Scope-of-Final-Exam.pdf

DYNAMICS NEWTON’S LAWS OF MOTION NEWTON’S LAWS of motion FORCE Push or a pull exerted by an object on another. In mechanics, it is It is a vector quantity because it has both magnitude and direction. An external force is one whose source lies outside of the system being considered....

DYNAMICS NEWTON’S LAWS OF MOTION NEWTON’S LAWS of motion FORCE Push or a pull exerted by an object on another. In mechanics, it is It is a vector quantity because it has both magnitude and direction. An external force is one whose source lies outside of the system being considered.  NEWTON’S LAWS of motion Force between two bodies that are in direct contact with each other is called CONTACT FORCE Force that acts even if the interacting bodies are separated by a distance is called NONCONTACT OR ACTION-AT-A-DISTANCE FORCE Examples of Contact Force Friction and the force exerted by your muscles when you lift an object. Examples of Noncontact Forces Gravitational Force, Electrostatic Force between charged bodies and magnetic force  NEWTON’S LAWS of motion FOUR FUNDAMENTAL FORCES OF NATURE GRAVITATIONAL FORCE is the attractive force exerted by objects with the mass ELECTROMAGNETIC FORCE is the force that holds atoms and molecules together. STRONG NUCLEAR FORCE is the force between protons and neutrons in nucleus WEAK NUCLEAR FORCE plays a role in the radioactive decay of some nuclei NEWTON’S LAWS of motion ISAAC NEWTON he was credited for being the first to describe the motion of massive objects and formulate the three laws of motion. NEWTON’S LAWS of motion constitute the fundamental principles of dynamics, which deals with force in relation to the motion of an object Newton’s first, second, and third laws of motion are also called the law of inertia, the law of  NEWTON’S FIRST LAW  LAW OF INERTIA The Law of inertia states: “ a body at rest will remain at rest and a body in motion will continue to move with constant velocity unless acted upon by an unbalanced external force” Net Force or Resultant Force is the vector sum of all the forces acting on a body A resultant force that is not equal to zero is considered an UNBALANCED FORCE. INERTIA is the property of a body that LAW OF INERTIA INERTIAL REFERENCE FRAME A frame of reference where Newton’s first law of motion holds is called INERTIAL REFERENCE FRAME. Thus, a frame of reference that is at rest or moving with constant velocity with respect to an observer is inertial. Furthermore, a frame of reference that is moving with constant velocity with respect to an inertial frame is also inertial. Accelerated frames of reference are not inertial. Earth, despite its rotation, is often considered an inertial frame because its angular speed of 7.27 x 10 ^-5 radians/s is  NEWTON’S second LAW Law of acceleration The first part of the second law implies that the magnitude of the net force (F) acting on a body and the magnitude of the acceleration it produced are directly proportional to each other. Recall in algebra that two quantities are directly proportional to each other if their ratio is constant (k). Thus, for a constant mass, 𝐅 = k 𝐚 Equivalently, if a force 1 F1 is applied to a body at one time and a force 2 F2 is applied to the same body at another time, then 𝐹1 𝑎1 Law of acceleration The second part of Newton’s second law of motion implies that the magnitude of the acceleration of a body produced by a net force acting on it is inversely proportional to its mass. The greater the mass of a body, the lesser the acceleration Recall in algebra that two quantities are inversely proportional to each other if their product is constant (k). Thus, for a constant force, ma=k Law of acceleration Newton’s second law of motion tells us that the acceleration of a body is dependent upon two variables: the net force F acting upon the body and its mass m. The combined effect of these two variables on the acceleration of a body may be written in equation form as F=ma Eq. (4.1) The SI unit of Force is 1 newton (N). A force of 1 N is the force that will give a 1 kg body an acceleration of 1 Law of acceleration A smaller unit of force is the dyne. A force of 1 dyne will give a 1 g body an acceleration of 1 cm/s^2 𝑘𝑔.𝑚 1 N = 1 𝑠2 𝑔.𝑐𝑚 1 dyne = 1 2 𝑠 1 N = 105 dynes Law of acceleration Three Important Things that must be remembered about Eq. (4.1) 1. Net force is the resultant of all the forces acting on a body. It should not include the forces being exerted by the body on another. 2. Force and Acceleration are vector quantities. Hence, one can write a separate equation for each component of the force and the corresponding component of the acceleration, in 3-D space. Thus Σ 𝐹𝑥 = 𝑚𝑎𝑥 Σ 𝐹𝑦 = 𝑚𝑎𝑦 and Σ 𝐹𝑧 = 𝑚𝑎𝑧 3. The equation may be applied to the entire system or to a certain part of the system. Newton’s third law LAW OF action and reaction Newton’s Third Law of Motion states “ that for every action, there is an equal but opposite reaction” Action and reaction forces are equal in magnitude but opposite in directions and are assigned arbitrarily.  Mass and weight WEIGHT of the body on Earth is the measure of the force of gravity exerted by the Earth on it. It is a vector quantity and is always directed toward the center of Earth. MASS is the amount of matter a body contains. It is a scalar quantity. The SI unit for mass is the kilogram. Mass and weight are related as w=mg The unit of weight is kg.m/s^2 which is equivalent to Newton. The mass of a body is constant, while its weight depends on the value of the acceleration due to gravity. The law of universal gravitation Newton’ s law of motion Newton’s law of motion Example problem 1 Example problem 2 Example problem 3 Example problem 4 Example problem 6 FLUIDS Phases of Matter The three common phases, or states, of matter are solid, liquid, and gas. 3 Phases of matter  Solid - maintains a generally fixed size and shape; usually it requires a large force to change the volume or shape of a solid.  Liquid - does not maintain a fixed shape it takes on the shape of its container, and it can flow; but like a solid it is not readily compressible, and its volume can be changed significantly only by a very large force.  Gas - has neither a fixed shape nor a fixed volume it will expand to fill its container. Fluids and Fluid Mechanics Fluids - a substance (such as a liquid or gas) tending to flow or conform to the outline of its container Fluid mechanics - is the study of fluid behavior (liquids, gases, blood, and plasmas) at rest and in motion. Fluid mechanics has a wide range of applications in mechanical and chemical engineering, in biological systems, and in astrophysics. Fluid Mechanics It is divided into:  Fluid statics, the study of fluids at rest Fluid dynamics, the study of the effect of forces on fluid motion. Density and Specific Gravity Density A golf ball and a table tennis ball are about the same size. However, the golf ball is much heavier than the table tennis ball. Now imagine a similar size ball made out of lead. That would be very heavy indeed! What are we comparing? By comparing the mass of an object relative to its size, we are studying a property called density Density is the ratio of the mass of an object to its volume. Density Formula Density is usually a measured property of a substance, so its numerical value affects the significant figures in a calculation. Notice that density is defined in terms of two dissimilar units, mass and volume. That means that density overall has derived units, just like velocity. Densities of substances Density can act as a conversion factor for switching between units of mass and volume. For example, suppose you have a sample of aluminum that has a volume of 7.88 cm3. How can you determine what mass of aluminum you have without measuring it? Since most materials expand as temperature increases, the density of a substance is temperature dependent and usually decreases as temperature increases. You known that ice floats in water and it can be seen from the table that ice is less dense. Alternatively, corn syrup, being denser, would sink if placed in water. Example An 18.2g sample of zinc metal has a volume of 2.55cm3. Calculate the density of zinc.  Example 1. What is the mass of 2.49cm3 of aluminum? 2. What is the volume of 50.0g of aluminum? Solution: Most solids and liquids have densities that are conveniently expressed in grams per cubic centimeter (g/cm3)(g/cm3). Since a cubic centimeter is equal to a milliliter, Density units can also be expressed as g/mL. Specific gravity Specific gravity, also called relative density, ratio of the density of a substance to that of a standard substance. The specific gravity is the ratio between the density of an object, and a reference substance. The specific gravity can tell us, based on its value, if the object will sink or float in our reference substance. Usually our reference substance is water which always has a density of 1 gram per milliliter or 1 gram per cubic centimeter. Take Note: The standard is usually water at 4 degrees Celsius for liquids and solids, while for gases it is usually air. Specific Gravity Specific Gravity or relative gravity is a dimensionless quantity that is defined as the ratio of the density of a substance to the density of the water at a specified temperature and is expressed as It is common to use the density of water at 4 OC as a reference point as water at this point has Calculating Specific Gravity Specific gravity is determined by dividing the density of a material by the density of water at 4 degrees Celsius. For the calculation, the density of the material and that of the water must be expressed in the same units. Example 1: Calculate the specific gravity of iron. The density of iron is 7850 kg/m3. The specific gravity of iron-related to water is calculated as follows: Example 2: If the density of gold is 19300 kg/m3, what is the specific gravity of gold? We can calculate the specific gravity of gold as follows: Example 3: If the specific gravity of ice is 0.92, then what is the density of ice? The density of ice can be calculated by interchanging the specific gravity formula as follows: Specific Gravity of Gas For gases, the specific gravity is normally calculated with reference to air. Specific gravity for gases is defined as the ratio of the density of the gas to the density of air at a specified temperature and pressure. The density of air at room temperature is 1.20 kg/m3. PRESSURE AND FORCE The pressure of almost any liquid or gas that is stored or moved must be known to ensure safe and reliable operations. Pressure is force divided by the area over which that force is applied. Force is anything that changes or tends to change the state of rest or motion of a body. Area is the number of unit squares equal to the surface of an object. Pressure increases with force or decreased area. In hydraulic actuators, pressure converts to linear motion using a piston. Force moves a load via the piston rod. Force depends on pressure and piston size. PRESSURE Atmospheric Pressure The pressure due to the weight of the atmosphere above the point where it is measured. See Figure 9-2. Atmospheric pressure changes at different elevations because at higher elevations there is less weight of air above that elevation than at lower elevations. At mean sea level, the standard pressure of air is 14.696 psi, usually rounded to 14.7 psi. This value is often Head pressure Actual height of a column of liquid. A container or vessel can be any shape, but head is only determined by the height of the liquid. For example, the head of water in water towers of different shape depends only on the height of the water. See Figure 9-3. Head is expressed in units of length such as inches or feet, and includes a statement of which liquid is being used. For Hydrostatic Pressure Formula Problems on Hydrostatic Pressure HYDROSTATIC PRESSURE The pressure due to the head of a liquid column. Frequently, this is referred to as pressure head. Pressure is independent of the shape of the container and depends only on the properties of the fluid and the height. For example, mercury and water have very different densities. Since mercury is much denser than water, a shorter column of HYDROSTATIC PRESSURE HYDROSTATIC PRESSURE Manometer Measurements PASCAL’S LAW Pascal’s law is a law stating that the pressure applied to a confined static fluid is transmitted with equal intensity There are many different ways to report pressure, depending on the application. Pressure is reported in many units as well as on different scales. The four common pressure scales are absolute, gauge, vacuum, and differential pressure. ABSOLUTE PRESSURE Pressure measured with a perfect vacuum as the zero point of the scale. When measuring absolute pressure, the units increase as the pressure increases. Absolute pressure cannot be less than zero and is unaffected by changes in atmospheric pressure. Certain equations that relate pressure to other variables call for the use of absolute pressure. Absolute zero pressure is a perfect vacuum. Absolute zero pressure cannot be reached in practice. gauge PRESSURE Pressure measured with atmospheric pressure as the zero point of the scale. When measuring gauge pressure, the units increase as the pressure increases. Negative gauge pressure is gauge pressure that is less than atmospheric pressure. Negative gauge pressure indicates the presence of a partial vacuum. The only difference between Vacuum pressure Pressure less than atmospheric pressure measured with atmospheric pressure as the zero point of the scale. When measuring vacuum, the units increase as the pressure decreases. The differences between absolute pressure and vacuum pressure are the zero point and direction of the scale. Vacuum pressure measurement is used when a process is maintained at less than atmospheric pressure. For example, a vacuum pressure gauge may be installed on the suction side of a pump differential pressure Difference in pressure between two measurement points in a process. The actual pressure at the different points may not be known and there is no reference pressure used. The two pressures may be above or below atmospheric pressure. Pressure drop is a pressure decrease that occurs due to friction or obstructions as an enclosed fluid flows from one point in a process to another. Archimedes Principle The upward buoyant force that is exerted on a body immersed in a fluid, whether partially or fully submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid. When an object is partially or fully immersed in a liquid, the apparent loss of weight is equal to the weight of the liquid displaced by it. The weight due to gravity is opposed Apparent by the thrust provided by the fluid. weight= Weight of object (in the air) The object inside the liquid only – Thrust force (buoyancy) Archimedes’ Principle Formula In simple form, the Archimedes law states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. Mathematically written as: Fb = ρ x g x V Where Fb is the buoyant force, ρ is the density of the fluid, V is the submerged volume, and g is the acceleration due to gravity. Archimedes’ Principle Examples Calculate the resulting force, if a steel ball of radius 6 cm is immersed in water. Bernoulli’s Principle The total mechanical energy of the moving fluid comprising the gravitational potential energy of elevation, the energy associated with the fluid pressure and the kinetic energy of the fluid motion, remains constant. Where p is the pressure exerted by the fluid, v is the velocity of the fluid, ρ is the density of the fluid and h is the height of the container. Bernoulli’s equation gives great insight into the Bernoulli’s principle States that the total energy of a small amount of an incompressible liquid flowing from one point to another remains constant throughout the displacement. Principle of Continuity If the fluid is in streamline flow and is in- compressible then we can say that mass of fluid passing through different cross sections are equal. The rate of mass entering = Rate of mass leaving ρA1V1=ρA2V2 Bernoulli’s Equation at Constant Depth When the fluid moves at a constant depth that is when h1 = h2, then Bernoulli’s equation is given as: EXAMPLE: Water is flowing in a fire hose with a velocity of 1.0 m/s and a pressure of 200,000 Pa. At the nozzle the pressure decreases to atmospheric pressure (101,300 Pa), there is no change in height. Use the Bernoulli equation to calculate the velocity of the water exiting the nozzle. The density of water is 1000 kg/m3 and gravity g is 9.8 m/s2. EXAMPLE: Through a refinery, fuel ethanol is flowing in a pipe at a velocity of 1 m/s and a pressure of 101300 Pa. The refinery needs the ethanol to be at a pressure of 2 atm (202600 Pa) on a lower level. How far must the pipe drop in height in order to achieve this pressure? Assume the velocity does not change. The density of ethanol is 789 kg/m3 and gravity g is 9.8 m/s2. ELECTRICITY PHYSICS I Electric charge a basic property of matter carried by some elementary particles. Electric charge, which can be positive or negative, occurs in discrete natural units and is neither created nor destroyed. Electricity comes from the Greek word for amber — “electron” (ηλεκτρον) EXAMPLE: A current of 3.8 A flows in a wire for 12 minutes (a) How much charge passes through any point in the circuit during this time? (b) How many electrons would this represent? EXAMPLE: A 9V battery is connected across a 250 ohms resistor. (a) how much current passes through the resistor? (b) how much power is dissipated by the resistor? (c) How much power is delivered by the battery? ELECTRICITY Electricity is around us everywhere we go and quite literally powers our modern world. Although the vast majority of people use electricity on a daily basis and can’t imagine living without it, many people don’t know exactly what electricity is or how electricity works. “Electricity is briefly defined as the flow of electric charge.”  ORIGIN OF ELECTRICITY Thomas Alva Edison - was an American inventor and businessman who has been described as America's greatest inventor. He developed many devices in fields such as electric power generation, mass communication, sound recording, and motion pictures. These inventions, which include the phonograph, the motion picture camera, and early versions of the electric light bulb, have had a widespread impact on the modern industrialized world. ORIGIN OF ELECTRICITY The word “electricity” is the most important invention and may evoke an image of complex modern technology: lights, motors, electronics, and computers. Electricity – is the flow of electric charge though conductors in one direction. Two types of Electricity Electrostatics – Study of electric charges at rest. Electrodynamics – Study of electric charges at motion. ORIGIN OF ELECTRICITY  The electrical nature of matter is inherent in atomic structure. An atom consists of a small, relatively massive nucleus that contains particles called protons and neutrons.  It’s charges and masses: Proton – positive charge ; Neutron – neutral charge ; Electron – negative charge; ELECTRIC CHARGE The magnitude of the charge on the proton exactly equals the magnitude of the charge on the electron; the proton carries a charge (+) e, and the electron carries a charge (-) e. The SI unit for measuring the magnitude of an electric charge is the coulomb (C), and e has been determined experimentally to have the value. The symbol e represents only the magnitude of the charge on a proton or an electron and does not include the algebraic sign that indicates whether the charge is positive or negative. LAW OF ELECTRIC CHARGES The two types of electric charge were referred to as positive and negative by the American statesman, philosopher, and scientist Benjamin Franklin. The Law of electric charge – “Unlike charges attract; like charges repel” LAW OF CONSERVATION OF CHARGES Law of conservation of electric charge, which states that: The net amount of electric charge produced in any process is zero; or, said another way, No net electric charge can be created or destroyed. COULOMB LAW OF ELECTROSTATIC The French physicist Charles Augustin de Coulomb (1736–1806) carried out a number of experiments to determine how the electric force that one point charge applies to another depends on the amount of each charge and the separation between them. Formula: COULOMB’S LAW The magnitude F of the electrostatic force exerted by one point charge Q1 on another point charge Q2 is directly proportional to the magnitudes Q1 and Q2 of the charges and inversely proportional to the square of the distance r between them where k is a proportionality constant: COULOMB’S LAW It is common practice to express k in terms of another constant , by writing is called the permittivity of free space and has a value that is given according to Significance of electrical forces: They are responsible for: Electron binding to a (+) nucleus, forming a stable atom. Atoms bonding together into molecules, liquids, and solids. THE ELECTRIC FIELD Electric field is defined as the electric force per unit charge. The direction of the field is taken to be the direction of the force it would exert on a positive test charge. The electric field is radially outward from a positive charge and radially in toward a negative point charge. FORMULA: CHARACTERISTICS OF ELECTRIC FIELD LINES: They start on, and run outward from positive (+) charges. They run toward, and terminate on, negative (-) charges. No two field lines ever cross. “Electric field lines always begin on a positive charge and end on a negative charge and do not start or stop in mid space. Furthermore, the number of lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge.” ELECTRIC DIPOLE Shows the electric field lines due to two equal charges of opposite sign, a combination known as an Electric Dipole. The electric field lines are curved in this case and are directed from the positive charge to the negative charge. A +10𝜇C point charge is 25cm away from a -20 𝜇C point charge. Calculate the magnitude of the electric force between them. A +100𝜇C charge is placed at the origin. A -50 𝜇C charged is placed at x=2m and a +200 𝜇Cis placed at x=-4m. (a) What is the net electric force acting on the +100 𝜇C? (b) (b) What is the net electric force acting on the + 200 𝜇C? PLEASE ALSO WATCH THE YOUTUBE VIDEO ABOUT IMPULSE AND MOMENTUM CONSERVATION - INELASTIC & ELASTIC COLLISIONS HTTPS://WWW.YOUTUBE.COM/WATCH?V=FFAEBQMVKQA PLEASE ALSO WATCH THE YOUTUBE VIDEO ABOUT WORK, ENERGY, AND POWER. HTTPS://WWW.YOUTUBE.COM/WATCH?V=_MR1DP8-F8W HTTPS://WWW.YOUTUBE.COM/WATCH?V=ZVRH9D5PW8G