Physics Section MCAT Review Sheets
Physics Section MCAT Review Sheets
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Batteries In a battery chemical potential energy is converted to electrical potential energy In a battery there are two electrodes made of different substances embedded in an electrolyte The electrolyte interacts with the electrodes creating a net negative charge on one the anode and the net positive charge on the other the cathode Charges are separated and a potential difference is created between the two external projections of the electrodes called the terminals The electromotive force created by the battery creates a charge flow called a current The size of this current is measured in charge per unit time or Qt or coulombs per second The name given to this unit is amperes A So one ampere equals one coulomb per second Rule number 34 Current equals charge divided by time or I Qt For a current to exist a source of EMF and a conductor is required There must also be a circuit which is a path between the points of unequal electric potential at the EMF source along which the charge can flow Current is the flow of positive charge So when electrons are flowing in one direction the current is in the opposite direction In an electric circuit current flows from the positive terminal on a battery the cathode to the negative terminal the anode Center of Gravity For an object that does not have its mass uniformly distributed we can find the center of gravity by determining where a single rope could be attached to keep the objects longest plane in rotational equilibrium parallel to the Earth Remember that in a non uniform objects or assembly the center of gravity is closer to the heavier end than it is to the lighter end So the rope would be hanging near the heavier side of the assembly Statics When an object stands still it simply means that it has a velocity of zero and that its velocity is not changing The object is said to be in translational and rotational equilibrium An object is in translational equilibrium if its velocity is not changing vertically or horizontally An object is in rotational equilibrium if its velocity is not changing about any axis It is important to remember that if something is not moving or if a series of things linked together are not moving then every single point in the whole system is in equilibrium Hydrostatic Pressure Fluid pressure is the pressure that would be exerted on an object if it was submerged in a uid Fluids have uid pressure even if nothing is submerged in them At any given depth a uid s uid pressure is equal to the pressure that it would exert on a submerged object Rule number 21 If fluid is inside a closed container and is subject to no forces other than gravity then the uid pressure at any point in the uid is equal to the uid s density times G times the height of the uid sitting above the point This rule applies regardless of the shape of the container in which the uid is located The reason for this is Pascal s Law which states that when pressure is increased at any point in a contained uid the increase is uniformly distributed throughout the uid Now what about uid filled containers that are open to the atmosphere Rule number 22 Total pressure in the uid equals gauge pressure plus atmospheric pressure Do not forget that gases are also uids and the laws that apply to uids apply to gases too Fluids produce buoyancy Rule number 23 Any object that is partly or wholly immersed in any uid experiences a buoyant force equal to the weight of the uid it displaces Buoyant force equals volume of displaced uid times density of displaced uid times gravity This is known as Archimedes principle Plates Now let us talk about plates When two plates with equal and opposite charges are close to each other we can approximate the electrostatic field strength at any point between them very closely Rule number 28 Electric field between parallel conductive plates of the same size but oppositely charged equals charge on a plate divided by the permittivity constant times the plate area Rule number 29 The potential energy within the electric field between charged plates equals the magnitude of the charge times the field strength times the distance from the opposite plate or PEqEd The electrostatic potential difference between two plates is the potential energy that a particle with a charge magnitude of l Coulomb would have if it was situated on the plate of like charge and it is measured in volts Rule number 30 The electrical potential difference between two parallel plates of equal size and opposite charge equals the electrostatic field strength times the distance between the plates or VEd Doppler Effect Suppose a police car loudly sounding its siren is approaching a passenger standing in the street When the police car is approaching the passenger hears its siren having a high pitch But as it passes by the siren s pitch falls off That is because of the Doppler Effect The Doppler Effect arises whenever a source of waves is moving in relation to its observer or an observer is moving in relation to the source of waves The result is that the waves will have different wavelengths and frequencies than expected When a source of Waves approaches an observer the waves crunch up meaning that from the observer s view point the waves have shorter wavelength and a higher frequency As a source of waves recedes from an observer the waves stretch This means from the observers viewpoint the waves have longer wavelength and lower frequency Rule number 41 Doppler Effect The Doppler Effect is summarized in terms of frequency in the following equation The frequency observed by the observer equals the actual frequency of sound being emitted times the velocity of sound in air plus or minus the velocity at which the observer is moving over the velocity of sound in air plus or minus the velocity at which the source is moving Notice that if neither the observer nor the source is moving then the frequency observed is equal to the actual frequency You will have to predict when to choose plus or minus When the observer approaches the source the frequency observed must increase When the source approaches the observer the frequency observed must increase When the observer recedes from the source the frequency observed must decrease When the source recedes from the observer the frequency observed must decrease Circular and Projectile Motion Think about an object moving forward in a horizontal direction at a constant velocity If a vertical force comes along the force has no component that acts in the horizontal direction therefore it cannot change the objects speed If an object is moving the magnitude of its velocity cannot be changed by a force that is perpendicular to the direction of motion So what happens is the force does change the velocity of the object but it does so by changing the objects direction not its speed Change in direction is a change in velocity Now imagine a large object traveling through space in a straight line with no forces to change its velocity It will travel forever in a straight line until some force comes along to change the situation Now imagine that a planet 300000 miles away from the object is in a line that is perpendicular to the motion of the object All of a sudden the object experiences a vertical force This is the force of gravity exerted by the planet The planet and the object attract each other with the force given by Newton s Law of universal gravitation F G mlm2 r2 where ml and m2 equal the masses of the objects r equals the distance between the object and G equals Newton s constant 67 x 1011 Newton meter squared per kilogram squared The object changes direction and begins to follow a circular path orbiting the planet The object just turned into a satellite and actually at each instant the satellite does have its original horizontal velocity but then in the next instance before the satellite can get away the force of gravity changes its direction and bends it toward the planet This keeps happening instant by instant So the satellite moves in a circle around the planet The satellite does not crash and it does not slow down because no force ever interfered with the magnitude of its velocity It keeps traveling at the same speed with the direction that is constantly changing that is called centripetal acceleration Centripetal acceleration means acceleration toward the center of a circular orbit Centripetal acceleration is due to some force acting on the object in the direction of the center of the orbit In the case of a satellite orbiting the earth the force is the force of gravity on the satellite For an object moving at a constant speed in a circular orbit there is an important relationship among the speed the radius of the orbit and the centripetal acceleration Rule number 9 For an object moving at a constant speed in a circular orbit centripetal acceleration equals speed divided by radius or a V2 r If an object is moving in a circular path but it is not moving at a constant speed then it is experiencing two forces One force exerts an acceleration toward the center of the orbit The other causes acceleration instant by instant along a line that is tangent to the orbit The two acceleration vectors together produce a resultant acceleration vector that points each instant somewhere between the two The resultant vector represents the direction of acceleration at a given instant Projectile Motion Supposed you kick a football it ascends with a certain velocity at a certain angle Let us say the angle is 30 degrees and the velocity is 10 meters per second The football is a projectile and its velocity has two vector components One is vertically upward and one is horizontal The vertical component of the velocity equals 10 X cosine 30 which equals to 154 The horizontal component of the velocity equals 10 X cosine 60 which equals 952 Once the football is launch there are no horizontal forces acting on it The vertical force acting on the football is gravity which slows the ascending football with an acceleration of 98 meters per second squared During the course of ight the football s horizontal velocity remains constant because no horizontal force acts on the football During the course of flight the upward vertical velocity is reduced Ultimately it is reduced to zero and then with the force of gravity continuing to operate The football acquires a downward velocity How long does it take until the football reaches the highest point in its path At the instant we kick the football it had an upward velocity of 154 meters per second The Earth s gravity is causing the football to slow down We want to know how much time before the football in terms of vertical motion comes to a stop in midair So that its final velocity equals zero The formula we need is Vfinal Vinitial 80 If Vfinal 0 then Vinitial equals 154 meters per second So that 0 154meter per second 98 meters per second times time When we solve for time time 016 seconds Now substituting this time in the formula X Vinitialt 12 AT2 we can solve the equation for X to find how high the ball was kicked A projectile is just like two different moving objects One has an initial horizontal velocity that never changes and the other has an initial upward velocity but it experiences the force of gravity The upward vertical velocity is ultimately reduced to zero and then converted to a downward vertical velocity accelerated at 98 meters per second until the object hits the earth The highest point in the proj ectile s path is the point at which the vertical velocity has been reduced to zero Electricity and Magnetism Suppose a rod is made of copper and that it has more electrons than protons That means that the copper rod is negatively charged Copper is a transition metal so its valence electrons are very mobile So if this rod touches something it will make it negatively charged by passing its electrons to it That is called contact charge When a charged object touches another object and gives its charge to that other object the other object is said to undergo contact charge Any and every substance element compound or mixture of compounds will readily produce and undergo contact charge if it has a large number of relatively mobile electrons On the other hand if a substance does not have a large number of relatively mobile electrons it will not readily produce or undergo contact charge Conductor Remember the copper rod it is called a good conductor that is because one it readily gives up electrons to an object which relative to itself is positive and by the same token two it readily receives electrons from an object that relative to itself is negative Insulator The opposite of conductor is insulator To say that something is a poor conductor is the same as saying it is a good insulator Contact charge is one way to transfer charge Here are two other ways one rubbing two induction Remember that rubbing is different from contact charge Now that you know about transferring charge you should know about the relationship between force and charge This relationship is given by Coulomb s Law Coulomb s Law allows us to figure out the force that two charged particles produce when they are separated by a certain distance Coulomb s Law also tells us that the force of attraction or repulsion between two separated charges is proportional to Q1XQ2R2 When there is a force between two particles there is an area all around the particles which would exert a force on any charged particle that happened to be there This area is called an electrostatic field The electrostatic field is stronger in some places that it is in others The electrostatic field strength for any point in an electrostatic field is equal to the force that a charged of 1 would experience if it was placed there Electrostatic field strength is measured in Newton per Coulomb Rule Number 27 Force experienced by a charge in an electric field equals field strength times charge or F EQ Fluids in Motion Think about uid owing in a cylindrical pipe of uniform radius What makes the uid ow is a pressure difference between the ends of the pipe These things tend to slow down the ow of uid Narrowness of the pipe 2 A thin pipe impedes uid ow Length of the pipe 2 The sides of the pipe impose frictional force on the uid The longer the pipe the greater the force Viscosity This is the cohesive molecular forces in a uid Greater viscosity means greater frictional resistance to ow Viscosity tends to decrease with increasing temperature Turbulence Fluid ow becomes turbulent at speeds above a certain level In turbulent ow eddies and whirlpools create frictional force that impedes the ow The opposite of turbulent ow is laminar or streamline ow There is a formula that describes these relationships but you do not have to know it However you should know some of the quantitative relationships that arise from this formula Rule number 24 Fluid ow When uid ows in a length of cylindrical pipeAll other things being equal ow at every point in the pipe is directly proportional to the pressure difference between the two ends of the pipe All other things being equal ow at every point in the pipe is greater if the radius of the pipe is greater and less if the radius of the pipe is less Flow is inversely proportional to the uid s viscosity Flow is inversely proportional to the length of the pipe All other things being equal ow is less if it is turbulent and greater if it is streamline You also need to know something about ideal ow Ideal ow is ow of an imaginary uid that has no viscosity to impede its ow is completely incompressible and ows in a streamline fashion Rule number 25 At any point in a system of continuously owing uid ow is equal to area times uid viscosity There is one more thing you should know about ideal ow in a pipe of uniform radius The pressure is lowest at points of highest elevation and greatest at points of lowest elevation It is important also that you know a few things about uid that is owing in a system whose pipes or channels vary in size First in a single system of continuously owing uid ow is the same at all points Second at any point in the system of continuously owing uid ow at any point in the system is equal to the cross sectional area of the pipe times the velocity of the uid Third if a system is at equal elevation at all points then at areas of wider caliber pressure is higher and velocity is lower At areas of narrower caliber pressure is lower and velocity is higher Summary of uids in motion Actual ow 1 Within a length of cylindrical pipe of uniform dimension flow between any two points is directly proportional to pressure difference between the two ends 2 Within a length of cylindrical pipe of uniform dimension flow between any 2 points is greater with greater radius and lesser with lesser radius 3 Within a length of cylindrical pipe of uniform dimension flow is inversely proportional to pipe length 4 Within any system of flow flow between any two points is inversely proportional to fluid viscosity 5 Within any system of flow flow between any two points decreases with increased turbulence Ideal flow 1 In a system of ideal flow flow equals area times velocity 2 In a system of ideal flow flow is the same at all times 3 In any system of ideal flow area and velocity are inversely proportional which means that if area is doubled velocity is halved If velocity is doubled area is halved 4 In a system of ideal flow reduced area produces lower pressure and greater velocity Increased area produces greater pressure and lower velocity Forces Acceleration requires force The only way to accelerate a body is to apply force If a body has no force acting on it then its velocity will never change If a body is moving at 200 kilometers per hour in the westward direction it will continue moving at that velocity forever unless some force acts on it If a body is stationary it will continue to be stationary forever unless some force acts on it Force has direction It is a vector quantity Force is measured in newtons Rule number 5 When a force acts on a body it produces an acceleration equal to the force divided by the mass of the body Remember this equation in any of these 3 forms AFM FMA MFA When we say an object weighs 400 pounds what we are really saying is that the earth is pulling on that object with a force of 400 pounds The object s mass is about 182 kilograms and its weight is 182 kilograms times 98 msec2 or approximately 1780 newtons Force and Weight Rules 4 and 5 combined mean that every object on or near the earth experiences a downward force equal to its own mass times the acceleration produced by the earth s gravity which is 98 msec2 The force that an object experiences due to gravity is called the object s weight Weight is important in 2 ways 1 If an object weighs 500 newtons that means that gravity is causing that object itself to experience a downward force of 500 newtons 2 It also means that when that object rests or hangs on some other body or surface the object imposes a force of 500 newtons on that body or surface Since weight is a type of force it is measured in newtons The point at which all the weight of an object is being concentrated is called the object s center of gravity For objects that are of uniform mass throughout the center of gravity is at the geographic center of the object Bodies can experience more than one force at a time If a body experiences more than one force at a time it might or might not accelerate Whether a body will actually accelerate depends on the sum total of all the forces acting on it That sum is called net force Rule number 6 For bodies at rest When one body exerts a force on another the other body exerts an equal and opposite force back on the first Rotational force Torque If two kids are sitting on a seesaw they are exerting on the seesa6w a force about an axis A force that is on an object about an axis is called rotational force or torque Torque can be clockwise or counterclockwise When force is exerted about an axis the distance between the force and the axis is called the lever arm Rule number 7 Torque equals force times lever arm To calculate the net torque imposed on the seesaw all you have to do is this For each child take the force exerted and multiply it by the child s distance from the axis then subtract these two forces from each other and you will get the net force exerted on the axis of the seesaw Understand the Force of Friction Think about a box sitting on a ground and imagine you are going to push it to the right It turns out at a Very instant you begin to push a force starts working against you and that force is the force of friction between the box and the ground it is sitting on When an object is resting on a surface and we just begin to slide it along the surface the force of friction in the opposite direction is equal to the product of the following 1 The force that the object is exerting directly perpendicular to the surface 2 The coefficient of friction between the two surfaces The first quantity is equal to the weight of the object if the surface is horizontal If the surface is not horizontal then the first quantity is equal to the component of the object s weight that is perpendicular to the surface This is called the normal force Rule number 8 Force of friction equals normal force times coefficient of friction Different materials have different coefficients of friction It turns out that for any two surfaces there are usually two coefficients of friction One applies at the instant before motion begins and the other applies after the motion is already in progress The first is called the coefficient of static friction and the second is called the coefficient of kinetic friction Capacitors These plates that we have been talking about are called capacitors Capacitors store energy That is because between oppositely charged conductive plates there is an electrostatic potential which represents potential energy Now the amount of energy a capacitor can store depends on the magnitude of the charge on each plate and the electrostatic potential between the plates Rule number 31 Energy stored by a capacitor equals magnitude of charge times the electrostatic potential between the plates divided by two or U lZQV Capacitance is a capacitors ability to hold a relatively large charge on its plates without producing too much of an electrostatic potential between its plates If a capacitor can hold a lot of charge and produce only a low electrostatic potential between its plates then it has a high capacitance If a capacitor produces a high electrostatic potential between its plates even when it is holding only a small charge then it has a low capacitance Rule number 32 Capacitance equals charge divided by potential difference or C QV Capacitance is measured in farads There are two features that determine the capacitance of a capacitor One the geometry of the plates increasing the size of the plates will increase capacitance And increasing the distance between the plates will decrease capacitance Two the material between the plates any material placed between the plates of a capacitor must be an insulator As an insulator this material is able to resist the permittivity of the electric field caused by the charged plates Some materials are better insulators than others This quality is called the dielectric constant of a material and is denoted by a K The better an insulator a material is the higher the dielectric constant Empty space has a dielectric constant of one and air has a dielectric constant very close to one Sometimes capacitors are connected to one another and you may have to find their total capacitance When separate capacitors are connected in series then one the potential difference across the resulting system is the sum of all the potential differences across the individual capacitors And two the reciprocal of the total capacitance of the system is equal to the sum of the reciprocals of the capacitance of each individual capacitor When separate capacitors are connected in parallel then one the charge across the resulting system is the sum of all of the charges across the individual capacitors And two the total capacitance of the system is equal to the sum of the capacitances of each individual capacitor Rule number 33 For capacitors connected in series lCtotal lCllC2lC3 and etc For capacitor connected in parallel Ctotal ClC2C3 and etc Capacitors have limits too If you kept raising the electrostatic force between two plates eventually the field would become so strong that electrons would move from the negatively charged plate to the positively charged plate causing the plates to become neutral When this happens the capacitor is said to discharge Optics You will get some questions about reflection refraction mirrors and lenses All of these stuffs put together means optics Optics involved light and we have already discussed light We said earlier that light travels at a speed of three times ten to the eight meters per second This is only true for light traveling in a vacuum When light travels through an actual medium like air water or etcetera it travels slower Every medium has something called a refractive index which tells how much slower light travels when it is in that medium than it does when it is in a vacuum Rule number 44 Index of refraction a medium s refractive index equals the speed of light in a vacuum divided by the speed of light in the medium or ncv When a ray of light is passing through one medium and is reflected from another the angle at which it hits the new medium is equal to the angle at which it bounces off In other words the angle of incidence is equal to the angle of reflection Sometimes a ray of light may hit a medium and not be reflected This light will go right through the medium However once it hits the medium it bends This bending is called refraction There is a rule that we can use to figure out the angle of refraction The rule is called Snell s Law Rule number 45 Snell s Law nlsinGl n2sin82 where n equals the index of refraction for the medium Power and Momentum When we talk about power we re talking about how much work gets done per second Rule Number 14 Definition of power power equals work divided by time or PWt Power is measured in watts and 1 watt equals 1 joule per second If we want to know how much force is necessary to keep a rocket in motion we use the formula FMA Now if we want to know how much power is necessary to keep the rocket in motion we use this formula Rule Number 15 Power necessary to keep a body in motion at constant velocity equals force necessary to keep it in motion times the velocity or PFv Power equals work per second equals mass times acceleration times displacement divided by time So there are two formulas for power When you want to know how much power is necessary to keep a body in motion at a constant velocity you use this formula PFv When you want to know how much power is necessary to move a body through a particular space you use PWt Momentum Momentum is the product of the mass and velocity of an object You should know that momentum is conserved just like energy Rule Number 16 Definition of momentum momentum equals mass times velocity or pmv This formula applies only for bodies traveling in a straight line Therefore it is often referred to as linear momentum We know of course that for every reaction there s an equal and opposite reaction Closely related to that principle is this one momentum is conserved Think about two objects a and b bumping into each other Before colliding each object has a velocity and a mass and hence a momentum The total momentum for the system the two objects is mv of object a plus mv of object b Now a collision between a and b will upset the situation After the collision each object may be traveling at a velocity different from the one with which it began If that happens each object will experience a change in mv which means each will experience a change in momentum But total momentum for the two objects won t change So if the velocity of one object decreases the velocity of the other will increase proportionately in order to maintain the same total momentum before and after the collision Collisions A collision occurs when two or more objects strike one another The important detail is whether or not they stick together Inelastic collisions occur when things collide and stick Elastic collisions occur when things bounce of one another As you know energy can neither be created nor destroyed In a pure elastic collision the kinetic energy of the objects before and after the collision will be the same However this is not true of inelastic collisions During inelastic collisions some energy is lost to the collision itself This is not to say that the energy has disappeared rather it has been changed into different forms like heat Here is what you need to understand about collisions Kinetic energy is conserved in elastic collisions Kinetic energy is not conserved in inelastic collisions Momentum is always conserved You should know the first and second laws of thermodynamics The first law of thermodynamics states that energy can t be created or destroyed Energy can change forms but it can t disappear Sometimes the first law of thermodynamics is called the law of conservation of energy In other words the total amount of energy in the universe is conserved It remains the same The second law of thermodynamics states that the universe tends toward maximum randomness or entropy Resistors Resistors resist the flow of current All conductors are also resistors since all conductors resist the flow of current to some extent Resistance is expressed in ohms A resistor is composed of substances which enable it to resist the flow of current The ability of a given material to resist current flow is called the resistivity Materials with the greatest resistivities are called insulators and include glass rubber and wood Semiconductors are a group of materials with moderate resistivities like silicon Conductors have very low resistivities Metals are good conductors Remember that the resistivity of a material is affected by the temperature In general resistivity increases with increasing temperature Ohm s Law states that voltage is linearly proportional to current Rule Number 35 Ohm s Law Voltage equals current times resistance or VIR Power is defined as the energy used per unit of time Electrical power is proportional to the square of the current owing through a resistor and equal to the current times the voltage Rule Number 36 Power equals current squared times resistance or PI2R Power is also current times voltage or PIV Finally power equals voltage squared divided by resistance or PV2R The unit of electrical power is the watt which is I joule per second Resistors can be connected to one another and you may have to calculate their total resistivity For resistors connected in series RTotal RlR2R3 and etc For resistors connected in parallel lRTotal lRllR2lR3 and etc Simple Harmonic Motion Simple harmonic motion is like a wave It has period frequency and amplitude Simple harmonic motion is always caused by some force If you know the displacement and something called the spring constant you can figure out how much force is involved in the motion at any moment Rule Number 42 Hooke s Law Force equals negative spring constant times displacement or F kx The negative sign in this equation indicates that in simple harmonic motion force is opposite to the direction of displacement If you were asked anything about a pendulum remember that the spring constant for a pendulum is approximately equal to the weight divided by the length At every other point in the cycle the pendulum s energy is a mixture of potential energy and kinetic energy Rule Number 43 Simple harmonic motion and energy For any object in simple harmonic motion kinetic energy l2mv2 where m is the mass and v is the velocity Potential energy 12kx2 where k is the spring constant and x is the length of the spring Total energy kinetic energy potential energy When the object s velocity is zero it is at maximum displacement and all of its energy is potential energy It has no kinetic energy When the object is at the zero force point it is at maximum velocity and all of its energy is kinetic energy It has no potential energy Elasticity and Density Elasticity If an object is subjected to a stress and it therefore undergoes strain it changes shape Now suppose the stress is removed some objects will return to their original shapes and some will not The ones that do are said to be elastic and the ones that do not are said not to be elastic All substances that obey Hooke s Law are elastic Density Every substance has a density A substance s density is the number of kilograms contained in one liter of the substance Rule number 20 Definition of Density Density equals mass divided by volume You should also know about specific gravity The specific gravity for any substance is the density of the substance divided by the density of water Remember that the density of water is 1000 grams per liter Stress and Strain Hooke s law provides that stress divided by strain equals a constant number That number is different for different substances and even for one substance it is different depending on what type of stress or strain we are talking about For our purposes there are 2 types of strain Tensile strain and shear strain Rule 17 Definition of Strain Tensile strain equals change in length divided by original length Shear strain equals distance moved divided by original height When a solid is subjected to a stress it changes shape and we call the change in shape a strain Rule 18 Definition of Stress Stress equals force divided by area or FA Stress is usually measured in pascals Pa One pascal equals one newton meter squared So stress creates strain Tensile stress creates tensile strain and shear stress creates shear strain Tensile stress is a measure of stretching or compressing force per area perpendicular to the force So in order to measure the tensile stress applied to a metal bar we take the force applied to it and divide it by the cross sectional area of the metal bar Shear stress is measured in pascals just like tensile stress Shear stress is equal to the tangential force over the area of the surface to which it is applied Moduli Modulus is the constant number that we talked about earlier When objects undergo shear strain the number is called shear modulus When they undergo tensile strain it is called Young s modulus Rule 19 For substances that obey Hooke s law shear modulus equals shear stress divided by shear strain Young s modulus equals tensile stress divided by tensile strain So if you know the tensile stress that is imposed on an object and you know the Young s modulus for the substance of which the object is made you can figure out the tensile strain that results from the stress Also if you know the shear stress that is imposed on an object and you know the shear modulus for the substance of which the object is made you can figure out the shear strain that results from the stress Voltage Let us define Voltage The electric potential is defined as the electric potential energy unit per charge and the change in electric potential energy produces a potential difference or Voltage Therefore the Voltage between two objects is the difference in electric potential between those two objects To make an electric current flow and keep it owing you need a mechanism for creating and maintaining a potential difference or Voltage The potential difference created by such a mechanism is called an electromotive force EMF often written as E and its units are Volts which are units of potential difference Work and Energy Energy is the capacity to do work Think of energy as a stored ability to do work Work is displacement of an object by applying force Rule Number 10 With respect to any body subjected to a constant applied force work done by an applied force equals force applied in the direction of displacement times displacement or W FD Work is measured in joules One joule equals 1 Newton meter Now suppose we take an object with a mass of 6 kg and lift it straight up from the floor with a constant force to a height of 2 m and we want to find the amount of work done on the object by the force applied In order to lift an object at constant speed one must apply an upward force equal in magnitude to the objects weight So W FD In this case Fmass X gravity and Dheight In order to find W we multiply 6 kg by 98 m per seconds squared by 2 m to get ll7 6 joules So the work done on the object against gravity is ll7 6 joules Energy can assume a variety of forms One form of energy is called kinetic energy And it represents the actual fact that a thing is in motion Kinetic energy like all forms of energy represents a stored capacity to do work Rule Number ll The kinetic energy of any object is equal to one half mass times velocity squared or KEl2 mv2 Kinetic energy is measured in joules Another form of energy is called potential energy This form of energy is not in motion When an object is picked up from the ground it gains potential energy More specifically it gains gravitational potential energy Potential energy is energy that is ready to perform work When we pick up an object from the floor and put it on the table we give it gravitational potential energy equal to the amount of work that would be required to lift it from the ground to the table Gravity applies a force on the object equal to its weight Work is force multiplied by displacement So potential energy equals the object weight multiplied by the height of the table Rule Number 12 Gravitational potential energy equals mgh where m is the mass of the object g is 98 m per second squared and h is the height of the table Let us say you take a 05 kg baseball and throw it up into the air at an angle Now suppose at sometime after it is thrown the baseball has traveled 4 m vertically upwards and it s velocity at that moment is 6 m per second If for that particular moment we want to figure out how much work was done on the baseball by the applied force we can do it without even knowing the force with which the ball was thrown the angle at which it was thrown or the amount of time passed since it was thrown Rule Number 13 For objects near the surface of the earth work done by a net force equals change in kinetic energy plus gravitational potential energy or WAKE APE Mirrors You do not need to know much about flat mirrors You should however know about the two types of spherical mirrors a concave mirror and a convex mirror To understand each type imagine a sphere A concave mirror would be on the inside of the sphere and a convex mirror would be on the outside of the sphere An important thing to know about spherical mirrors is that each one has a focal length Rule number 46 The focal length of a mirror equals one half times the radius of curvature At the end of the focal length sits the mirror s focal point In a convex mirror the focal point is behind or inside the mirror In a concave mirror the focal point is in front of the mirror You might be asked about the size and location of an object s image in a spherical mirror First of all remember that a mirror image can be located behind the mirror or in front of a mirror An image that is located behind the mirror is called a virtual image An image that is located in front of a mirror is called a real image If an image is located behind the mirror we say that its distance from the mirror is negative If an image is located on the front side of the mirror we say its distance from the mirror is positive This concept about positive and negative signs goes also for focal lengths and focal points Rule number 47 Images in mirrors One over focal length equals one over obj ect s distance from the mirror plus one over distance between the image and the mirror or lf lo li Now what is the size of the image Rule number 48 Magnification and mirrors Magnification equals the distance between the image and the mirror divided by the distance between the object and the mirror Do not forget that any image that appears behind the mirror A virtual image is upright but any image that appears in front of the mirror A real image is inverted Magnetic Fields Now let us talk about magnetic fields When you say electric field you are talking about a stationary charge and the attractive and repulsive forces it imposes on a positive charge lying in its vicinity Now when you say magnetic field you are talking about something different You are talking about a moving positive charge and the attractive and repulsive forces it imposes on a charge moving in its vicinity So remember one an electric field arises in connection with the charge that is stationary two a magnetic field arises in connection with the charge that is moving Also a magnetic field will impose a force only on a charge that is in motion itself Stationary charges are not affected by magnetic fields Electric current produces magnetic fields You know that a moving charge creates a magnetic field You also know that electric current is actually a way of describing a whole bunch of electrons moving through a conductor If the electrons are moving in one direction we say that the current or positive charge is moving in the other Now listen to this whenever current moves through a conductor it creates a magnetic field that runs in a circle around the conductor As the magnetic field runs around the conductor it might be directed one way or the other Finding the Direction You maybe given a current and asked to find the direction of the field that produces or you maybe given a particular magnetic field and asked to find the direction of the current that produced it To solve these problems we use the right hand rule Suppose you were shown the current and asked to tell about the direction of the magnetic field it produces Here is what you do take your right hand point your thumb in the direction of the current which is the direction in which positive charge is moving let your fingers curl naturally The magnetic field is running in the direction that your fingers are curled from knuckle to nail Magnetic fields have strength Magnetic strength is measured in a unit called the tesla T and the formula to find it is given in the following rule Rule number 37 Field strength equals constant times current over distance from the wire The constant use is called the permeability of free space and its value is l26Xl0 6 TMA Notice the field strength is directly proportional to current and inversely proportional to distance from the wire Another right hand rule you know that moving charge produces a magnetic field You should also know that the magnetic field will also exert a force on the charge And here is how you find the direction of that force Take your right hand point your thumb in the direction in which the charge is moving open your fingers and they will be in the direction of the magnetic field Sound Waves When we talk about sound Waves we usually mean sound waves we can hear The human ear can detect sounds in the frequency range of 20 hertz to 20000 hertz That is the same as saying 20 cycles per second to 20 000 cycles per second Another name for frequency is pitch When sound pitch is above the audible range it is called ultrasonic When sound pitch is below the audible range it is called infrasonic Loudness When we re talking about sound and we say loud we are talking about two closely related quantities intensity and loudness Intensity is measured in watts per square meter or Wm2 Loudness is measured in decibels dB Here is the equation that relates loudness to intensity Rule number 40 Loudness in decibels equals ten times the log of the intensity over the intensity at the threshold of hearing The threshold of hearing is 1012 watts per m2 This is what the formula is really saying If we multiply any given intensity by 10 we add 10 decibels to the associated loudness per intensity level But if we multiply any given intensity by 100 we add 20 decibels to the associated loudness per intensity level And if we multiply any given intensity by 1000 we add 30 decibels to the associated loudness per intensity level Waves and Periodic Motion There are two kinds of waves transverse and longitudinal In a transverse wave the medium moves in a direction perpendicular to the movement of the wave In a longitudinal wave the medium moves in the same direction as the Wave Period Frequency Wave Length and Amplitude Think about a transverse wave When We talk about the period of this wave we re talking about the amount of time it takes the wave to move through one complete cycle from peak to peak or from trough to trough If it takes 3 seconds for the wave to get from peak to peak or from trough to trough then the wave has a period of 3 seconds When we talk about the frequency of a wave we are talking about the number of complete cycles it produces in 1 second So if a wave has a period of 3 seconds it goes through one cycle in 3 seconds which means it goes through 13 of a cycle in a second Its frequency is l 3 of a cycle per second Frequency is measured in the unit hertz and one cycle per second equals 1 hertz Rule Number 38 For any wave frequency equals one over period and period equals one over frequency A Wave s Wavelength is the distance from crest to crest or from trough to trough So a long wavelength corresponds to a low frequency Wavelength is measured in meters or other units of length If you know the wavelength and the frequency you can figure out how fast the Wave is moving Rule Number 39 A Wave s velocity equals frequency times wavelength
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