Edexce PHYSICS revision notes.pdf

7/27/2019 Edexce PHYSICS revision notes.pdf

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PHYSICS

Describing motion

A distance-time graph can make it easier to represent motionA velocity (speed in a given direction)time graph can show the instantaneous speed

Gradient = change in YChange in X

Distance and displacementDISTANCEthe length of the path you have takenDISPLACEMENTthe straight line distance between two places

To describe displacement, you need to say how far you are away from the start and

Scalar only size or magnitudeVector quantity size and direction

1Motion

DISTANCE-TIME:

Shows distance from start Curved line is acceleration Straight line means its stopped moving Gradient represents the speed at that

oint

VELOCITY-TIME:

Gradient shows acceleration Straight line is constant speed Velocity means its stopped Area under the graph is the distance

travelled

ms-1

ms-1


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Acceleration is the rate of change of velocity with time, so it is also a vector. Accelerationhappens when there is:

A change in SPEED, or A change in DIRECTION, or A change in speed AND direction

If an objects speed is constant but its velocity is changing, we say it is also accelerating

With a train travelling at a constant speed in a circle, it is considered to be accelerating butits average velocity as it goes round the track back to its starting point is zero, as itsDISPLACEMENT is ZERO

Graphs of motionWhen something decelerates, it is negativeacceleration, so -1 ms-2A straight line on a velocity time graph is UNIFORM acceleration

ACCELERATION the rate of change of velocity with time

The graph shows the motion of a ball beingthrown up in the air, falling, and then beingcaught.

AThe ball is at restA to Dthe ball is thrown up with auniform upward accelerationD to Bit has a negative acceleration asthe ball accelerates downwards untilresting at BB to Ethe same velocity as D to B but itis negative as it accelerates downEThe ball is caught and brought to restby C

Metre (m)

Kilogram (kg)Seconds (s)Ampere (A)]Kelvin (K)Candela (cd)Mole (mol)

ms-2

SI units (Systme Internationale):


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Non-linear graphs (curved graphs)make strips/rectangles under the graph, calculate thearea and add it up this is less accurate than a linear graph

Equations of motion

SUVAT

Using vectorsVectorsthe length of the arrow represents MAGNITUDE and the direction of the arrowrepresents the DIRECTION of the vector

You can either MEASURE the displacement(labelled the resultant) or use trigonometry orPythagorass theorem to calculate itThe sum of two or more vectors quantities iscalled their RESULTANT

THE PARALLELOGRAM RULE:This rule can be applied whenever vectors act at the same time or from the same point.

Relative motionwhen an object is moving, it is important to give some sort of informationabout what its motion is relative to.

s = displacement (m)

u = initial velocity (ms-1)

v = final velocity (ms-1)

a = acceleration (ms-2)

t = time (s)


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Eg. If someone is running along a moving walkway with a velocity of 2 ms -1 relative to thewalkway, but if the walkway has a velocity of -2 ms -1, the person will remain in the samepositive relative to the ground.

Causes of motionTHE BALL AND THE PENDULUM:Galileo did the pendulum experiment and found that it rose nearly the same height eachtime.He reasoned that if a ball rolls down a slope onto an infinitely long flat surface, it willcontinue moving until something else causes it to stop.

GALILEO realised the importance of distinguishing between motions horizontally andvertically in a gravitational field

Newtons first law of motionMotion on earth is opposed by frictional forces

Newton formed three laws of motion (which sometimes break down under certainconditions) which are very nearly correct under all circumstances

So, an object has a constant velocity until a force acts on it. This law defines what a forceIS and DOESa force is something which can cause accelerationThe sum of ALL THE forces acting on the body (sigma F)If a body has a number of forces, F1, F2 Fn acting on it, it will remain in a state of constantmotion only if:. (That is the sum on all the forces from F1 toFn) is equal to zero

This can be calculated separately for HORIZONTAL and VERTICALFORCESBecause a force can cause acceleration, it is a vector quantity, with both magnitude anddirection. It therefore requires a way of representing both direction and magnitude on a

1.2Forces

The first law:Every object continues in its state of rest or uniform motion in a straight line unless made to

change by the total force acting on it


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diagram. A diagram which shows all the forces acting on a body in a certain situation iscalled a FREE BODY DIAGRAM. This doesnt show forces acting on objects other thanthe one being considered.

CENTRE OF GRAVITYthe weight of an object acting through a single point (the centre)The centre is the point at which gravity appears to act, similar to an objects centre of mass

For uniform objects, the centre of the mass will be at the intersection of all lines ofsymmetry, especially in the middle of the object

Drag forcesDrag forces are made up of two types of forcesFRICTION and AIR RESISTANCEaresult of matter in contact with matter

FRICTIONalways occurs when two surfaces rub on each other. Although appearingsmooth, they are slightly rough, causing friction.Friction OPPOSES any motion, but cannot actually CAUSE motion. When an object stops,

so does friction

Friction can be measured using a force meter and moving something across a surface at aconstant velocityFor an object which is not accelerating,

meaning that the frictionalforce resisting motion must be exactlybalanced by the pulling force of the hand

AIR RESISTANCE (or aerodynamic drag)caused when a body moves through air.

Caused by an object having to push airout of the way in order to move throughit. Air resistance depends on speed, thefaster the object moves, the greater the

aerodynamic drag (think of a car)

As aerodynamic drag increases, objectswith a constant driving force tend toreach a max. velocity when theyaccelerate

Free fall and terminal velocityifsomeone jumps from a height, they willaccelerate due to their own weight (N)

and air resistance will affect themAcceleration of free fall or accelerationdue to gravity (9.81 ms-2)


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Newtons second law of motion

In an experiment, the acceleration can be measured for various values of the resultantforce acting on the trolley while its mass is kept constant. On a graph ofaccelerationagainst resultant force, a straight line will show that ACCELERATION ISPROPORTIONAL TO THE RESULTANT FORCE.There is a DIRECT RELATIONSHIP between F and a (a is proportional to F) i.e. F aa and m are INVERSELY PROPORTIONAL (a 1/m)

F a a F/m or F ma of F=kmaa 1/m

Force = kg ms-2 or N k=1 so F=ma

Inertia, mass and weightINERTIAthe tendency of an object to stay in its state of rest or uniform motion

- A car is harder to move than a smaller (in comparison) bike- Without a seatbelt, it can be hard to stop yourself moving in a car when the

brakes are applied

An objects INERTIA depends on its MASS. Mass has only size, with no direction (scalar)WEIGHTthe force acting on an object due to gravitationAll masses have a gravitational field around them. A mass is said to have a Gravitationalfield around it which causes the mass to attract another mass which is close to it. The sizeof the field depends on the size of the mass and whereabouts in the field you are.

If another mass is put in this field, a force will pull it towards the first mass.Weightcaused by gravitation. The size of the force varies with the strength of thegravitational field.

MASS is CONSTANT, WEIGHT VARIESWEIGHT - force with both magnitude and direction (vector)


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g= F/m g is Nkg-1W = mg

Electrical scalea piece of conducting metal is compressed or deformed by an objectsweight, changing its electrical resistance. It measures WEIGHT

A beam balance measures MASS as the FORCES have to be balanced

Newtons third law of motionForces come in pairs

These forces act on different bodies (i.e. a trolley and the person)

The missing force is the force of the ground on the person (which would be shown on afree-body diagram)

The push of the ground upwards o our feet is not a member of three thirds law pair,involving the pull of the earth downwards on us. The two third law pairs in this case aredifferent types of force pairs. One is a gravitational pair, the other is caused by contactbetween two surface (so if you jump, the contact pair doesnt exist but the gravitational

pair does).

Third law pairs of forces are always of the same typegravitational, electrostatic, contactetc.

StaticsWhen two forces are equal, they cancel each other out and the object theyre acting on isstationaryor in EQUILIBRIUM

VELOCITY diagrams are used to add forces, and to get them into or out of a triangle, thenuse Pythagoras theorem.

Principles for adding forces: Draw the forces acting at the same point Construct the parallelogram Draw in the diagonal from the point at which the forces act to the opposite cornerof the parallelogram Measure or calculate the size and direction of the resultant

The third law:If body A exerts a force on body B, then body B exerts a force of the same size on body A but in

the opposite direction


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RESOLVING FORCES

The bunting and rope pull on the pole as aresult of being pulled tight. The buntingpulls horizontally to the left while thebracing rope pulls down and to the right.

When you resolve the forces and work outwhat components are acting vertically andwhat are acting horizontally, you can seethe effects of the bunting. It pulls the pole

sideways and downwards. This is a STATIC EQUILIBRIUM

As the pole is at REST it fulfils Newtons first law. If something changes, then the pole willfall over as the forces arent balanced

Equilibrium: when an object has balanced forces acting on it and is in a state of rest

ProjectilesACCELERATION IN THE EARTHS GRAVITATIONAL FIELD

Projectilea force acts on an object which starts it moving then it is subject to a constantforce while it moves. In most cases this means the object is in free fall in the earthgravitational field

An object dropped accelerates vertically downward due to its weight.


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Fluida substance that can flownormally a gas or liquid, but some solids can sometimesbehave like this

Density

Fluid density is alsomass per unit volume

When an object is SUBMERGED in fluid, it feels an upward force caused by the fluidpressureUPTHRUSTThe size of the force is equalto the weight of the fluid that has been displaced by theobject.ARCHIMEDES PRINCIPLE

The mass of the fluid displaced is equal to the volume of the object x the density of thefluid

UPTHRUST is then:

Why does a brick sink?Density of water: 1000 kg m-3

If the volume of the brick is: 1.61 x 10-3

Weight of brick: 3.38kg

If we compare the weight of the brick with the upthrust when it is submerged, theresultantforce will be downwards.Weight = 3.38 x 9.81 = 33.2N downwardsUpthrust = 15.8N upwardsResultant = 33.215.8 = 17.6 N downwards

The brick will acceleratedownwards until it is at rest and balanced at the bottom

2.1Fluid flow

How to answer: (see page 53)

Mass of water displaced is:

This has a weight of:

So the upward force on the brick is:


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FloatingAn object floats when it DISPLACES its own weight in fluid. When an object is at thesurface of a fluid, there is NO UPTHRUST as no fluid has been displaced. As the objectSINKSDEEPER in the fluid, it displaces a greater volume of fluid, thus INCREASINGTHEUPTHRUST acting upon it. When the upthrust and weight are BALANCED equally,the object will FLOAT. So if it wants to float, it has to sink and displace enough fluid tomatch its weight.

HydrometerUsed to determine the density of afluid. The device has a constant weight, so it will sinklower in fluids oflesserdensitybecause a greater volume of less dense fluid must bedisplaced to balancethe counterweight ofthe hydrometer. Scale

markings indicate thedensity.

If used with alcoholicdrinks, it shows howmuch alcohol there is init. The lower thedensity, the greater thealcohol content, as

alcohol has a lowerdensity than the waterit is mixed with.

Fluid movementLAMINAR(streamline) occurs a lower speeds, and changes toTURBULENTas the fluid velocity increases past a certain valueThis changeover velocity will vary depending on the fluid in question and the shape of thearea through which it is flowing

If water is flowing through a pipe slowly, it isLAMINAR flow. Look at the laminar diagram, thearrows closestto the edge of the pipe are shorterthan the rest due to friction, meaning this layermoves slowerthan the other layers. The nextlayer will experience friction from the outermost

one, and so on until we get to the middle layer.Each layer closest to the centre will experienceless friction, thus allowing it to move faster. Theinner-most layer moves the fastest, as


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THE VELOCITY INCREASES THE NEARER YOU GET TO THE CENTREIf a liquid follows Newtons formulae for the frictional force between the layers instreamline flow, then is known as a NEWTONIAN LIQUIDThe laminar flow of water in a pipe continuous UNIFORMLY over time

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Drag actVISCOUS DRAG (the friction against you) is greater in water than in air. The frictionalforce is due to the fluids viscosity.

Low viscosity = low frictional force (e.g. air)High viscosity = high frictional force (e.g. treacle)Newton developed a formula for the friction in liquids which includes several factors, oneof which is THE LIQUID.The FLUID-DEPENDENT factor is called the COEFFICIENT OF VISCOSITY, ()The rate of flow of a fluid flowing through a pipe is inversely proportional to the viscosityof the fluid.

In industry, the rate of flow of liquid chocolate through pipes in the manufacture ofsweets will vary with the chocolates viscosity.

TEMPERATURE also affects viscosity. In general, liquids have a lower coefficient ofviscosity at higher temperature. For gases, viscosity increases with temperature.

Terminal velocityIn order to calculate an objects actual acceleration when falling, we refer to Newtonssecond law.

Laminarflowin the same place within the fluid, the velocity of the flow isCONSTANT over time.The lines of laminar flow are called STREAMLINES, at anypoint on any of thesestreamlines; the velocity of the flow will be constant over time.In turbulent flow, the fluid velocity in any given place CHANGES over time. Theflow becomes chaotic and eddies form, causing unpredictable higher and lowerpressure areas. Turbulent flow increases the drag on a vehicle and so increasesfuelconsumptionStreamline flow produces much less air resistance than turbulent . Thus by alteringthe aerodynamics of their suits, skiers can raise the velocity at which the airmovement past their body will change from laminar flow to turbulent flow. This is

the principle behind all streamline designs, such as sports cars and boats


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From this, we can calculate the resulting acceleration for falling objects; we need toinclude WEIGHT, UPTHRUST caused by the object being fluid in air and the VISCOUSDRAG force caused by the movement. The changing velocity makes the viscous dragdifficult to calculate, so we consider the equilibrium situation, in which the weight exactlybalances the sum of upthrust and drag, meaning that the falling velocity remainsCONSTANT, thus it is the TERMINAL VELOCITY.

Viscous dragViscous drag is the friction force between a solid and a fluid. Calculating this can besimple, so long as it is a SMALL REGULARLY SHAPED OBJECT (otherwise it is difficultas the turbulent flow creates and unpredictable situation)

Stokes LawViscous drag (F) on a small sphere at low speeds:

rRadius of the sphere (m)vVelocity of the sphere (ms-1) - coefficient of viscosity of the fluid (Pa s)

In such a situation, the drag force is directly proportional to the radius of the sphere anddirectly proportional to the velocity, neither of which is necessarily an obvious outcome.

Consider this: a ball bearing is dropped through a column of oil

Terminal velocity: weight = upthrust + stokes law

Ms is the mass of the sphere and vterm is the terminal velocity

Mass of the sphere, ms:

Weight of the sphere, Ws:

For the sphere, the upthrust = weight of fluid displaced

Mass of fluid, mf:

Weight of fluid, Wf:


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Rearrange:

= vterm =

Terminal velocity is proportional to the square of the radius. Therefore, a larger spherefalls faster. More complex situations have more complex equations. This isnt however acommon situation, however the principle that larger objects generally fall faster holds truefor most objects without a parachute.

Hookes LawThere is a direct relationship between stretching aspring and the force it exertsThe law states that the force F exerted by a spring isproportionalto itsextension, xK is negative as the force exerted by the spring is in theOPPOSITE DIRECTION to the extension

This law only applies up to a certainpoint, when this limit is reached, the extensionincreases more rapidly and the spring remains more permanently deformed when the load isremoved. This is called the ELASTICLIMITThe spring constant, k, is different for different springs. The larger the value of k, thestiffer the spring.

Hookes law isnt usually used when considering the stiffness of a particular material; solidsdoshow verysimilar behaviour to springs. This provides evidence for a model of solids inwhich the attractive and repulsive forces behave a little like springs.Beyond the elastic limit, materials no longer obey the law and the permanent deformation is

called plastic deformation. Some materials have a VERY low elastic limit and do not obeythe law at all. Plasticine for example.

Elastic strain energyThe average force used to stretch the spring is:

F

So work done:

(-kx)x = kx2

Elastic energy:Eela = Fx = kx

2

2.2Strength of materials


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This is the same thing as working out the areaunderthe force-extension graph

Stress, strain and the Young modulusTENSILE FORCEputs something in tension, i.e. tends to pull it apart

If we consider tensile force per unit area, this takes into account the samples areaof cross-section

If we consider extension per unit length, this takes into account the length of thesample

Tensile force per unit area = tensile stress (Nm-2 or Pa) =

Tensile strength = the tensile stress at which the material breaks

Extension per unit length = tensile strain =

Many materials, mainly metals, are found to obey Hookes

law for small tensile strains. Under these circumstances,

the quantity:

This quantity is the YOUNGMODULUS (Nm-2 or Pa)The STIFFER a material, the GREATER its Young modulus

Characteristics of solids


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Deforming solidsStiffnessthe ability for a material to resist a tensile forceTensile strengththe tensile stress at which a material failsIn many situations, the force on a material will be tending to reducethe volume, to squashthe material. This is known as a COMPRESSIVE force and puts the material underCOMPRESSION

Compressive force per unit area =compressive stress (Nm-2 or Pa) =

COMPRESSIVE STRENGTH= the compressive strength at which the MATERIAL BREAKSExtension per unit length = compressive strain =

Some materials have a very low tensile strength, but are strong when they are subjected tocompressive strengthsuch as brick and concrete. The strength of a material under sheerstrength is related to some extent its tensilestrength.

You can measure hardness by measuring the size of a dent produced by pushing a diamondinto the surface with a certain force.

As the stress increases, the sample begins NECKINGnarrowing at one pointElastic limitat this point the material stops behaving elastically and begins tobehave plastically. When the stress is removed, the material does not return to itsoriginal length

Yield pointthe material shows a large increase in strain for a small increase instressPlastic zonethe extension increases rapidly for small increase in force in thisregion. Solids which behave in this way are DUCTILE

STRENGTHa materials ability to withstand stress, whether is it tensile, compressive orshearDUCTILEshow plastic deformationBRITTLEmaterials that crack or break with littledeformationTOUGHmaterials able to withstand impactforces without breaking and require a largeforceto produce a small plastic deformationCOMBINATIONmore than one material, often gain the best properties of both. Carbonfibre and living wood are good examplesHARDmaterials which resist plastic deformation, usually by denting, scratching or cuttingMALLEABLEmaterials which show large plastic deformation before cracking orbreaking. The most malleable material is Gold


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A mineral scale by FRIEDRICH MOHS was used to compare hardness, based on the

principle that a material which could scratch another material should be higher (or at leastthe same) on the scale of hardness. This doesnt provide accurate values so isnt often usedin engineering

Materials in the real worldFor climbing ropes, the material must be a compromise between stiffness, breaking stress,cost and density.Climbing helmets have also been developed. Traditional, uncomfortable helmets were madefrom HDPE (high density polyethene) but newer ones are made from CFRP (carbon-fibrereinforced polymer. These materials are HARD, STRONG and not too BRITTLE

The helmets are tested thoroughly,investigatingtemperature, droppingit from aheight with a weight inside it. The compressivestress produced MUST NOT be more than thebreaking stress of the material or it will fail.ALSO, by law there must be no more than 8kNof peak force transmitted to the head.The design is also important, the shell willtransfer force out evenly over the skull due to

the internal webbing straps. The material it is made out of must also have enough strengthin itself. The toughness shows its ability to absorb energy during fracture. The higher, themore energy it can absorb.

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Edexce PHYSICS revision notes.pdf