Kinematics Final Cheat Sheet for Physics

Kinematics: Distance: how far an object has travelled from its starting point or point of origin. Scalar Displacement: How far an object is from the origin, measured in a straight line. Vector distance . Scalar speed= time displacement velocity= time . Vector Scalars Vectors Distance Displacement Speed Velocity Mass Weight Time Acceleration Temperature Gravity Energy Force Power Voltage Resistance Current ms-1 to kmh-1: multiply by 3.6 kmh-1 to ms-1: divide by 3.6 Newton’s 2nd Law: The acceleration of an object produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. F=ma Newton’s 3rd Law: For every action there is an equal and opposite reaction. Only the forces acting on an object will affect the motion of that object. Simple push and pull o F=ma o SOHCAHTOA Tension/towing o FrictionT =Friction1 + Friction2 … o o Fengine=mvehicle×avehicle + mtrailer×atrailer+ T =mtrailer×atrailer+ Frictiontrailer Elevator o Case 1: Constant velocity, 0 acceleration  ΣF=0  v =u+at 1 2 x=ut+ at 2 1 2 x=vt− at 2 v 2=u 2+ 2ax 1 x= t(u+v ) 2 o  Feels normal Case 2: Accelerating upwards  Σ F≠0  o  Range=V x ×Time V x =V l cosθ V y =V l sinθ Reactionforce=Weight  Feels lighter Pulley system o Case 1: Tabletop, 1 is on table, 2 is suspended  Full flight V ¿ θ ¿ l sin¿ ¿ ¿ ¿ ¿ Height=¿ 2 V l sinθ Time= g o Reactionforce=Weight  Feels heavier Case 3: Accelerating downwards  Σ F≠0 Projectile motion: o Reactionforce=Weight   o ΣF=W −Friction =ma Weight =m 2 g ΣF =W 1−W 2=m1 g−m Inclined plane Tension= m2 ( a + g ) o o o ∑pbefore =∑pafter 2 o Note that relative to √ o Uphill: o Downhill: ΣF=Drivingforce+mgsinθ − Fric Energy: KineticEnergy= 1 2 mv 2 2 √ v r 4 2 =mg+F c ΣF c = √ R −W =R sinθ V = √grtan θ W =R cosθ 2 F AB= V= g = ac = r2 o o 2 = Energy: o o 2 v 4π r = r t2 o o o 2 πr V= t 2 mv ΣF c = r F AB=Fc = o o o GM planet M satellite r 2 = Geostationary radius: √ GMplanett 2 4 π2 3 3 3 r1 r2 r3 Kepler’s Law: = = 3 t 1 3 t 23 t 3 r= 2 ΔV V final−V initial = v = a= t Δt r 3 … Area under graphs: v =c 1− o −2 √ GMplanet o o GMplanet 2 πr = t r o 2 t0 t2 ms v r l0 Υ l= o −2 √ v =c 1− o Muons: G=6.67× 10 Nm kg o o o G MA M B Satellites: √ Proper time: o Measured by one observer from one perspective at one location. o t=t 0 Υ 2 r2 GMplanet g= r2 o Arelative v ¿ B ¿=v A −v B 1 Υ= ≥1 2 v 1− 2 c Proper length: o The distance between two points measured by an observer who is stationary relative to the two points. gr tanθ is measured from the horizontal −11 will be negative Vertical circular motion: o Case 1: Trough  ΣF c =R−mg θ o o ΣF=Drivingforce−mgsinθ− Fric 2h ×V cosθ g l √ V= R=m g + Planetary motion: Gravity: All sticky head-on collisions are inelastic o Newton’s 1st Law: If an object has 0 net force acting on it, it will remain at rest or continue moving with an unchanged velocity. u2 u1 Maximum o m 1 u1 + m 2 u 2= (m 1 +m 2) v o √ 2 2 m1 u1 +m 2 u 2 = ( m 1+ m2) v Scenario 3: Head-on collision o o o Scenario 2: 1 and 2 moving same direction, 2 is slower. o m1 u1 + m2 u 2= (m1 +m 2) v mv r ΣF c = o m1 u2= ( m1+ m2 ) v 2 If elastic, , then R=0 V = √gr o Banking: o Scenario 1: 1 moves into 2 (stationary) o m1 u= ( m1+m2) v If elastic, E=areaunderthe graph×m Relativity: 2 o Measured in kgms-1 Always conserved o gravity / radius (velocity at which vehicle becomes airborne) o Case 3: Vertical loop  At trough, same as Case 1  At peak, same as Case 2  V = gr (minimum velocity to remain in loop) Cornering: o Circular motion: Simple circular motion: 1 2 Height= gt 2 2h Time= g Range=Time×Vx = Forces: ∆p ∆p=m∆v =m ( v−u ) ∆p F= t is impulse, o Range=Time×Vx =Time×Vl cosθ Half flight Vector o o for a graph, √ KEbefore > KEafter Transferred/transformed into heat and sound. Momentum: o p=mv Tension= m1 a+ Friction Case 2: Actual pulley, 1 is heavier, 2 is lighter  ∆Energy (Watts) time F×t graph ¿ mΔv o o   Area under Collisions: If elastic, KEbefore= KE after o o (lighter) If ΣF c =mg force / radius E=areaunderthegraph  v R=m( −g) r  orkdone=Σ Force×Distance( x)=∆E If inelastic, for a graph, 2 (Joules) o Must be in the same direction Power=  (heavier) Case 2: Peak  ΣF c =R+ mg o W o  o 2 v + g) r R=m(  Gravitational PotentialEnergy=mgh 1 2 Elasticstoredenergy= kx 2 o Restoringforce=−kx ∆F o Springconstant k= ∆x √ l2 2 l0 l c−v l t BA= c+v 2l 0 2lΥ t 0= = c c 1 µs=1 ×10−6 s t AB= Negatively charged particle, close to the speed of light. Half-life of ~5 micro-seconds. However, many reach Earth’s surface: evidence for time dilation and length contraction. Etotal=E k + E0=Υ mc Erest =mc 2 2 Ekinetic=(Υ −1)mc 1 eV=1.6×10−19 J 2 Electric Fields: Law of Conservation of Electric Charge: Net charge cannot be created; it can only be transferred. Conductors: allow the free flow of electrons, eg metals Insulators: restrict the free flow of electrons, eg glass, wood, plastic EMF: Electromotive Force o Energy transferred to one coulomb of charge o Measured in Volts o 1V = 1J C Elementary charge: Electrons, Beta particles go against conventional current Neutrons not affected -net charge of 0 F=qvB (magnitude) o q -charge o v -velocity o B -magnetic field strength FBI rule to find direction +¿=1.6×10−19 C −¿= p¿ e¿ kq Electric Field Strength: E= 2 r 9 o in air k =8.99× 10 o q=charge o r=distance o F B= F C 2 mv qvB= r Coulomb’s Law: o o o F= kq1 q2 r2 radiusof curvature= N If F is positive, it will be repulsive. If F is negative, it will be attractive F=qE =ma Parallel plates: o E= Other: GPE = mgh v =u+at 1 2 x=ut+ at 2 1 2 x=vt− at 2 v 2=u 2+2ax 1 x= t(u+v ) 2 ΔV Vm−1 d o ΔV=potentialdifference Any charged particle placed in an electric field will experience a force (attraction/repulsion) e−¿ =9.1× 10−31 kg m¿ p+¿ =1.67×10−27 kg m¿ P=VI 2 Ploss=I R V=IR WD=F ×d=E×q×d=ΔKE= Magnetic Fields: Magnetic Field Strength: mv p = qB qB Magnitude of velocity constant, direction nonconstant B= kI r Equal to 0 at Δ ϕ=0 (maxs and mins of ϕ ) How to increase EMF: Increase rate of rotation Increase number of loops Increase strength of magnetic field Increase area of loop Lenz’s Law: The induced flow of electricity will produce a magnetic field that opposes the change in flux that created it. Use RH grip rule to determine direction of current (clockwise vs anticlockwise) Direction of EMF ≡ Direction of conventional current Transmission Structure: Power station  Step-up transformer  Power lines  Step-down transformer  Power lines  Step-down transformer  Homes Homes use 240V 50Hz AC in Australia Step-up: Increased voltage, lowered current Step-down: Lowered voltage, increased current Power Loss: mv 2 2 Milikans I ¿ =I out k =2× 10−7 I =current ( amps) o r=radialdistance ( m) Conventional current: +→−¿ Root Mean Square o o Right hand grip rule: o Thumb points in direction of conventional current o Fingers indicate direction of magnetic field: clockwise/anticlockwise Oersted’s experiment: o Compass deflects depending on direction of field o If angle of deflection = 45 degrees, magnetic field strength = Earth’s magnetic field o Will never reach 90 degrees, as Earth’s magnetic field always present. DC Motors: F=nBIl (constant) o n -number of loops o B -magnetic field strength (Tesla) o I -current (Amps) o l -length (m) FBI rule to find direction Torque ( Nm )=Fr=nBIlr o r -radius (m) In motor: T =Frcosθ = nBIlrcosθ o θ measured from the horizontal of the perm. magnets Particles in Magnetic Fields: Protons, Alpha particles, positrons follow conventional current RMSVoltage= Cost: Waves: Waves can be either longitudinal (sound, vibrates in direction of propagation) or transverse (light, vibrates perpendicular to direction of propagation) Frequency: cycles per second, measured in hertz Period: time of one full cycle f= Thus, step-up transformers reduce Power Loss Protection: Fuse -single wire, one use. When current goes too high, wire breaks. Circuit breaker -When current goes too high, induced magnetic field causes switch to activate Residual Current Device (RCD) -Checks that RMS: without being reflected absorbed or scattered. Two types of reflection: o Diffuse – piece of paper o Specular – mirror Opaque surfaces: o Do not transmit any light o Absorb all colours except the colour we consider them to be o Black absorbs all colours o White reflects all colours Transparent surfaces: o Allow light to pass through them o Also absorb all colours all colours except those that give them colour Angle of incidence = Angle of reflection, as measured from the normal √ peak 2 V peak V peak =V ¿ peak = 2 √2 1 p Less optically dense  more optically dense: o Slows o θi > θr More optically dense  less optically dense o Speeds up o θr >θ i Refractiveindex= Snell’s Law: o sin (i ) n 2 v 1 = = =Relativerefractiveind sin ( r ) n 1 v 2 Refractive indexes are averages – different wavelengths Large angles of refraction  dispersion Separates colours ROYGBIV Critical angle: θc o o The angle at which the refracted ray will skim across the surface θr =90 o o Wavelength: distance between two peaks, troughs, etc Amplitude: distance from rest to max/min Polarisation: The ability of a material to filter certain aspects of light -e.g. glare A polarized wave is a transverse wave for which the oscillations occur in a single plane If two polarisers are placed in series: o If parallel, all that passes through the first will pass through the second o If perpendicular, none will pass through Angle can be adjusted to alter what aspects of light are filtered Use Snell’s Law to find When θi > θc , total internal reflection occurs Dispersion: the separation of white light into colours or of any radiation according to wavelength. Doppler effect: an increase (or decrease) in the frequency of sound, light, or other waves as the source and observer move towards (or away from) each other. Observer: Frequency increases as source approaches observer and decreases as source moves away from observer Driver: Frequency constant if observer is stationary relative to sound source Standing waves: the result of the superposition of two waves with the same amplitude and frequency travelling in opposite directions within the same medium. Characterised by nodes and antinodes, and appear not to be travelling. Refraction: The change in direction of a wave passing from one medium to another Harmonics: Priced in kilowatt hours (kwh) Total$= Powerrating ×hours×charged 1000 Transformers: V 1 I 2 N1 = = V 2 I1 N 2 Generation Flux: Measures the amount of magnetic field passing through an area ϕ=BA , where B is perpendicular to A ϕ=0 , where B is parallel to A Δ ϕ=ϕ final −ϕ initial =ΔBA=ΔAB Electromotive force/Potential Difference: Joules/Coulomb; Voltage Induced by and proportional to ε =IR= o o o P Δϕ Δϕ =Bvl=−n I Δt B=magfield v =velocity l=lengthof conducter LH FBI rule for direction Pos and neg maximums occur at ϕ=0 L to R loops increases: L to R step-up L to R loops decreases: L to R step-down DC transformer: AC transformer with an electronic device connected to the output Light: Top speed in a vacuum: 2.998×108 Three different events occur when light strikes a surface: o Reflection -the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. o Absorption -when matter captures electromagnetic radiation, converting the energy of photons to internal energy. o Transmission -When light travels through a medium such as glass speedof light∈avacuum speedof light∈themedium v =fλ Velocity decreases, wavelength decreases Frequency remains constant E=hf −34 2 −1 h=6.62607004×10 m kg s Fixed at both ends: o o 2L n v nv f n= = λn 2 L Where f n represents the nth λn = o harmonic Open at one end: o o 4L n nv f n= 4L λn = o No even harmonics, no resonance Resonance: the reinforcement or prolongation of sound by reflection from a surface or by the synchronous vibration of a neighbouring object. Wave resonance: Forced oscillations at the resonant frequency of a wave medium create constructive interference through the superposition of the travelling wave and its reflection. Interference: the combination of two or more electromagnetic waveforms to form a resultant wave in which the displacement is either reinforced or cancelled. Antinode doubles the amplitude Node creates 0 amplitude Diffraction: the process by which a beam of light or other system of waves is spread out as a result of passing through a narrow aperture or across an edge Wavelength, frequency, and velocity are all constant, only direction changes