IB physics Data booklet review
Graphs: Average velocity: slope of the straight line joining the initial andfinal position on the position -time graph. (Instantaneous) velocityat a given point: slope of the tangent line at given time on the position -time graph. Average Acceleration: slope of the straight line joining the initial andfinal position on the velocity - time graph (Instantaneous) acceleration at a given point: slope of the tangent line at given time on the velocity - time graph
Displacementis the area under velocity– time graph Change in velocity is the area under acceleration– time graph
Air resistance provides adrag force to objects in free fall. ▪ The drag force increases as the speed of the falling object increases resulting in decreasing downward acceleration ▪ When the drag force reaches the magnitude of the gravitational force, the falling object will stop accelerating and fall at a constant velocity. ▪ This is called theterminal velocity/speed. In vacuum In air
Inertia is resistance an object has to a change of velocity Mass is numerical measure of the inertia of a body (kg) Weight is the gravitational force acting on an object . W = mg Force is an influence on an object that causes the object to accelerate • 1 N is the force that causes a 1-kg object to accelerate 1 m/s2. Fnet(resultant force)is the vector sum of all forces acting on an object Free Body Diagramis a sketch of a body and all forces acting on it.
Newton’s first law:An object continues in motion with constant speed in a straight line (constant velocity) or stays at rest unless acted upon by a net external force. Object is intranslational equilibrium if no change in velocity Newton’s second law: • Δpis the change in momentum produced by the net force F in time Δt. • Δp= Δ(mv) 1. velocity changes, mass doesn’t change: Δp= mΔv → F = ma If a net force is acting on an object of mass m, object will acquire acceleration Direction of acceleration is direction of the net force. 2. mass changes, velocity doesn’t change: Δp = vΔm → F = v Δm/Δt in (kg/s) Newton’s third law: Whenever object A exerts force on object B, object B exerts an equal in magnitude but opposite in direction force on object A
Normal/Reaction force(Fn or R) is the force which is preventing an object from falling through the surface of another body . That’s why normal force is always perpendicular (normal) to the surfaces in contact. when you have to draw FREE BODY DIAGRAM (object and all forces acting on it), there is a requirement to draw as many normal/reaction forces as there are points of contacts . For example if you have a 2-D car (with two wheels) you have to draw two normal /reaction forces. Each on one wheel. Table with two legs – the same thing. Emu with two legs – the same thing Friction forceis the force that opposes slipping (relative motion ) between two surfaces in contact; it acts parallel to surface in direction opposed to slipping. Friction depends on type and roughness of surfaces and normal force.
vertical direction: F sin θ + Fn = mg Horizontal direction: F cos θ – Ffr = ma
Fn Ffr mg mg q Fn Ffr q q q q mg cos mg sin = direction perpendicular tothe incline: Fnet = ma = 0 Fn= mg cos θ Along the incline direction: Fnet= ma mg sin θ – Ffr = ma
Linear momentumis defined as the product of an object’s mass and its velocity: p = mv vector!(kg m/s) Impulseis defined as the product of the net force acting on an object and time interval of action: FΔt vector! (Ns) Impulse F∆t acting on an object will produce the change of its momentum Δp: F∆t = ∆p Δp = mv - mu Ns = kg m/s Achieving the same change in momentum over a longer time requires smaller force, and over a shorter time requires greater force. WHEN YOU TRY TO FIND CHANGE IN MOMENTUM REMEMER TO LABEL VELOCITIES AS POSITIVE OR NEGATIVE The impulse of a time-varying forceis represented by the area under the force-time graph.
Law of Conservation of Momentum:The total momentum of a system of interacting particles is conserved - remains constant, provided there is no resultant external force. Such a system is called an “isolated system”. momentum of the system after collision = momentum of the system before collision for isolated system (p = pi ) vector sum REMEMBER TO DRAW A SKETCH OF THE MASSES AND VELOCITIES BEFORE AND AFTER COLLISION. LABEL VELOCITIES AS POSITIVE OR NEGATIVE. Elastic collision: both momentum and kinetic/mechanical energy are conserved. That means no energy is converted into thermal energy Inelastic collision: momentum is conserved but KE is not conserved. Perfectly inelastic collision: the most of KE is converted into other forms of energy when objects after collision stick together. To find how much of KE is lost in the system, subtract KE of the system after collision from KE of the system before the collision. If explosion happens in an isolated system momentum is conserved but KE increases (input of energy from a fuel or explosive material.)
Workis the product of the component of the force in the direction of displacement and the magnitude of the displacement. (scalar) W = Fdcos Ѳ (Fd = F cos Ѳ) (Joules) Work done by a varying force F along the whole distance travelled is the area under the graph FcosѲ versus distance travelled. Energyis the ability to do work. Work changes energy. Potential energyis stored energy. (Change in) Gravitational potential energy ∆EP = mg ∆h Elastic potential energy = work is done by external force in stretching/compressing the spring by extension x. EPE = W = ½ kx2 Kinetic energyis the energy an object possesses due to motion EK = ½ mv2
Work done by applied/external forceis converted into (changes) potential energy (when net force is zero, so there is no acceleration). Work – Kinetic energy relationship: work done by net force changes kinetic energy: W = ∆KE = final EK – initial EK = ½ mv2 – ½ mu2 the work done by centripetal forceis zero: Wnet = 0 → Wnet = ∆KE → no change in KE → no change in speed; centripetal force cannot change the speed, only direction. Examples: gravitational force on the moon, magnetic force on the moving charge.
Conservation of energy law: Energy cannot be created or destroyed; it can only be changed from one form to another. For the system that has only mechanical energy (ME = potential energies + kinetic energy) and there is no frictional force acting on it, so no mechanical energy is converted into thermal energy, mechanical energy is conserved ME1 = ME2 = ME3 = ME4 mgh1 + ½ mv12 = mgh2 + ½ mv22 = • • • • • • f friction cannot be neglected we have to take into account work done by friction force which doesn’t belong to the object alone but is shared with environment as thermal energy. Friction converts part of kinetic energy of the object into thermal energy. Frictional force has dissipated energy: ME1 – Ffr d = ME2 (Wfr = – Ffr d)
Power is the rate at which work is performed or the rate at which energy is transmitted/converted. scalar (1 W(Watt) = 1 J/ 1s ) Another way to calculate power Efficiency is the ratio of how much work, energy or power we get out of a system compared to how much is put in.
Centripetal acceleration causes change in direction of velocity, but doesn’t change speed. It is always directed toward the center of the circle. Centripetal force Period T: time required for one complete revolution/circle speed around circle of radius r:
Macroscopic level: temperature gives indication of the degree of hotness or coldness of a body, measured by thermometer Thermal equilibriumoccurs when all parts of the system are at the same temperature. There is noexchange of thermal energy/please do not mention heat.(This is how a thermometer works) Thermal energyof a system =internal energy—the sum total of the potential energy and kinetic energy of the particles making up the system. Potential energyof the molecules arises from the forces (bonds/ because of intermolecular forces) between them. Kinetic energyof the molecules arises from the translational, rotational, ad vibrational motion of the particles. Microscopic level: (absolute) temperature directly proportional to theaveragekinetic energy of the molecules of a substance: (KE)avg = kT. k is Boltzmann constant Heatis thethermal energythat flows/is transferred from one body or system of higher temperature to another of lower temperature.
Relative atomic massis the mass of an atom in units of 1/12 of the mass of a carbon-12 atom. The moleis the amount of substance that contains the same number of atoms/molecules as 0.012 kg of carbon-12. Molar Massis the mass of one mole of a substance (kg/mol). 1 mole of a gas at STP occupies 22.4 l (dm3) and contains 6.02 x 1023 molecules/mol.
Heat/Thermal Capacityis the amount of thermal energy needed to raise the temperature of a substance/object by one degree Kelvin. C = → Q = C ΔT unit: (C) = J K-1 Specific heat capacityis the quantity of thermal energy required to raise the temperature of one kilogram of a substance by one degree Kelvin. c = → Q = mc ΔT unit: (c) = J kg-1K-1 amount of thermal energy needed to increase the temperature of m kgof a substancewith specific heat capacity c by ΔT amount of thermal energy released when the temperature of m kgof a substancewith specific heat capacity c decreases by ΔT homogeneous substance: C = mc
Latent heatis the thermal energy that a substance/body absorbs or releases during a phase change at constant temperature. L = Qatconst. temp.unit: J Specific latent heatis the thermal energy required for a unit mass of a substance to undergo a phase change. L = → Q = mLunit: (L) = J/kg Ifelectrical energyis converted into increase of internal energy of the system, then: • Qadded = electrical energy = Pt = IVt = Qabosorbed • P – power, I – current, V – voltage, t - time
4 Phases (States) of Matter solid, liquid, gas and plasma; ordinary matter – only three phases
Phase transition is the transformation of a thermodynamic system from one phase to another. Changes: S → L melting or fusion L → S freezing or solidification S → G sublimation G → S deposition or desublimation L → G vaporization G → L condensation includes boiling and evaporation
While melting, vibrational kinetic energy increases and particles gain enough thermal energy to break from fixed positions. Potential energy of system increases. Melting pointof a solid is the temperature at which it changes state from solid to liquid. Once at the melting point, any additional heat supplied does not increase the temperature. Instead is used to overcome the forces between the solid molecules increasing potential energy. ◌ At the melting point the solid and liquid phase exist in equilibrium. While freezing, particles lose potential energy until thermal energy of the system is unable to support distance between particles and is overcome by the attraction force between them. Kinetic energy changes form from vibrational, rotational and part translational to merely vibrational. Potential energy decreases (It is negative!!! = attraction: intermolecular forces become stronger). While boiling, substance gains enough potential energy to break free from inter-particle forces. Similar to evaporation, the only difference being that energy is supplied from external source so there is no decrease in temperature. While condensing, the energy changes are opposite to that of boiling.
The distinguishing characteristic of a phase transition is an abrupt changein one or more physical properties, in particular the heat capacity, and the strength of intermolecular forces. During a phase change, the thermal energy added or released is used to change (increase/decrease) the potential energy of the particles to either overcome or succumb to the inter-molecular force that pulls particles together. In the process, the average kinetic energy will not change, so temperature will not change.
Evaporationis a change of phase from the liquid state to the gaseous state that occurs ata temperature below the boiling point. Evaporation causes cooling. A liquid at a particular temperature has a range of particle energies, so at any instant, a small fraction of the particles will have KE considerably greater than the average value. If these particles are near the surface of the liquid, they will have enough KE to overcome the attractive forces of the neighbouring particles and escape from the liquid as a gas. The escape of the higher-energy particles will lower the average kinetic energy and thus lower the temperature. The rate of evaporationis the number of molecules escaping the liquid per second. Evaporation can be increased by • increasingtemperature/more particles have a higher KE • Increasingsurfacearea/more particles closer to the surface • Increasing air flow above the surface (gives the particles somewhere to go to)/ decreasing the pressure of the air above liquid
Kinetic Model of an Ideal Gas P – pressure, V – volume, • N – number of particles, k – Boltzmann constant, T - temperature • PV = NkT=nRT (for Jerry) Gas pressureis the force gas molecules exert due to their collisions (with a wall – imaginary or real), per unit area. P = Assumptions of the kinetic model of an ideal gas. • Gases consist of tiny hard spheres/particles called atoms or molecules. • The total number of molecules in any sample of a gas is extremely large. • The molecules are in constant random motion. • The range of the intermolecular forces is small compared to the average separation of the molecules • The size of the particles is relatively small compared with the distance between them • No forces act between particles except when they collide, and hence particles move in straight lines. • Between collisions the molecules obey Newton’s Laws of motion. • Collisions of short duration occur between molecules and the walls of the container and the collisions are perfectly elastic (no loss of kinetic energy).
Temperature is a measure of the average random kinetic energy of the molecules of an ideal gas. Macroscopic behavior of an ideal gas in terms of a molecular model. • Increase intemperatureis equivalent of an increase in average kinetic energy (greater average speed). This leads to more collisions and collisions with greater impulse. Thus resulting in higher pressure. • Decrease involume results in a smaller space for gas particles to move, and thus a greater frequency of collisions. This results in an increase in pressure. Also, depending on the speed at which the volume decreases, particles colliding with the moving container wall may bounce back at greater speeds. This would lead to an increase in average kinetic energy and thus an increase in temperature. • An increase in volume would have an opposite effect.
Application of the "Kinetic Molecular Theory" to the Gas Laws • Microscopic justification of the laws
Pressure Law (Gay-Lussac’s Law) • Effect of a pressure increase at a constant volume • Macroscopically: • at constant volume the pressure of a gas is proportional to its temperature: • PV = NkT → P = (const) T • Microscopically: • ∎ As T increases, KE of molecules increase • ∎ That implies greater change in momentum when they hit the wall of the container • ∎ Thus microscopic force from each molecule on the wall will be greater • ∎ As the molecules are moving faster on average they will hit the wall more often • ∎ The total force will increase, therefore the pressure will increase
The Charles’s law • Effect of a volume increase at a constant pressure • Macroscopically: • at constant pressure, volume of a gas is proportional to its temperature: • PV = NkT → V = (const) T • Microscopically: • ∎ An increase in temperature means an increase in the average kinetic energy • of the gas molecules, thus an increase in speed • ∎ There will be more collisions per unit time, furthermore, the momentum • of each collision increases (molecules strike the wall harder) • ∎ Therefore, there would be an increase in pressure • ∎ If we allow the volume to change to maintain constant pressure, • the volume will increase with increasing temperature
Boyle-Marriott’s Law • Effect of a pressure decrease at a constant temperature • Macroscopically: • at constant temperature the pressure of a gas is inversely proportional to its volume: • PV = NkT → P = (const)/V • Microscopically: • ∎ Constant T means that the average KE of the gas molecules remains constant • ∎ This means that the average speed of the molecules, v, remains unchanged • ∎ If the average speed remains unchanged, but the volume increases, this means • that there will be fewer collisions with the container walls over a given time • ∎ Therefore, the pressure will decrease
What do all of them have in common? Oscillatory motion, but not just any. IT IS SIMPLE HARMONIC MOTION
Graphical treatment and math • To analyse these oscillations further, we can plot graphs for these motions. • You can plot a displacement – time graph by attaching a pen to a pendulum and moving paper beneath it at a constant velocity, or by shining the light on and oscillating spring.
the shadow should look like this graph The shape of this displacement – time graph is cosine curve. The amplitude is x0 is initial displacement displacement x = x0 cos ωt where angular frequency is: ω = 2πf= 2π/T
Simple Harmonic Motionis periodic motion in which the acceleration/ restoring force is proportional to and in opposite direction of the displacement. a = − ω2x. spring: a = F/m = – kx/ m = – (k/m)x = = − ω2xω2 = k/m General equation for the position of a particle undergoing simple harmonic motion: x = x0cosωt. x0 – amplitude, f – frequency f = 1/T T – period for full oscillation angular frequency = 2 f (how many full circles 2 per second) = 2/T
Dependence on time x = x0cosωt. v = dx/dt = – x0 sin ωt = – v0 sin ωt a = dv/dt = – 2x0cosωt = – a0cost a = – 2x x0, v0, a0 positive maximumvalues Data booklet
Dependence on position v = = – x0 sin ωt = = v = EK = ½ m v2 = ½ m2 ( ) EK for x = 0 → EK(max) = ½ m2 EK(max) = EP(max) = ETotal Data booklet potential energy at any moment = total energy – KE EP = ½ m2 x2 Energy (total) of SHM is proportional to amplitude2 ( Perioddoes not depend on amplitude!!!!!!
Damping: Due to the presence of resistance/friction forces on oscillations in the opposite direction to the direction of motion of the oscillating particle Amplitude of oscillations decreases Friction force is a dissipative force. "to damp" is to decrease the amplitude of an oscillation. Decreasing the amplitude doesn’t change period. Light/under damping: The decay in amplitude is relatively slow and the oscillator will make quite a few oscillations before finally coming to rest. Critical/heavy damping: occurs if the resistive force is so big that the system returns to its equilibrium position without passing through it. The mass comes to rest at its equilibrium position without oscillating. The friction forces acting are such that they prevent oscillations. Over-damping: the system returns to equilibrium without oscillations, but much slower than in the case of critical damping.
Natural frequencyis the frequency an object will vibrate with after an external disturbance. Forced oscillations: when an external periodic force with frequency fD is applied on a free system with a natural frequency f0 , the system may respond by switching to oscillations with a frequency equal to the driving frequency fD. Variation of the amplitude of vibrations of an object subjected to the forced frequency close to its natural frequency of vibration. Qualitative description of the factors that affect the frequency response and sharpness of the curve. ▪ For a small degree of damping, the peak of the curve occurs at the natural frequency of the system. ▪ The lower the degree of damping, the higher and narrower the curve. ▪ At very heavy damping, the amplitude is essentially constant. Resonanceis increase in amplitude of oscillation of a system exposed to a periodic driving force with a frequency equal to the natural frequency of the system.
WAVES ▪ Useful: microwave oven, radio. . ▪ Harmful: bridges, aero plane wings, internal organs in the case of heavy machinery . When a wave (energy)propagatesthrough a medium, oscillations of the particles of the medium aresimple harmonic. Progressive waves transfer energy through a distortion that travels away from the source of distortion. There isnonet transfer of medium. ▪ Transverse wavesare waves in which the particles of the medium oscillate perpendicular to the direction in which the wave is traveling. ◌ EM waves: light, radio waves, microwaves: need no medium, electric and magnetic field oscillate perpendicular to each other and to the direction of wave propagation. ◌ Earthquake secondary waves, waves on a stringed musical instrument, waves on the rope. ◌ Transverse wave can not propagate in a gas ( and actually pure transverse can not propagate in liquid either) ▪ Longitudinal wavesare waves in which the particles of the medium vibrate parallel to the direction in which the wave is traveling. ◌ Sound waves in any medium, shock waves in an earthquake, compression waves along aspring
A wavefrontis set of points having the same phase/displacement. Arayis an arrow drawn on a diagram to show the direction of propagation of waves. It is always at right angles to the wavefront. Energy of a wave of amplitude A is proportional to the amplitude2 : E ∞ A2 Although the speed of a wave depends only on the medium, there is a relationship between wavelngth 𝜆 , frequency f (period T) and the speed Waves that need medium to travel through are calledmechanical waves. Electromagnetic waveis made up of changing electric and magnetic fields perpendicular to each other and to the propagation of the wave. They travel through vacuum with the SAME SPEED!speed of light c ≈ 3 x 108 m/s
Index of refraction nof a medium is the ratio of the speed of light in a vacuum, c, and the speed of light, v, in that medium: As the speed of light in air is almost equal to c, nair ≈ 1 Refraction: When a wave passes from one medium to another, its speed changes resulting in a change in direction of the refracted wave Snell’s lawstates that for a given pair of media, the ratio of the sines of the angles of incidence and refraction is equal to the ratio of velocities in the two media The refracted ray is refracted more in the medium with greater n, slower speed of light = = = = v = 𝜆 f ; frequency doesn’t change in refraction, so in the medium with smaller wave speed, wavelength will be smaller.
Chromatic dispersionis phenomenon in which the index of refraction depends on wavelength/frequency, so the speed of light through a material varies slightly with the frequency of the light and each λ is refracted at a slightly different angle. The longer λ, the smaller index of refraction. nred < nblue , red light is refracted less than blue light Dispersion is the phenomenon which gives separation of colours in prism/rainbow and undesirable chromatic aberration in lenses. Diffractionis the spreading of a wave into a region behind an obstruction (into a region of geometrical shadow). Diffraction effects are more obvious when wavelength of the wave is similar in size to aperture/obstacle or bigger. remember: big λ (compared to aperture or obstacle), big diffraction effects