PHYSICS FINAL EXAM FORMULA SHEET Parabolic Motion 1 x t xi vit 2 vx t vix vicos theta 3 y t yi viyt 0 5gt2 4 Vy t viy gt viy visin theta 5 x t xi vit 0 5at2 6 v t vi at 7 VF 2 Vi 2 2ad Work and Energy P W t W F x m a x W Fcos theta x W KE W F X 5mv2 PEi mgh KEi 0 5mv2 Momentum net T P mv P mv Fnet P T K 1 2mv2 P2 2m Impulse J F J P Cons of momentum P1 T P2 T P1 P2 0 no external forces momentum is conserved Elastic collision total mech E is conserved Inelastic collision Mech E not conserved Inelastic Consv m1v1i m2v2i m1v1f m2v2f M1V1 M1 M2 Vf M1V1I M2V2I M1 M2 Vf Elastic v1i v2i v2f v1f given m s and vi s after conservation V1f M1 M2 M1 M2 V1I M1 M2 than V1F 0 V2F 2M1 M1 M2 V1I M1 M2 than V2F V1F 2D Inelastic Vf M1V1I M2V2I M1 M2 2D Elastic V1I V1IX V1IY same for V2and VFs Kinetic E is conserved Center of Mass xm m ym m Y Coordinate X Coordinate xcm ycm Oscillation T period one complete cycle f frequency 1 T A amplitude max dist frm rest x Acos wt Vmax WAmplitude Amax W2Amplitude w angular frequency 2pi T or w 2pi f GM R2 Simple harmonic motion oscila spring T 2pi sqrt m k w sqrt k m k spring constant F k delta x KE 1 2MV2 PE 1 2kX2 Mgh 1 2kx2 E 1 2kA2 V sqrt k m A2 X2 VX wAsin wt Fnet m ac aX k m x w2Acos wt SHM and circular MTN wt 2pi T t x Acos wt Tcos mg 0 vertical Tsin mv 2 r horizontal Pendulum FS mgsin s L aS g L s T period 2pi sqrt L g Rotaional motion convert to rad s s r w rad s 2pi revolutions rev sec v m s wr s arc length w 2pi T T angular acceleration rads sec 2 w T Rotational Kinematics w w0 t 0 w0t 1 2 t2 w2 w2 0 2 Tangential Motion vT rw aT r Centripetal acceleration ac rw2 or ac v2 r Rotational Inertia I m r2 1 I 2 Ke 2 Torque torque rFsin F m a 0 I F D Trans eqib Fnet 0 Rotational equib torque 0 Mech equib both 0 Angular momentum L angular momentum Iw KE L2 2mr2 Cons if no external torque Gravitation GmM R 2 GmM R 2 ac F mac G 6 67 10 11 N m2 Kg2 Period of Planets R3 T2 Ks or T2 R3 Ks Keplers 3rd Object falling to Planet from separation PEi KEi PEf KEF PEi GMstar m r 0 r infinity KEi 0 PEf GMstar m r where r rstar KEf 0 5mv2 e eccentricity sqrt 1 b a 2 c constant arnd sun a3 T2 c 3 36x1018m3 s2 V2 2GMstar Rstar R3 T2 Gm 4pi2 UE Gm1m2 r Emech GmM 2r Escape speed Vesc sqrt 2GM R Elasticity F A Y L L Stress strain Compression F A B V V Stress volume strain Pressure P F A V Pa pascal N m2 P pgh P P0 pgh Buoyancy Submerged B Fg so watergV Mobjg pressure waterg h top h bottom obj Vobj g water Vobj g Buoyancy Partially Submerged W Mobjectg obj Vobj g obj Vobj g water Vdisplaced g Vdisplaced Vobj obj water H obj Vobj water A B Mwater displaced g B water Vdisplaced g B water h A g H height of portion under water Object on bottom F ma a 0 Bouncey normal weight 0 Held by scale B w t 0 Held down by object B w t 0 Pressure at depth h P P0 fluid g h Bournulies P1 Vel A1V1 A2V2 Since P V2 gh is constant when Velocity increases pressure decreases Rate of flow Q piR4 P1 P2 8 co of visc L Waves V T V f Intensity I I P A Power Area The speed of sound V sqrt Bulks mod Sound Level Db 10 log I I0 I0 10 12 2r1 I1 I2 r2 Doppler Effect v vobserver v vsource Thermal Expansion L L0 T 2 gh1 P2 V2 2 gh2 2 A A0 T 2 V V0 T 3 Coff Off linear expansion Ideal Gas Law PV nRT in nothings extracted than P1V1 T1 P2V2 T2 V of molecule Sqrt 3RT Molar Mass and V sqrt 3kbT mass of particle PV 2 3N 1 2mv2 micro PV NkbT macroscopic T 2 3 1 kb 1 2mv2 Average KE 1 2mv2 3 2kbT Total KE 3 2NkbT 3 2nRT N particles n mols Heat Transfer Conduction Rate of Energy transfer P P Q T watts P kA Th Tc x kA Th Tc x Radiation P AeT4 Watts 5 6696x10 8 A Surface Area E emissivity T Temp kelvin Balance with surroundings P Ae T4 T0 4 Piston problems WORK Isobaric W F y and W PA y P F A W P Vf Vi Isovolumetric W 0 volume is constant Thermodynamics U Q W change internal Engy Isobaric Q and W are NON zero Q mcspecfic t Q mhvap U 5 2nR T W P V Adiabatic Q 0 U W Ekin 3 2nR T PiVi5 3 PfVf S 0 5 3 Isothermal T 0 U O W nRT ln Vf Vi Isovolumetric V 0 U 3 2Rn T W 0 and U Q GENERAL PV T constant First Law U 3 2 PV and U 3 2PV U 3 2 PfVf PiVi Work area under PV diagram Engine W Power Time W Qh Qc Efficency W Qh Kelvin Efficency 1 Qc Qh or Qh Qc Qh Coeff of Preformance COPfridge Qc W COPheater Qh W Qc energy added to engine Qh energy given from engine Carnot Engine W Qh Qc Efficency 1 Tcold Thot E 1 Qc Qh Kelvin S 0 Qhot Thot Qcold Tcold Entropy S Q T reversible processes Calorimitry Tfinal mcoldccoldtcold mhotchotthot mcoldccold mhotchot c unknown mknowncknown Tfin Tknown munknown Tfinal Tunknown
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