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Copy of Physics IB

overview of IB physics
by

Graeme Anderson

on 27 May 2011

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Transcript of Copy of Physics IB

D Core Topic 1:Physics and physical measurement 1.1 The realm of physics 1.2 Measurement and uncertainties 1.3 Vectors and Scalars Orders of Magintude Distance Mass Time The universe
10 to the 25 metres Distance from Earth to Sun
1.5 times 10 to the 11 metres Distance from Sun to nearest star
4 times 10 to the 16 metres The radius of the Earth
6.4 times 10 to the 6 metres The size of a grain of sand
2 times 10 to the -4 metres The radius of a hydrogen atom
3.1 times 10 to the -11 metres Size of sub atomic particles
10 to the -15 metres Use scientific notation Recognize prefixes and sufixes Age of the universe
10 to the 18 seconds Earth goes around the Sun
1 year Moon goes around the Earth
1 month Human heartbeat
1 second Passage of light across a nucleus
10 to the -23 seconds Mass of the universe
10 to the 50 kg Mass of the Sun
2 times 10 to the 30 kg Mass of the Earth
6 times 10 to the 24 kg Aproximate mass of a man
75 kg Mass of an electron
10 to the -30 kg SI Units Uncertainty Accuracy and Precision Random and Systematic Error Random errors are always present in measurement and can be diminished through repetition Systematic errors occur due to problems in the equipment or method and have to be dealt with directly The red line represents the actual values The green stars are not on the line due to large random errors The blues stars are not on the line due to large systematic errors Summary Calculations For addition and subtraction use absolute uncertainty For multiplcation, division and powers use percentage uncertainty For functions like sine and cosine use the maximum and minimum to aproximate the uncertainty Don't forget to use SI format Use ms and not m/s -1 Additional Notes This might be useful Use in graphs are used to show uncertainties, and remember to not say a graph is linear unless the best-fit line goes through all the error bars Vectors are quantities with direction
e.g. velocity, force... Scalars are quantities without direction
e.g. speed, mass... Vectors are represented in print by bold symbols, for example, F Use graphical methods
to deal with vectors Multiplying a vector by a scalar is equivalent to lenghtening the vector by the factor of the scalar Multiplication of vectors and scalars V times 5 V 5 V Note that direction is preserved Division of vectors by scalars is equivalent to the multiplication of a vector with the inverse of a scalar F divided by 2 F F/2 Basics S times -1 S -S Note: multiplication by a negative number causes a change in direction Addition of Vectors Vector A Vector B A and B should have equal lenght (magnitude) A+B=C C Just put the head of the first on the tail of the second A-B=D This is equivalent to:
A+(-B)=D D Using these methods you can split a vector into vertical and horizontal components 1.1 The realm of physics 1.2 Measurement and uncertainties 1.3 Vectors and Scalars Topic 2: Mechanics 2.1 Kinematics 2.2 Force and dynamics 2.3 Work, energy and power 2.1 Kinematics Data booklet notes u is the initial velocity
v is the final velocity
t is time
s is displacement displacement is a vector quantity
distance is a scalar Aditional notes and examples Displacement is the distance moved in a specific direction Methods of findining displacement Newton's second law Convert between these forms to solve problems centripetal acceleration remember that w (lower case omega) is equal to (2pi)/T, and that the acceleration (a) is thus equal to r*w^2 the inclusion of cosine theta here is meant to show that this is only the component of force in the same direction as the force If the angle is 0 then W=Fs First a useful link http://www.youtube.com/user/khanacademy When in doubt go to KhanAcademy Basic definitions Displacement is the distance travelled in a certain direction
it is a vector quantity and is denoted by the symbol s Velocity is the rate of change of displacemnt with respect to time
it is a vector quantity, its magnitude is called speed
it is denoted by the symbol u if initial and v if final this means that it is the derivative of displacement withrespect to time, it also means that we can find the average velocity of an object using 2 points on a graph, or the instantaneous velocity using calculus For example if a car is moving North East at a speed of 90 km*h^(-1). This means that its velocity is 90 km*h^(-1) North East, but we could also define it as 45 km*h^(-1) North. This is because 50 percent of the speed is taking the car North, and 50 percent is taking it West, finding the component of a velocity in a specific direction is useful for problems involving work Work can be defined as W=F*s*cos(theta); where cos(theta) is the component of the force parallel to the displacement. For example: you are holding a string attached to a box on the floor, when you pull the string it forms an angle with the floor, the cosine of the angle gives the amount of force being put into work, the rest of the force is perpendicular to the direction of motion (it is straigth up). Acceleration is the rate of change of velocity with respect to time
it is a vector quantity denoted by: a, there is no name for the magnitude of acceleration Now we delve deeper Equations of motion The suvat equations are only applicable to uniformly accelerated linear motion note that 3, 4, 5 and 6 are obtained from 1 and 2 Remember: acceleration due to gravity is 9.81 m*s^2 or 9.81 N*kg^(-1) Falling O o l l l l ; . . . . At first I fell with
velocity v, but then I reached terminal velocity due to air resistance, if I had had a parachute, I would have reached terminal velocity much sooner! Graphs Acceleration time graphs follow the same basic format Using calculus makes interpreting the graphs much easier, and if you know both differentiation and integration, then this part of the syllabus wil not be a problem Here are some tips on working with graphs When moving from s to v to a, what we are doing is differentiating, thus if we make graphs for the motion of an object, the y values of v-t graph will be the gradients of the s-t graph. Thus when going fromt s to v to a we use the following transformations y=constant y=zero slope=constant slope=zero slope= linear eq. (mx+b) slope= constant It may not be evident whether or not the slope is a linear equation, but complex curves are usualy not dealt with in the IB. There are a few sign you can look for which imply the graph is parabolic though You recieve a v-t graph depicting an object falling from great hight. The curve appears to start out with a slope equal to a positive, non-zero constant, but then slowly bends until the slope reaches zero and then stays there. Here you would be requiered to explain that the object at first has acceleration g, but then, due to air resistance the objects acceleration would drop to zero, and the object would reach terminal velocity when the force of the falling object is equal to the force of air resistance. You can use the shape of the curve to check if the line is parabolic, or if the graph is a s-t graph, and the acceleration is uniform (as it will be in most IB problems), then the graph is parabolic Example s v a slope area under
curve graph v a s v slope and area under curve 2.4 Uniform circular motion 2.2 Force and dynamics Free body diagrams O l l l l o Mass=100kg :) acceleration due to gravity near the surface of the Earth is approximatly 10 metres per second squared. However, it might be easier to remember this 10 Newtons per kilogram, becuase weight equals mass times g (acceleration due to gravity). Thus if we multiply my weight, 100kg, by g, 10Nkg^(-1), we get that I weigh 1000N. Weight equals mass times acceleration due to gravity W=mg if you need a bit more explanation come closer I'll wisper it to you weight force of Earth on the creepy physics guy Use vector techniques to add the force together.
If you can't find the resultant force then go to the vector section. hint: the forces cancel each other Newton's first law Newton's second law Newton's third law A body will remain at rest or move with constant velocity unless acted upon by an unbalanced force This is also called translational equilibrium Use free body diagrams to detrmine whether or not the body is in translational equilibrium Intuition Example 1 Example 2 Problem Find the value of F for which the system is in equilibrium o 10N 10N -------------------------- pi/4 pi/4 F F 10N Solution -------------------------- pi/4 pi/4 10N o Step 1 recognise that the vectors must cancel for the body to be in equilibrium Add vectors graphically Step 2 10N 10N F Here you should see that the sum is zero, and that -F is thus equal to the sum of the remaining sides Now F can be found using the Pythagorean Theorem What does this mean a b c F Apply Pythagorean theorem 10N 10N Step 3 ((10n)^2+(10N)^2)^(1/2)=F Problem? Step 1 pi/6 F1 Problem Find the value of F1 and F2 for which the system is in equilibrium Step 3 o 30N Step 2 -------------------------- 10N Solution F2 o F1 10N*cos(pi/6) 30N F2 10N*sin(pi/6) Resolve vectors into horizontal and vertical components Assume both vertical and horizontal components add up to zero F1+10N*cos(pi/6)=0 F2+30N+10N*sin(pi/6)=0 Isolate the variables to find the answer F1=-10N*cos(pi/6) since we are trying to find the magnitude of the force don't pay attention to the sign. F2=-30N-10N*sin(pi/6) F1=8.7 F2=35 The rate of change of momentum of a body is directly proportional to the unbalanced force acting on the body that takes place in the same direction This can be summarized as:
F=ma or F=(delta p)/delta t) F is the slope in a p-t graph
(delta p) is the area under a F-t graph momentum=p=mv In a closed system momentum is conserved o m1 v1 o v2 o o m2 becomes m1*v1=m2*v2 Example If a body A exerts a force on body B then body B will exert an equal and opposite force on body A You need to be able to discus examples of this, if you understand the law it should not be difficult, but here are some examples to work on A falling body Recoil of a gun Jumping off a boat A box on the floor 2.3 Work, energy and power definitions Work is displacement in the direction of a force
W=F*d*cos(theta) Energy is the ability to do work Energy has different forms and two main types Kinetic (motion, heat) Potential (Gravitational, elastic) Ek=1/2 mv^2 Ep=m*g*(delta h) Energy cannot be created or destroyed, it can only be converted to a different form. 0 l 0 l l 0 0 ) Collisions Elastic Inelastic Force displacement graphs In a force displacement graph, the area under the curve is the work done W=F*delta s In the case of a stretching spring the slope of the graph (F/delta s) is called k, the elastic constant. s F Area under the curve is W Slope is equal to k In this graph the area under the curve is 1/2 base*height
which in this case is
1/2F*delta s Since F/delta s equals k
F=k*delta s Substituting for F gives
W=1/2 k*delta s^2 Or, in the more common form
W=1/2 k*x^2 An important equation power is work per time H=50m H=30m } Delta H=20m m=100kg Gravitational potential energy Here the most important thing to notice is that the difererence in height is what matters not the heigh itself W=m*g*delta h so here
W=100kg*10N/kg*20m
W=50J It is extremely important that you can convert from gravitational potnetial to kinetic energy 1/2 m*v^2=m*g*h Force towards centre Motion perpendicular to force 2.4 Uniform circular motion Sources Centripetal force can have various sources Gravity is the source of centripetal force which keeps the Moon in orbit around the Earth Friction is the source of of centripetal fource when a car is making a turn Centripetal acceleration a=(v^2)/r a=(r*4pi^2)/(T^2) Topic 3: Thermal physics 3.1 Thermal concepts 3.2 Thermal properties of matter specific heat capacity latent heat Thermal energy 3.1 Thermal concepts Hot Cold Heat Temperature determines the flow of thermal energy D V Temperature in Kelvin is equal to temperature in Celsius plus 273. It is important to use this scale because it is absolute (zero K is absolute zero)! ) the internal energy of a
substance is the total potential energy
and random kinetic energy of the
molecules of the substance ( 7 The internal energy is the total energy contained by a thermodynamic system Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold Thermal energy refers to the non-mechanical transfer of energy between a system and its surroundings The mole The mole is defined as the amount of substance that contains as many elementary entities (e.g., atoms, molecules, ions, electrons) as there are atoms in 12 g of the isotope carbon-12 The molar mass of a substance is the mass per unit mole of the substance The Avogadro constant expresses the number of elementary entities per mole of substance and it has the value 6.02*10^23 mol^(-1) 3.2 Thermal properties of matter Definitions The thermal capacity of a body is the amount of energy required to raise the temperature of the body by 1K Thermal capacity Specific heat capacity Specific latent heat Pressure C=Q/(delta T) When solving a problem involving thermal capacity you will usually be required to find the energy (Q) using the thermal capacity (C) and the change in temperature (delta T) Use the equation Q=C*delta T
Remember that this works both for increases and decreases in temperature The specific heat capacity (c) of a material is the energy required to raise the temperature of 1 Kg of the material by 1K c=Q/(m*delta T) When solving a problem involving thermal capacity you will usually be required to find the energy (Q) using the thermal capacity (C), mass (m) and the change in temperature (delta T) Use the equation Q=m*C*delta T
Remember that this works both for increases and decreases in temperature The specific latent heat (L) of a material is the energy required to change the phase of 1 Kg of a material without changing the temperature L=Q/m Again the most common form of the equation is obtained by isolating Q:
Q=m*L
Again the formula works for both heating and cooling Pressure is equal to force per unit area P=F/A Changes of phase Boiling vs. evaporation Evaporation takes place at the surface of a liquid, and at all temperatures Boiling occurs throughout the liquid, and at a specific temperature During a phase transition all of the energy gained or lost by the body goes into changing the phase of the body Gases Ideal gas The model makes a few assumptions The molecules are perfectly elastic The molecules are spheres The molecules are identical There are no forces between the molecules exept when they collide This means that the particles have constant velocity between collisions The particles have virtually no volume Temperature is a measure of the average random kinetic energy of the molecules of an ideal gas. PV=nRT P is the pressure V is the volume n is the number of moles R is the gas constant T is the temperature in Kelvin You need to understand the implications of this model Examples If you decrease the volume of a gas under constant temperature, the number of collisions between the particles and the walls of the contianer will increase which means the pressure goes up. If you increase the pressure of a constant volume of gas the amount of collisions between the walls of the container and the particles must have increased, but since the volume of the gas didn't change, the velocity of the particles must have increased. Since the temperature is proportional to the average kinetic energy of the gas, the temperature must have increased Energy in Energy out Efficiency Efficiency is equal to work out devided by work in No process is 100% efficient,
some energy is always lost as heat Topic 4: Simple harmonics motion and waves 4.1 Kinematics and simple harmonic motion 4.2 Energy changes during simple harmonic motion 4.3 Forced oscillation and resonance 4.4 Wave characteristics 4.5 Wave properties Data booklet notes w is the angular velocity T is the period Ep=1/2(mw^2(x^2)) The potential energy is: If you add the kinetic and potential energy you get: Ek+Ep=Et since x zero is a constant, the total energy of a body undergoing SHM is constant from (1/2)mv^2 a=-xw^2 remember: Examples -------------------- _________________________ _________________________ 0 A B GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG GGGGGGGGGGGGGGGGGGGGG C D AB-Pendulum CD-Mass on a spring What is SHM? In SHM the acceleration is proportional to the distance from a fixed point. The acceleration is always directed towards the fixed point. a=-xw^2 definitions Equilibrium position Amplitude Period Frequencey Angular frequency Phase/Cycle The state of the system when it is not disturbed.
Ex: when the pendulum is at position 0 The maximum displacement from equilibrium
Unit: m; symbol x ; displacement is x;
points A and B on the pendulum One complete oscilation (A-B-A on the pendulum)
In circular motion a cycle is 2pi (1 rotation)
Phase refers to a fraction of a period, a phase diffrence describes the defference between 2 oscilation The period is the time it takes to complete a cycle
Symbol: T; unit s Number of occurences per unit time (f=1/T)
symbol: f; unit: s^-1 or Hertz A scalar measure of the rate of rotation
symbol: w(lower case omega); unit: radian per second;
w=2*pi*f or w=(2*pi)/T 4.1 Kinematics and simple harmonic motion
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