60 =1 =1 60 1 Each number and its unit must be treated together.  CLASS EXAMPLE II: Changing units Because multiplying any quantity by unity leaves the quantity unchanged, we can introduce conversion factors wherever we find them useful. In chain – link conversion, we use the factors to cancel the unwanted units. For example, to convert 2 min to seconds, we have æ 60 s ö 2 min = (2 min) (1) = (2 min) ç ÷ = 120 s è 1min ø If you introduce a conversion factor in such a way that unwanted units do not cancel, invert the factor and try again. In conversions, the units obey the same algebraic rules as variables and numbers.  ACCURACY, UNCERTAINTY AND SIGNIFICANT FIGURES I In science, accuracy and precision have different meanings. Accuracy refers to how close a given measurement is to an accepted standard. Precision refers to the reproducibility of a measurement and is not necessarily related to the accuracy of the measurement. In general it is desirable to have both good accuracy and precision. Unfortunately sometimes accuracy is limited by uncontrollable factors, i.e. difficult in measuring internal parts of the body accurately (amount of mineral in bones). DEXA has a precision of ≈1% and an accuracy of 3 to 4 % but it is used for managing osteoporosis. Accuracy, Precision, Uncertainty - Illustration Accuracy = a description of how close a measurement is to the correct or accepted value of the quantity measured. Precision = the degree of exactness of a measurement. uncertainty = a numeric measure of confidence in a measurement or result. A lower uncertainty indicates greater confidence. Prof. Vered Aharonson 2018 26  ACCURACY, UNCERTAINTY AND SIGNIFICANT FIGURES II The numerical values of physical quantities cannot be given with infinite precision. A common convention used in science to indicate precision is known as significant figures. The numerical value of a physical quantity will be given to a number of significant figures, Depending on the nature of the calculation. The number of significant figures is, with some conditions, the number of digits given. In example: he acceleration due to gravity may be given as 9.8 ms−2 or as 9.81 ms−2. In 9.8 ms−2 there are two digits so there are two significant figures (2 s.f.) In 9.81 ms−2 there are three significant figures (3 s.f.). Numbers with more significant figures are more precise than numbers with fewer significant figures. Significant Figures - illustration Even though this ruler is marked in only centimeters and half-centimeters, if you estimate, you can use it to report measurements to a precision of a millimeter.  ACCURACY, UNCERTAINTY AND SIGNIFICANT FIGURES III If a physical quantity is given to two significant figures there is an implicit uncertainty in the final digit. 9.8 ms−1 may be read as 9.8 ± 0.05 ms−1. This implicit uncertainty implicate on the use of inexact numerical values in calculations. In example, the solution to a calculation involving quantities given to two significant figures should not be given to four or five significant figures. Practically: How many significant figures should be quoted in a solution of a calculations? What if the numbers used in the calculation have different numbers of significant figures?  ACCURACY, UNCERTAINTY AND SIGNIFICANT FIGURES IV For our purposes, three simple rules of thumb will suffice: 1. Use all available digits in the calculation. Round the solution and not the intermediate steps. 1. When multiplying or dividing two numbers the solution should be rounded to the same number of significant figures as the number in the calculation that had the least significant figures. 𝟐. 𝟑×𝟑. 𝟏𝟓𝟏𝟓𝟗 = 𝟕. 𝟐𝟒𝟖𝟔𝟓𝟕 = 𝟕. 𝟐 3. When adding or subtracting numbers the solution should be rounded to the same number of decimal places as the number in the calculation that had the least number of decimal places. 𝟏𝟎. 𝟏 + 𝟏𝟐. 𝟑𝟔𝟕 + 𝟎. 𝟒𝟓𝟗 = 𝟐𝟏. 𝟗𝟐𝟔 = 𝟐𝟏. 𝟗 (𝟏 𝒅. 𝒑. )  ACCURACY, UNCERTAINTY AND SIGNIFICANT FIGURES V Example Number of Scientific Significant Notation Figures Leading zeros are never significant. Imbedded zeros are always 0.00682 3 6.82 x 10-3 Leading zeros significant. are not Trailing zeros are significant only if significant the decimal point is specified. 1.072 4 1.072 (x 100) Imbedded zeros are always Hint: Change the number to scientific significant. notation. It is easier to see. 300 1 3 x 102 Trailing zeros are significant only if 300. 3 3.00 x 102 the decimal point is specified 300.0 4 3.000 x 102 32 ACCURACY, UNCERTAINTY AND SIGNIFICANT FIGURES VI CLASS EXAMPLE III When adding or subtracting numbers the solution should be rounded to the same number of decimal places as the number in the calculation with the least number of decimal places. 33 ACCURACY, UNCERTAINTY AND SIGNIFICANT FIGURES VIII CLASS EXAMPLE IV The answer must be rounded off to 2 significant figures, since 1.6 only has 2 significant figures. The answer must be rounded off to 3 significant figures, since 45.2 has only 3 significant figures  KINEMATICS I MOTION The universe, earth, and everything in it, moves. Even seemingly stationary things, such as roadway, move with Earth’s rotation! The classification and comparison of motions (called Kinematics) is often challenging. What exactly do you measure, and how do you compare?  KINEMATICS II Position To locate an object means to find its position relative to some reference point, often the origin (or zero point) of an axis. The origin is where x = 0, y = 0. The x and y axes are always perpendicular to each other. Objects positioned to the right of the origin of coordinated (0) on the x axis have an x coordinate to be positive; then points to the left of 0 have a negative x coordinate. The position along the y axis is usually considered positive when above 0, and negative when below 0.  KINEMATICS III Distance and displacement The distance an object travels is defined as the length of the path that the object took in travelling from one place to another. Distance is a scalar quantity. Displacement, on the other hand, is the distance travelled, but with a direction associated. Δ𝑥 = 𝑥! − 𝑥" Displacement is a vector quantity. For example, if the particle moves from x1 = 5m to x2= 200 m and the back to x1 = 5m, the displacement from start to finish is zero.  KINEMATICS IV Speed and Velocity An important aspect of the motion of a moving object is how fast it is moving – its speed or velocity. The average velocity, defined as the displacement divided by the elapsed time. Δ𝐱 𝐯= Δt The SI unit for average velocity is the meter per second (m/s). Velocity, is used to signify both the magnitude (numerical value) of how fast an object is moving and also the direction in which is moving.  KINEMATICS V Speed and Velocity Average speed is a different way of describing “how fast” a particle moves. The average velocity involves the particle’s displacement The average speed involves the total distance covered, independent of direction.  KINEMATICS VI Acceleration An object whose velocity is changing is said to be accelerating. For instance, a whose velocity increases in magnitude from zero to 80 km/h is accelerating. Acceleration specifies how rapidly the velocity of an object is changing. Average acceleration is defined as the change in velocity divided by the time taken to make this change. 𝛥𝒗 𝛼= 𝛥𝑡 A common unit of acceleration is the meter per second per second, m / s 2.  ACCELERATION DUE TO GRAVITY All objects falling freely towards the Earth have the same acceleration. The value of this constant acceleration is given by : 𝒈 = 𝟗. 𝟖𝟏 𝒎⁄𝒔𝟐. g is called the acceleration due to gravity. CLASS EXAMPLE V Which of the following graphs represents an object at rest? A. (A). B. (B). C. (C). D. (D). E. (E). Figure: Graphs Describing Object Motion or Lack of.  SUMMARY I Physics requires the use of units. Fundamental physical quantities are: LENGTH, TIME, MASS, ELECTRICAL CURRENT, TEMPERATURE, AMOUNT OF SUBSTANCE AND LUMINOSITY. The SI system of units is a metric system, a system based on the number 10. elapsed time (Δt ) The time interval between two events. distance (d or Δx) The length of a path between two spatial positions. displacement (d or Δx) The vector equivalent of distance, which specifies the distance and direction of one point in space relative to another. It depends only on the initial and final spatial positions, and is independent of the path taken from one position to the other.  SUMMARY II speed (v) A scalar measure of the rate of motion. The SI unit of speed is metres per second (m/s or m/s). velocity (v) A vector measure of the rate of motion, which specifies both the magnitude and direction of the rate of motion. acceleration (a) A measure of the rate of change of the velocity. Acceleration is a vector quantity. The SI units of acceleration are 𝒎⁄𝒔𝟐. All objects falling freely towards the Earth have the same acceleration. The value of this constant acceleration is given by : 𝒈 = 𝟗. 𝟖𝟏 𝒎⁄𝒔𝟐. g is called the acceleration due to gravity.  REFERENCES Authors Title Edition Publisher Year ISBN Kirsten Franklin, Paul Introduction to Biological John Wiley & Muir, Terry Physics for the Health and 1st Edition 2010 9780470665930 Sons Scott and Paul Life Sciences Yates J.R. Cameron, Medical J.G. Skofronick Physics of the body 2nd Edition Physics 2017 9781930524941 and R.M. Publishing Grant I.P. Herman Physics of the Human Body 2nd Edition Springer 2016 978331923930 Martin Zinke Cengage Physics of the Life Sciences 3rd Edition 2016 9780176558697 Allmag Learning R.K.Hobbie Intermediate Physics for 5th Edition Springer 2015 9783319126814 and B.J.Roth Medicine and Biology FORCES AND NEWTON’S LAWS Dr Anastasia Hadjiconstanti Prof Vered Aharonson Aknowledgements: Dr C.Zervides  LECTURE LOB’S 6. DESCRIBE THE CONCEPT OF FORCE. 7. UNDERSTAND THE RELATIONSHIP BETWEEN FORCE AND MOTION. 8. IDENTIFY ACTION-REACTION PAIRS OF FORCES. 9. UNDERSTAND NORMAL, FRICTION AND TENSION FORCES.  FORCE I The Oxford English Dictionary gives a number of definitions of the noun ‘force’. But in physics terminology force is a measurable influence that causes something to move. Or: Force is anything that is measurable and causes a change in the motion of an object. Newton’s first law: Any object continues at rest, or at constant velocity, unless an external force acts on it.  FORCE II An external force gives an object an acceleration. The acceleration produced is proportional to the force applied, and the constant of proportionality is the mass. Newton’s second law is summarised by the following equation: 𝑭 = 𝒎𝜶 The SI unit of force is the newton. One newton (1 N) is the force which would accelerate a 1 kg mass at an acceleration of 1 m/s2.  FORCE III Since any object of mass m near the surface of the Earth falls with acceleration downwards, there must be a force acting on it. This downward force is due the earth’s gravity. The acceleration is called acceleration of gravity , and is the same for any object moving under the sole influence of gravity This important quantity has a special symbol to denote it : the symbol g. The direction of this force is down toward the center of the Earth. The magnitude of the force, W, is: 𝑾 = 𝒎𝒈 – this is the object’s weight Note: the weight of an object is a FORCE not a MASS !! When we step on our bathroom scales and are told our mass in kilograms, we are being given our weight in Newton with a zero removed.  FORCE IV Question The force of gravity acts on an object when is falling. When an object is at rest on the Earth, the gravitational force on it does not disappear. This force, continues to act. Why, then, doesn’t the object move? From Newton’s second law, the net force on an object that remains at rest is zero. There must be another force on the object to balance the gravitational force.  FORCE V – THE Normal Force For an object resting on a table, the table exerts an upward force. The table is compressed slightly beneath the object. The force exerted by the table is often called a contact force, since it occurs when two objects are in contact. When a contact force acts perpendicular to the common surface of contact, it is called the normal force (“normal” means perpendicular); ! It is labeled F N  FORCE VI - Newton’s third law Newton’s third law states that forces come in pairs. For every force that is applied to a body, there is a force applied by that body. The force applied by one object on another object is called the action. If the ‘action’ is the force exerted by an object A on an object B. Then according to Newton’s third law, object B will exert a force of equal size, but in the opposite direction, on object A. This second force is the ‘reaction’ to the force exerted by object A. Remember: the “action” force and the “reaction” force are acting on different objects.  FORCE VII - CLASS EXAMPLE I The two forces are both acting on the statue, which remains at rest, so the vector sum of these two forces must be zero (Newton’s second law). Hence FG and FN must be of equal magnitude and in opposite directions. But they are not the equal and opposite forces as per Newton’s third law. Why? The action and reaction forces of Newton’s third law act on different objects, whereas the two forces shown in figure act on the same object. FORCE VIII - CLASS EXAMPLES II  KINDS OF FORCE Fundamental Forces of nature Specific Forces 1. Electromagnetic force 1. Normal force 2. Gravitational force 2. Tension force 3. Strong nuclear forces. 3. Friction force 4. Weak nuclear forces  TENSION I When a cord (or a rope, cable, or other such object) is attached to a body and pulled tight, the cord pulls on the body with a force directed away from the body and along the cord. The force is often called a tension force because the cord is said to be in state tension (or to be under tension).  TENSION II The cable is assumed to be: Massless: meaning its mass is negligible compared to the body’s mass) and Unstretchable: the cable exists only as a connection between the two bodies. It pulls on both bodies with the same force magnitude T  FRICTION I If we either attempt to slide or slide a body over a surface, the motion is resisted by a bonding between the body and the surface. The resistance is considered to be a single force, called either the frictional force or simply friction. This force is directed along the surface, opposite the direction of the intended motion. In the first case (tends to move) the resistance is called static friction while in the second case (motion) is called kinetic friction.  FRICTION II The coefficients calculated from f = μN are known as the coefficients of static and kinetic friction, respectively. The coefficient of kinetic friction is always smaller than the coefficient of static friction.  SUMMARY I Newton’s first law states that any object continues at rest, or at constant velocity, unless an external force acts on it. Newton’s second law is summarised by the following equation: 𝑭 = 𝒎𝜶 Newton’s third law states that forces come in pairs. For every force that is applied to a body, there is a force applied by that body. The force applied by one object on another object is referred to as the action.  SUMMARY II Normal force (N) The perpendicular component of the contact force between two objects in physical contact with each other. Tension force (T ) A force that tends to stretch intermolecular bonds. Friction force ( f ) A force that resists the relative motion between two surfaces in contact.  REFERENCES Authors Title Edition Publisher Year ISBN Kirsten Franklin, Paul Introduction to Biological John Wiley & Muir, Terry Physics for the Health and 1st Edition 2010 9780470665930 Sons Scott and Paul Life Sciences Yates J.R. Cameron, Medical J.G. Skofronick Physics of the body 2nd Edition Physics 2017 9781930524941 and R.M. Publishing Grant I.P. Herman Physics of the Human Body 2nd Edition Springer 2016 978331923930 Martin Zinke Cengage Physics of the Life Sciences 3rd Edition 2016 9780176558697 Allmag Learning R.K.Hobbie Intermediate Physics for 5th Edition Springer 2015 9783319126814 and B.J.Roth Medicine and Biology STATICS OF THE BODY Dr Anastasia Hadjiconstanti Prof Vered Aharonson Aknowledgements: Dr C.Zervides  LECTURE LOB’S 10. DESCRIBE THE CONCEPT OF EQUILIBRIUM. 11.DESCRIBE THE CONCEPT OF TORQUE. 12.EXPLAIN MOTION IN ONE PLANE AND LEVERS. 13.INVESTIGATE STATICS IN THE BODY. 14.INVESTIGATE THE PRINCIPLE OF MOMENTS. 15.DESCRIBE THE CONCEPT OF CENTRE OF GRAVITY / CENTRE OF MASS.  INTRODUCTION I We will investigate the statics of the body by: reviewing forces, torques, and equilibrium, then applying these conditions to statics in a plane and a lever. We will analyse examples of statics in the body including: the lower arm, knee. hips, shoulder,  INTRODUCTION II Some of these are related to injuries in the body (hip & back). The study of forces in equilibrium is called “STATICS” – the study of bodies which are not accelerating. A system is in dynamic equilibrium when it is in equilibrium and also in motion, which implies that the system is travelling at constant velocity and/or rotating at a constant rate. We will focus on the study of the force balance of an object at rest. STATICS is a very important area of biomechanics.  REVIEW OF FORCES, TORQUES AND EQUILIBRIUM I Each force F can be resolved into components in the x, y, and z directions (Fx, Fy, Fz). In a static condition the sum of the forces F in each of the x, y, and z directions is zero: ! 𝑭𝒙 = 𝟎, ! 𝑭𝒚 = 𝟎, ! 𝑭𝒛 = 𝟎. These forces can be in balance EITHER for the entire body OR for any part of the body.  REVIEW OF FORCES, TORQUES AND EQUILIBRIUM II Each torque τ can be resolved into components in the x, y, and z directions (τx, τy, τz). In a static condition, the torques τ about the x, y, and z axes also each sum to zero for the entire body and for any body part: ! 𝝉𝒙 = 𝟎, ! 𝝉𝒚 = 𝟎, ! 𝝉𝒛 = 𝟎.  REVIEW OF FORCES, TORQUES AND EQUILIBRIUM III A system is said to be in equilibrium when the net force on that system is zero and the net torque on the system is also zero. A system is in static equilibrium when it is in equilibrium and stationary. Static equilibrium occurs when: a seesaw is perfectly balanced, or in the ankle when an individual stands on tip toe, or in the elbow joint when an individual holds an object.  REVIEW OF FORCES, TORQUES AND EQUILIBRIUM IV A system is in stable equilibrium if it will return to equilibrium after it has been subject to a small displacement. A system is in an unstable equilibrium if it will not return to this equilibrium having been subject to a small displacement. Clearly, an object with a much narrower top and broader base will be more unstable when placed on its top and more stable when placed on its base.  STANDING: STABILITY I Stability is essential during standing, as well as during any type of motion. First consider the body as a rigid mass. The criterion for overall stability during standing is for the center of mass to be over the area spanned by the feet. This means that a vertical line passing through the center of mass passes in this area of the support base.  STANDING: STABILITY II Otherwise, torques would not be balanced => unstable => topple over. When the center of mass is above the area spanned by the feet: the right foot causes a - torque and the left foot causes a + torque, and they cancel out.  STANDING: STABILITY III When the center of mass is to the left of the foot area both torques are negative. When it is to the right both torques are positive. The torques cannot balance in either case, and there is instability. STAND UP AND TRY IT! TRY TO LEAN OVER!  STANDING: STABILITY IV We are most stable when the line of gravity is near the center of the support base. When we lean the line of gravity can pass through the periphery of this base or outside this base. The term center of gravity is also often used in stability analysis.  WHAT IS A TORQUE I? Torque is the tendency of a force to rotate an object about: an axis, fulcrum (the point at which a lever pivots) or pivot. Torque can be thought of as a twist. The physical quantity which causes an object to begin to rotate or move in a circle, or to change its rate of rotation, is a torque. A torque is not a force in the Newtonian sense: it is a moment.  WHAT IS A TORQUE II? The amount of turning produced by the force applied to a rod will depend: on the magnitude of the force (F) and the length of the rod (d). The product of these two factors gives the torque, τ: 𝝉 = 𝐅𝐝 Torque is measured in units of N m. The torque provides us with a useful way to measure the turning effect (i.e., the tendency to cause rotation) of a force applied to a rod, which we call a moment arm or lever.  WHAT IS A TORQUE III? CLASS EXAMPLE I 𝝉 = 𝐅𝐝 A longer lever arm (distance from the point at which the force is applied to the axis of rotation) is very helpful in rotating objects. It actually defines the rotating ability of the force. https://youtu.be/46mPNzoScKs  WHAT IS A TORQUE IV? Positive torque : => motion in the counter-clockwise direction. Negative torque: => motion in the clockwise direction. Any force that causes a counterclockwise rotation about a pivot point is said to cause a positive torque. Any force that causes a clockwise rotation is said to cause a negative torque. WHAT IS A TORQUE V?  STATICS: MOTION IN ONE PLANE AND LEVERS I Many problems involve motion in one plane. Thus the equilibrium equations can be reduced to three: ! 𝑭𝒙 = 𝟎, ! 𝑭𝒚 = 𝟎, ! 𝝉𝒛 = 𝟎. These problems can be classified as one of three types of levers.  STATICS: MOTION IN ONE PLANE AND LEVERS II For a system in static equilibrium, all torques are balanced so that there is no net torque. Since there is no net ‘tendency to rotate’, the system will remain motionless. At equilibrium, the sum of the clockwise moments equals the sum of the counterclockwise moments. This condition is called the PRINCIPLE OF MOMENTS. Therefore, at equilibrium we can write: ! 𝑭𝒄𝒘𝒅𝒄𝒘 = ! 𝑭𝒄𝒄𝒘𝒅𝒄𝒄𝒘  STATICS: MOTION IN ONE PLANE AND LEVERS III First class lever, weight (load) + muscle (effort) act on opposite sides of fulcrum and in the same direction. LEAST COMMON LEVER IN THE BODY. One type of the first class lever is a seesaw or teeter totter. A second type is the head atop the spinal cord.  STATICS: MOTION IN ONE PLANE AND LEVERS IV Second class lever, muscle (effort) + weight (load) act on same side of fulcrum, and weight (load) nearer the fulcrum. SECOND MOST COMMON LEVER IN THE BODY. One example is standing on tiptoes.  STATICS: MOTION IN ONE PLANE AND LEVERS V Third class levers, muscle (effort) + weight (load) are on same side of fulcrum, with muscle (effort) nearer to the fulcrum. MOST COMMON LEVER IN THE BODY. One example of a third class lever is the balancing of the lower arm by the biceps brachii inserted on the radius. STATICS: MOTION IN ONE PLANE AND LEVERS VI  STATICS: MOTION IN ONE PLANE AND LEVERS VII In the human body… https://www.youtube.com/watch?v=d1wS_OlJzmI&ab_channel=Bifrost  IN CLASS EXAMPLE 1 Find for each type of lever, the muscle force M needed to maintain equilibrium. Positive torque 𝒅𝒘 & 𝝉𝒛 = 𝟎 ⇒ 𝑾𝒅𝒘 − 𝑴𝒅𝒎 = 𝟎 ⇒ 𝑴 = 𝑾 𝒅𝒎 Negative torque Positive torque 𝒅𝒘 & 𝝉𝒛 = 𝟎 ⇒ 𝑴𝒅𝒎 − 𝑾𝒅𝒘 = 𝟎 ⇒ 𝑴 = 𝑾 𝒅𝒎 Negative torque Positive torque 𝒅𝒘 & 𝝉𝒛 = 𝟎 ⇒ 𝑴𝒅𝒎 − 𝑾𝒅𝒘 = 𝟎 ⇒ 𝑴 = 𝑾 𝒅𝒎 Negative torque  STATICS IN THE BODY: THE LOWER ARM Examine the equilibrium of the forearm balanced by the contraction of the biceps brachii inserted on the radius. In equilibrium, the biceps brachii force counters the potential rotation about the elbow joint by the weight held in the hand.  IN CLASS EXAMPLE 2 The elbow joint is essentially a hinge. The forearm rotates about the elbow joint, and the muscles of the upper arm, in particular the biceps muscle, attach to the bones of the forearm just below the joint. In this example we will calculate the force which the biceps muscle must apply to the forearm to hold a 4 kg weight horizontally in the hand. The mass of the forearm and the mass held in the hand both contribute to the clockwise moment, giving a total clockwise moment of 𝑚 𝑚 2.5 𝑘𝑔×9.81 " ×0.15 𝑚 + 4 𝑘𝑔×9.81 " ×0.40 𝑚 = 19.37 𝑁𝑚 𝑠 𝑠 The only counter-clockwise moment is provided by the biceps muscle, thus if the weight is held stationary the clockwise and counter-clockwise moments must be equal so that 𝐹 ×0.04 𝑚 = 19.37 𝑁𝑚 #$%&'( 19.37 𝑁𝑚 𝐹#$%&'( = = 𝟒𝟖𝟒 𝑵 0.04 𝑚 IN CLASS EXAMPLE 2 COMMENT Thus holding a 4 kg weight in the hand (i.e., at the end of a lever arm) requires that the biceps muscle supply enough force to hold a 49 kg weight if that weight were not at the end of a lever. The arm is optimised for speed rather than strength. The lever arrangement by which we lift objects in our hands does not maximise lifting strength. However this organisation of muscles and limbs does greatly increase the speed with which the hand is able to move. The human arm is better at throwing spears than it is at lifting rocks. Note that this analysis also explains why it is easier to lift heavy weights if they are tucked into the arm rather than held in the hand.  CENTRE OF GRAVITY / CENTRE OF MASS I Could we consider a single point where the weight of the object is acting? pivot point  CENTRE OF GRAVITY / CENTRE OF MASS II In order to make use of the full power of the principle of moments, we will make use of another concept. The centre of mass or the centre of gravity when dealing with a uniform gravitational field. When a long ruler is carefully balanced on a pivot, the pivot point is located at the centre of gravity. pivot point EXERCISE FOR HOME Find the muscle force M needed to provide balance when the biceps brachii is inserted 4 cm from the elbow joint. The forearm is 0.146H long and the hand length is 0.108H where H is the body height. The weight in the hand is about (0.146 +0.108/2)H = 0.2H from the elbow joint. Note that H = 180 cm and the weight W = 100 N. Assume that forearm and upper arm make a 90 degree angle and neglect the mass of the forearm.  SUMMARY I The study of forces in equilibrium is called “STATICS”. In a static condition the sum of the forces F in each of the x, y, and z directions is zero: ! 𝑭𝒙 = 𝟎, ! 𝑭𝒚 = 𝟎, ! 𝑭𝒛 = 𝟎. In a static condition, the torques τ about the x, y, and z axes also each sum to zero for the entire body and for any body part: ! 𝝉𝒙 = 𝟎, ! 𝝉𝒚 = 𝟎, ! 𝝉𝒛 = 𝟎.  SUMMARY II static equilibrium A static equilibrium occurs when a system is in equilibrium and stationary. dynamic equilibrium A dynamic equilibrium occurs when a system is in equilibrium and also in motion. Dynamic equilibrium implies that the system has constant velocity and rate of rotation. stable equilibrium An equilibrium is stable if the system will return to equilibrium if it is subject to a small displacement. unstable equilibrium An equilibrium is unstable if the system will not return to this equilibrium if it is subject to a small displacement.  SUMMARY III Torque is the tendency of a force to rotate an object about: an axis, fulcrum (the point at which a lever pivots) or pivot. Positive torque : => motion in the counter-clockwise direction. Negative torque: => motion in the clockwise direction.  SUMMARY IV Many problems involve motion in one plane. Thus the equilibrium equations can be reduced to three: ! 𝑭𝒙 = 𝟎, ! 𝑭𝒚 = 𝟎, ! 𝝉𝒛 = 𝟎. These problems can be classified as one of three types of levers. First class lever, weight (load) + muscle (effort) act on opposite sides of fulcrum and in the same direction. LEAST COMMON LEVER IN THE BODY.  SUMMARY V Second class lever, muscle (effort) + weight (load) act on same side of fulcrum, and weight (load) nearer the fulcrum. SECOND MOST COMMON LEVER IN THE BODY. Third class levers, muscle (effort) + weight (load) are on same side of fulcrum, with muscle (effort) nearer to the fulcrum. MOST COMMON LEVER IN THE BODY.  SUMMARY VI centre of mass The point at which the total mass of a body may be considered to be concentrated (for many purposes) in analysing its motion. centre of gravity The point where the total weight of a material body may be thought to be concentrated. In a uniform gravitational field, this coincides with the centre of mass, but the centre of mass does not require a gravitational field.  REFERENCES Authors Title Edition Publisher Year ISBN Kirsten Franklin, Paul Introduction to Biological John Wiley & Muir, Terry Physics for the Health and 1st Edition 2010 9780470665930 Sons Scott and Pa Life Sciences ul Yates I.P. Herman Physics of the Human Body 2nd Edition Springer 2016 978331923930 Martin Zinke Cengage Physics of the Life Sciences 3rd Edition 2016 9780176558697 Allmag Learning R.K.Hobbie Intermediate Physics for 5th Edition Springer 2015 9783319126814 and B.J.Roth Medicine and Biology Physics in Biology and Academic P. Davidovits 4th Edition 2012 9780763730406 Medicine Press