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Physics Equation List :Form 4

Introduction to Physics

Relative Deviation

Relative Deviation = Mean Deviation ×100% Mean Value

Prefixes Prefixes Tera Giga Mega Kilo deci centi milli micro nano pico Units for Area and Volume 1 m = 102 cm 1 m = 10 cm

2 4 2

Value 1 000 000 000 000 1 000 000 000 1 000 000 1 000 0.1 0.01 0.001 0.000 001 0.000 000 001 0.000 000 000 001

Standard form 1012 109 106 103 10-1 10-2 10-3 10-6 10-9 10-12

Symbol T G M k d c m n p

(100 cm) (10,000 cm ) (1,000,000 cm3)

2

1 cm

= 10-2 m

(

1 m) 100

1 m3 = 106 cm3

1 cm2 = 10-4 m2

(

1 m2 ) 10,000 1 m3 ) 1,000,000

1 cm3 = 10-6 m3

(

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Average Speed

Force and Motion

Average Speed = Total Distance Total Time

Velocity

v= s t

Acceleration

v = velocity s = displacement t = time

(ms-1) (m) (s)

a=

v-u t

a = acceleration v = final velocity u = initial velocity t =time for the velocity change

(ms-2) (ms-1) (ms-1) (s)

Equation of Linear Motion

Linear Motion

Motion with constant velocity

Motion with constant acceleration

Motion with changing acceleration

v=

s t

v = u + at 1 s = (u + v)t 2

Using Calculus (In Additional Mathematics Syllabus)

1 s = ut + at 2 2

v 2 = u 2 + 2as

u = initial velocity v = final velocity a = acceleration s = displacement t = time (ms-1) (ms-1) (ms-2) (m) (s)

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Ticker Tape

Finding Velocity:

velocity =

s number of ticks × 0.02s

1 tick = 0.02s

Finding Acceleration:

v-u a= t

a = acceleration v = final velocity u = initial velocity t = time for the velocity change (ms-2) (ms-1) (ms-1) (s)

Graph of Motion Gradient of a Graph The gradient 'm' of a line segment between two points and is defined as follows: Gradient, m = or m= y x Change in y coordinate, y Change in x coordinate, x

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Displacement-Time Graph Velocity-Time Graph

Gradient = Velocity (ms-1)

Gradient = Acceleration (ms-2) Area in between Displacement the graph and x-axis =

Momentum

p = m×v

p = momentum m = mass v = velocity

(kg ms-1) (kg) (ms-1)

Principle of Conservation of Momentum

m1u1 + m2u2 = m1v1 + m2 v2

m1 = mass of object 1 m2 = mass of object 2 u1 = initial velocity of object 1 u2 = initial velocity of object 2 v1 = final velocity of object 1 v2 = final velocity of object 2 Newton's Law of Motion Newton's First Law In the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with a constant velocity (that is, with a constant speed in a straight line). (kg) (kg) (ms-1) (ms-1) (ms-1) (ms-1)

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Newton's Second Law

mv - mu F t

The rate of change of momentum of a body is directly proportional to the resultant force acting on the body and is in the same direction. F = Net Force m = mass a = acceleration (N or kgms-2) (kg) (ms-2)

F = ma

Implication When there is resultant force acting on an object, the object will accelerate (moving faster, moving slower or change direction). Newton's Third Law Newton's third law of motion states that for every force, there is a reaction force with the same magnitude but in the opposite direction. Impulse

Impulse = Ft

F = force t = time m = mass v = final velocity u = initial velocity

(N) (s) (kg) (ms-1) (ms-1)

Impulse = mv - mu

Impulsive Force

F=

mv - mu t

F = Force t = time m = mass v = final velocity u = initial velocity

(N or kgms-2) (s) (kg) (ms-1) (ms-1)

Gravitational Field Strength

F g= m

Weight

g = gravitational field strength F = gravitational force m = mass

(N kg-1) (N or kgms-2) (kg)

W = mg

W = Weight (N or kgms-2) m = mass (kg) g = gravitational field strength/gravitational acceleration

(ms-2)

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Vertical Motion

· · · ·

If an object is release from a high position: The initial velocity, u = 0. The acceleration of the object = gravitational acceleration = 10ms-2(or 9.81 ms-2). The displacement of the object when it reach the ground = the height of the original position, h.

· · · ·

If an object is launched vertically upward: The velocity at the maximum height, v = 0. The deceleration of the object = -gravitational acceleration = -10ms-2(or -9.81 ms-2). The displacement of the object when it reach the ground = the height of the original position, h.

Lift In Stationary

·

When a man standing inside an elevator, there are two forces acting on him. (a) His weight which acting downward. (b) Normal reaction (R), acting in the opposite direction of weight. The reading of the balance is equal to the normal reaction.

·

R = mg

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Moving Upward with positive acceleration Moving downward with positive acceleration

R = mg + ma

Moving Upward with constant velocity

R = mg - ma

Moving downward with constant velocity.

R = mg

Moving Upward with negative acceleration

R = mg

Moving downward with negative acceleration

R = mg - ma

R = mg + ma

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Smooth Pulley With 1 Load T1 = T2 Stationary: T1 = mg Accelerating: T1 ­ mg = ma Moving with uniform speed: T1 = mg

With 2 Loads

Finding Acceleration: (If m2 > m1) m2g ­ m1g = (m1+ m2)a Finding Tension: (If m2 > m1) T1 = T2 T1 ­ m1g = ma m2g ­ T2 = ma

Vector Vector Addition (Perpendicular Vector) Magnitude =

x2 + y2

Direction =

tan -1

| y| | x|

Vector Resolution

| x |=| p | sin | y |=| p | cos

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Inclined Plane Component parallel to the plane Component perpendicular to the plane = mgsin = mgcos

Forces In Equilibrium

T3 = mg

T2 sin = mg

T2 cos = T1

T3 = mg

T2 cos = T1 cos

T2 sin + T1 sin = mg

T1 tan = mg

Work Done

W = Fx cos

W = Work Done (J or Nm) F = Force (N or kgms-2) x = displacement (m) = angle between the force and the direction of motion

(o )

When the force and motion are in the same direction.

W = Fs

W = Work Done F = Force s = displacement

(J or Nm) (N or kgms-2) (m)

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Energy Kinetic Energy

1 EK = mv 2 2

EK = Kinetic Energy m = mass v = velocity

(J) (kg) (ms-1)

Gravitational Potential Energy EP = Potential Energy EP = mgh m = mass g = gravitational acceleration h = height Elastic Potential Energy

(J) (kg) (ms-2) (m)

1 EP = kx 2 2 1 EP = Fx 2

Power and Efficiency Power

EP = Potential Energy k = spring constant x = extension of spring F = Force

(J) (N m-1) (m) (N)

W P= t

P=

Efficiency

E t

P = power W = work done E = energy change t = time

(W or Js-1) (J or Nm) (J or Nm) (s)

Efficiency =

Useful Energy × 100% Energy

Or

Efficiency =

Hooke's Law

Power Output × 100% Power Input

F = kx

F = Force k = spring constant x = extension or compression of spring

(N or kgms-2) (N m-1) (m)

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Force and Pressure

Density

m = V

= density

Pressure m = mass V = volume (kg m-3) (kg) (m3)

F P= A

Liquid Pressure

P = Pressure (Pa or N m-2) A = Area of the surface (m2) F = Force acting normally to the surface (N or kgms-2)

P = h g

h = depth = density g = gravitational Field Strength

(m) (kg m-3) (N kg-1)

Pressure in Liquid

P = Patm + h g

h = depth = density g = gravitational Field Strength Patm = atmospheric Pressure

(m) (kg m-3) (N kg-1) (Pa or N m-2)

Gas Pressure Manometer

P = Patm + h g

Pgas = Pressure Patm = Atmospheric Pressure g = gravitational field strength (Pa or N m-2) (Pa or N m-2) (N kg-1)

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U=tube

h1 1 = h2 2

Pressure in a Capillary Tube

Pgas = gas pressure in the capillary tube Patm = atmospheric pressure h = length of the captured mercury = density of mercury g = gravitational field strength Barometer Pressure in unit cmHg Pa = 0 P b = 26 P c = 76 P d = 76 P e = 76 P f = 84

(Pa or N m-2) (Pa or N m-2) (m) (kg m-3) (N kg-1)

Pressure in unit Pa Pa = 0 P b = 0.26×13600×10 P c = 0.76×13600×10 P d = 0.76×13600×10 P e = 0.76×13600×10 P f = 0.84×13600×10 (Density of mercury = 13600kgm-3)

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Pascal's Principle

F1 F2 = A1 A2

F1 = Force exerted on the small piston A1 = area of the small piston F2 = Force exerted on the big piston A2 = area of the big piston Archimedes Principle Weight of the object, W Upthrust,

= 1V1 g

F = 2V2 g

1 = density of wooden block

V1 = volume of the wooden block 2 = density of water V2 = volume of the displaced water g = gravitational field strength

Density of water > Density of wood

Density of Iron > Density of water

Vg = T + mg

F=T+W

Vg + T = mg

T+F=W

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Heat Heat Change

Q = mc

m = mass c = specific heat capacity = temperature change Electric Heater (kg) (J kg-1 oC-1) (o) Mixing 2 Liquid Heat Gain by Liquid 1 = Heat Loss by Liquid 2

Energy Supply, E = Pt Energy Receive, Q = mc Energy Supply, E = Energy Receive, Q

m1c11 = m2 c2 2

Pt = mc

E = electrical Energy (J or Nm) P = Power of the electric heater (W) t = time (in second) (s) Q = Heat Change (J or Nm) m = mass (kg) c = specific heat capacity (J kg-1 oC-1) = temperature change (o) Specific Latent Heat

m1 = mass of liquid 1 c1 = specific heat capacity of liquid 1 1 = temperature change of liquid 1 m2 = mass of liquid 2 c2 = specific heat capacity of liquid 2 2 = temperature change of liquid 2

Q = mL

Q = Heat Change m = mass L = specific latent heat Boyle's Law (J or Nm) (kg) (J kg-1)

PV1 = P2V2 1

(Requirement: Temperature in constant) Pressure Law

P P2 1 = T1 T2

(Requirement: Volume is constant)

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Charles's Law

V1 V2 = T1 T2

(Requirement: Pressure is constant) Universal Gas Law

PV1 PV2 1 = 2 T1 T2

P = Pressure V = Volume T = Temperature (Pa or cmHg .......) (m3 or cm3) (MUST be in K(Kelvin))

Light

Refractive Index Snell's Law Real depth/Apparent Depth

n=

n = refractive index i = angle of incident r = angle of reflection

sin i sin r

(No unit) (o) (o )

n=

n = refractive index D = real depth d = apparent depth

D d

(No unit) (m or cm...) (m or cm...)

Speed of light

Total Internal Reflection

n=

c v

n=

n = refractive index c = critical angle

1 sin c

(No unit) (o )

n = refractive index (No unit) c = speed of light in vacuum (ms-1) v = speed of light in a medium (like water, glass ...) (ms-1)

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Lens Power

P=

P = Power f = focal length Linear Magnification

1 f

(D(Diopter)) (m)

m=

hi ho

m=

v u

(No unit) (m or cm...) (m or cm...) (m or cm...) (m or cm...)

hi v = ho u

m = linear magnification u = distance of object v = distance of image hi = heigth of image ho = heigth of object Lens Equation

Conventional symbol positive negative

1 1 1 + = u v f

u v f

Real object Real image Convex lens

Virtual object Virtual image Concave lens

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Astronomical Telescope Magnification,

Pe m= Po

m = linear magnification Pe = Power of the eyepiece Po = Power of the objective lens fe = focal length of the eyepiece fo = focal length of the objective lens Distance between eye lens and objective lens d = fo + fe

fo m= fe

d = Distance between eye lens and objective lens fe = focal length of the eyepiece fo = focal length of the objective lens Compound Microscope Magnification

m = m1 × m2 = = Height of first image , I1 Height of second image, I 2 × Height of object Height of first image , I1 Height of second image, I 2 Height of object, I1

m = Magnification of the microscope m1 = Linear magnification of the object lens m2 = Linear magnification of the eyepiece Distance in between the two lens

d > fo + fe

d = Distance between eye lens and objective lens fe = focal length of the eyepiece fo = focal length of the objective lens

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