Physics Equation List :Form 4 Introduction to Physics

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1 Physics Equaion Lis :Form 4 Inroducion o Physics Relaive Deviaion Relaive Deviaion Mean Deviaion 00% Mean Value Prefixes Unis for Area and Volume Prefixes Value Sandard form Symbol Tera T Giga G Mega M Kilo k deci d ceni c milli m micro μ nano n pico p m 0 cm (00 cm) m 0 4 cm (0,000 cm ) m cm 3 (,000,000 cm 3 ) cm 0 - m ( 00 m ) cm 0-4 m ( cm m 3 ( 0,000 m ) 3,000,000 m ) hp://

2 Average Speed Force and Moion Average Speed Toal Disance Toal Time Velociy v s v velociy (ms - ) s displacemen (m) ime (s) Acceleraion a v u a acceleraion (ms - ) v final velociy (ms - ) u iniial velociy (ms - ) ime for he velociy change (s) Equaion of Linear Moion Linear Moion Moion wih consan velociy Moion wih consan acceleraion Moion wih changing acceleraion v s v u + a s ( u + v) Using Calculus (In Addiional Mahemaics Syllabus) s u + a v u + as u iniial velociy (ms - ) v final velociy (ms - ) a acceleraion (ms - ) s displacemen (m) ime (s) hp://

ime for he velociy change (s) Graph of Moion Gradien of a Graph The gradien 'm' of a line segmen beween

3 Ticker Tape Finding Velociy: velociy s number of icks 0.0s ick 0.0s Finding Acceleraion: a v u a acceleraion (ms - ) v final velociy (ms - ) u iniial velociy (ms - ) ime for he velociy change (s) Graph of Moion Gradien of a Graph The gradien 'm' of a line segmen beween wo poins and is defined as follows: Change in y coordinae, Δy Gradien, m Change in x coordinae, Δx or Δy m Δ x hp:// 3

4 Displacemen-Time Graph Velociy-Time Graph Gradien Velociy (ms - ) Gradien Acceleraion (ms - ) Area in beween he graph and x-axis Displacemen Momenum p m v p momenum (kg ms - ) m mass v velociy (ms - ) Principle of Conservaion of Momenum Newon s Law of Moion Newon s Firs Law mu + mu mv + mv m mass of objec m mass of objec u iniial velociy of objec (ms - ) u iniial velociy of objec (ms - ) v final velociy of objec (ms - ) v final velociy of objec (ms - ) In he absence of exernal forces, an objec a res remains a res and an objec in moion coninues in moion wih a consan velociy (ha is, wih a consan speed in a sraigh line). hp:// 4

5 Newon s Second Law mv mu Fα F ma The rae of change of momenum of a body is direcly proporional o he resulan force acing on he body and is in he same direcion. F Ne Force (N or kgms - ) m mass a acceleraion (ms - ) Implicaion When here is resulan force acing on an objec, he objec will accelerae (moving faser, moving slower or change direcion). Newon s Third Law Newon's hird law of moion saes ha for every force, here is a reacion force wih he same magniude bu in he opposie direcion. Impulse Impulse F Impulse mv mu F force ime (N) (s) m mass v final velociy (ms - ) u iniial velociy (ms - ) Impulsive Force F mv mu F Force (N or kgms - ) ime (s) m mass v final velociy (ms - ) u iniial velociy (ms - ) Graviaional Field Srengh g F m g graviaional field srengh (N kg - ) F graviaional force (N or kgms - ) m mass Weigh W mg W Weigh (N or kgms - ) m mass g graviaional field srengh/graviaional acceleraion (ms - ) hp:// 5

The deceleraion of he objec -graviaional acceleraion -0ms - (or -9.8 ms - ). The displacemen of he objec when i reach he ground he heigh of he original posiion, h.

6 Verical Moion If an objec is release from a high posiion: The iniial velociy, u 0. The acceleraion of he objec graviaional acceleraion 0ms - (or 9.8 ms - ). The displacemen of he objec when i reach he ground he heigh of he original posiion, h. If an objec is launched verically upward: The velociy a he maximum heigh, v 0. The deceleraion of he objec -graviaional acceleraion -0ms - (or -9.8 ms - ). The displacemen of he objec when i reach he ground he heigh of he original posiion, h. Lif In Saionary When a man sanding inside an elevaor, here are wo forces acing on him. (a) His weigh, which acing downward. (b) Normal reacion (R), acing in he opposie direcion of weigh. The reading of he balance is equal o he normal reacion. R mg hp:// 6

Moving Upward wih posiive acceleraion Moving

Moving Upward wih consan velociy Moving downward

R mg R mg Moving Upward wih negaive acceleraion

7 Moving Upward wih posiive acceleraion Moving downward wih posiive acceleraion R mg + ma R mg ma Moving Upward wih consan velociy Moving downward wih consan velociy. R mg R mg Moving Upward wih negaive acceleraion Moving downward wih negaive acceleraion R mg ma R mg + ma hp:// 7

8 Smooh Pulley Wih Load Moving wih uniform speed: T T T mg Saionary: Acceleraing: T mg T mg ma Wih Loads Finding Acceleraion: (If m > m ) Finding Tension: (If m > m ) m g m g (m + m )a T T T m g ma m g T ma Vecor Vecor Addiion (Perpendicular Vecor) Magniude x + y Direcion an y x Vecor Resoluion x p sinθ y p cosθ hp:// 8

9 Inclined Plane Componen parallel o he plane Componen perpendicular o he plane mgsinθ mgcosθ Forces In Equilibrium T3 mg T sinθ mg T cosθ T T anθ mg T3 mg T cosθ T cosα T sinθ + T sinα mg Work Done W Fxcosθ W Work Done (J or Nm) F Force (N or kgms - ) x displacemen (m) θ angle beween he force and he direcion of moion ( o ) When he force and moion are in he same direcion. W Fs W Work Done (J or Nm) F Force (N or kgms - ) s displacemen (m) hp:// 9

10 Energy Kineic Energy EK mv E K Kineic Energy (J) m mass v velociy (ms - ) Graviaional Poenial Energy EP mgh E P Poenial Energy (J) m mass g graviaional acceleraion (ms - ) h heigh (m) Elasic Poenial Energy EP EP kx Fx E P Poenial Energy (J) k spring consan (N m - ) x exension of spring (m) F Force (N) Power and Efficiency Power W P E P P power (W or Js - ) W work done (J or Nm) E energy change (J or Nm) ime (s) Efficiency Useful Energy Efficiency 00% Energy Or Power Oupu Efficiency 00% Power Inpu Hooke s Law F kx F Force (N or kgms - ) k spring consan (N m - ) x exension or compression of spring (m) hp:// 0

11 Force and Pressure Densiy ρ m V Pressure ρ densiy (kg m -3 ) m mass V volume (m 3 ) P F A P Pressure (Pa or N m - ) A Area of he surface (m ) F Force acing normally o he surface (N or kgms - ) Liquid Pressure P hρg h deph (m) ρ densiy (kg m -3 ) g graviaional Field Srengh (N kg - ) Pressure in Liquid P P + hρ g am h deph (m) ρ densiy (kg m -3 ) g graviaional Field Srengh (N kg - ) P am amospheric Pressure (Pa or N m - ) Gas Pressure Manomeer P P + hρ g am P gas Pressure (Pa or N m - ) P am Amospheric Pressure (Pa or N m - ) g graviaional field srengh (N kg - ) hp://

field srengh (N kg - ) Pressure in uni cmhg Pressure in uni Pa P a 0 P a 0 P b 6 P b 0.6 3600 0 P c 76 P c 0.

12 Uube hρ h ρ Pressure in a Capillary Tube Baromeer P gas gas pressure in he capillary ube (Pa or N m - ) P am amospheric pressure (Pa or N m - ) h lengh of he capured mercury (m) ρ densiy of mercury (kg m -3 ) g graviaional field srengh (N kg - ) Pressure in uni cmhg Pressure in uni Pa P a 0 P a 0 P b 6 P b P c 76 P c P d 76 P d P e 76 P e P f 84 P f (Densiy of mercury 3600kgm -3 ) hp://

Pascal s Principle F A F A F Force exered on

Force exered on he big pison A area of he big

objec, F ρ V g Uphrus, ρ densiy of wooden

Densiy of wood F T + W ρ Vg T + mg Densiy of

13 Pascal s Principle F A F A F Force exered on he small pison A area of he small pison F Force exered on he big pison A area of he big pison Archimedes Principle W ρ V g Weigh of he objec, F ρ V g Uphrus, ρ densiy of wooden block V volume of he wooden block ρ densiy of waer V volume of he displaced waer g graviaional field srengh Densiy of waer > Densiy of wood F T + W ρ Vg T + mg Densiy of Iron > Densiy of waer T + F W ρ Vg + T mg hp:// 3

14 Hea Hea Change Q mcθ m mass c specific hea capaciy (J kg - o C - ) θ emperaure change ( o ) Energy Supply, E Energy Receive, Q Elecric Heaer P mcθ Energy Supply, E Energy Receive, Q P mcθ E elecrical Energy (J or Nm) P Power of he elecric heaer (W) ime (in second) (s) Mixing Liquid Hea Gain by Liquid Hea Loss by Liquid mcθ mcθ m mass of liquid c specific hea capaciy of liquid θ emperaure change of liquid m mass of liquid c specific hea capaciy of liquid θ emperaure change of liquid Q Hea Change (J or Nm) m mass c specific hea capaciy (J kg - o C - ) θ emperaure change ( o ) Specific Laen Hea Q ml Q Hea Change (J or Nm) m mass L specific laen hea (J kg - ) Boyle s Law PV PV (Requiremen: Temperaure in consan) Pressure Law (Requiremen: Volume is consan) P T P T hp:// 4

15 Charles s Law (Requiremen: Pressure is consan) Universal Gas Law Refracive Index V T PV T V T PV T P Pressure (Pa or cmhg.) V Volume (m 3 or cm 3 ) T Temperaure (MUST be in K(Kelvin)) Ligh Snell s Law Real deph/apparen Deph sini n sin r n refracive index (No uni) i angle of inciden ( o ) r angle of reflecion ( o ) n refracive index D real deph d apparen deph n D d (No uni) (m or cm ) (m or cm ) Speed of ligh c n v n refracive index (No uni) c speed of ligh in vacuum (ms - ) v speed of ligh in a medium (like waer, glass ) (ms - ) Toal Inernal Reflecion n sin c n refracive index (No uni) c criical angle ( o ) hp:// 5

16 Lens Power P Power f focal lengh P f (D(Dioper)) (m) Linear Magnificaion m hi h o m v u h h i o v u m linear magnificaion u disance of objec v disance of image h i heigh of image h o heigh of objec (No uni) (m or cm ) (m or cm ) (m or cm ) (m or cm ) Lens Equaion + u v f Convenional symbol posiive negaive u Real objec Virual objec v Real image Virual image f Convex lens Concave lens hp:// 6

17 Asronomical Telescope Magnificaion, m P P e o m f f o e m linear magnificaion P e Power of he eyepiece P o Power of he objecive lens f e focal lengh of he eyepiece f o focal lengh of he objecive lens Disance beween eye lens and objecive lens Compound Microscope d f o + f e d Disance beween eye lens and objecive lens f e focal lengh of he eyepiece f o focal lengh of he objecive lens Magnificaion m m m Heigh of firs image, I Heigh of second image, I Heigh of objec Heigh of firs image, I Heigh of second image, I Heigh of objec, I m Magnificaion of he microscope m Linear magnificaion of he objec lens m Linear magnificaion of he eyepiece Disance in beween he wo lens d > f o + f e d Disance beween eye lens and objecive lens f e focal lengh of he eyepiece f o focal lengh of he objecive lens hp:// 7

1. VELOCITY AND ACCELERATION

1. VELOCITY AND ACCELERATION 1.1 Kinemaics Equaions s = u + 1 a and s = v 1 a s = 1 (u + v) v = u + as 1. Displacemen-Time Graph Gradien = speed 1.3 Velociy-Time Graph Gradien = acceleraion Area under