Physics formula ICSE_Standard 10

Physics Formula guide for ICSE standard 10

Author Srikanth K S All rights reserved Page 1

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Contents How to solve a problem in Physics ......................................................................................................... 2

Important terms and their units ............................................................................................................. 2

Chapter 1 Force ....................................................................................................................................... 3

1.1 Formula Quick reference: Force ................................................................................................... 3

Chapter 2 Work Power and Energy ......................................................................................................... 3

2.1 Formula quick reference: Work power and Energy ...................................................................... 3

Chapter 3 Machines ................................................................................................................................ 5

3.1 Formula and quick reference card: ............................................................................................... 5

3.2 Inclined plane and gear ................................................................................................................. 6

Pulley ................................................................................................................................................... 7

Chapter 4 Refraction of Light .................................................................................................................. 8

Refraction of Light through a prism .................................................................................................... 8

Chapter 5 Refraction of Light through a Lens ......................................................................................... 9

Chapter 7 Sound ..................................................................................................................................... 9

Chapter 8 Current electricity ................................................................................................................ 10

8.1 Formula and quick reference card: ............................................................................................. 10

8.2 Electro-Motive force, Terminal voltage and internal resistance of a cell ................................... 11

Chapter 9 Electrical Power and Household Circuits ............................................................................. 12

Chapter 9 Calorimetry ........................................................................................................................... 12



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How to solve a problem in Physics 1. Read the problem at least twice

2. Write down what is given in the problem

3. Draw a diagram Ensure to draw the direction in case of ray diagrams and different forces.

4. Write down the formulae that will help you to solve the problem

5. Solve the problem by proper substitution.

6. Simplify your answer

7. Don’t forget to write the units

Important terms and their units Term Description SI Unit

Length Meters m

Mass Kilo gram Kg

Time Seconds s

Force Newton , CGS unit Dyne N

Force SI unit to CGS unit conversion 1N = 105 dynes

Velocity Meters per second m/s

Acceleration Meters per second squared m/s2

Moment of force In SI Units its Newton meter Nm

Moment of force In CGS Units its dyne centimeter dyne cm

Remember 1Nm = 107 dyne cm 1kgf X m = 9.8Nm 1gf X cm = 980 dyne cm

Work 1 joule = 1 newton X 1 meter Joule

Remember 1 Joule = 107 erg

Power 1 Joule/ second Watt

Remember 1 W = 1 Js-1 = 107 erg s-1

1 HP = 746 W = 0.746 kW

Energy 1 joule = 1 newton X 1 meter Joule

Electrical Energy is expressed as Kilowatt hour

Energy of sub atomic particles 1eV = 1.6 X 10-19 J Electron volt (eV)

Machines Mechanical advantage, Velocity ratio Unit less

Wavelength Symbol λ m

Frequency Hertz Hz

Current Amphers A

Voltage Volts V

Resistance Ohms Ω



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Chapter 1 Force

1.1 Formula Quick reference: Force Newton’s second law Force is directly proportional to the rate of change

of momentum and indirectly proportional to rate of change of time

Momentum Momentum is the product of mass and velocity

Change in momentum ( )

Rate of change of momentum

Rate of change of momentum

Force = Mass X Acceleration

1 N = 105 Dynes Newton is the SI unit and Dyne is CGS Unit

Gravitational unit of force

Equation of motion

1Nm = 107 dynes cm 1kgf X m = 9.8 Nm 1 gf X cm = 980 dyne cm

Principle of moments Sum Clock wise moments = Sum anti clockwise moments

Chapter 2 Work Power and Energy

2.1 Formula quick reference: Work power and Energy Work Work done = Force X

Displacement

Work

When the work done by the force when the displacement is not along the force

Positive Work

When , example Positive work done by a force of gravity in free fall

Zero work done , when

Work done when a coolie is carrying some load on his head moves horizontally. Note : Zero work done by centripetal force.

Negative work done Work done is –ve when Example when a ball is thrown up in the air.

Work done by force of



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gravity

Unit of work = 1 joule = 1 N * 1 m

Kilo joules = 1000 Joules

CGS Unit of work 1 erg = 1dyne x 1cm

Conversion of Joules to ergs

1 Joule = 107 erg 1N = 105 dyne and 1m = 102 cm 105 X 102 =107 erg

Power The rate of doing work is called power

Power is also the product of force and average speed

Unit of power SI Unit of power is Watts

-1

Conversion of SI unit to CGS Units

-1 = 107 ergs -1

1 HP = 746 W = 0.746 kW

Energy The energy of a body is the ability to do work

Unit of energy -1 X 3600 s = 3.6kJ

1 Kilowatt hour = 3.6 X 106 J

Heat energy Heat energy is usually measured in calorie. 1 Calorie of heat energy required to raise the temperature of 1g of water from 14.5o C to 15.5o C

Relationship of Calorie and Joule

Electron volt The Energy of atomic particle is very small. It is measured in terms of electron volt (eV)

1eV = 1.6 X 10-19 J

Different forms of energy

Kinetic energy The energy processed by a body by virtue of its state of motion

The kinetic energy possessed by a moving body can be measured as the amount of work which the moving body can perform before it comes to rest

Measurement of kinetic energy

2

Relationship between momentum and kinetic energy

2

( )

Work energy theorem Work done by a force on a moving body is equal to the increase in kinetic energy.



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Proof

On Simplification

(

)

( )

( )

Types of Kinetic energy Translational kinetic energy Car moving in a straight path Free falling object

Rotational kinetic energy Spinning top

Vibrational kinetic energy Movement to and fro from a mean position example plucking a guitar string

Potential energy Energy possessed by a body at rest

Forms of potential energy

Mechanical potential energy 1. Gravitational potential energy 2. Elastic potential energy

Gravitational potential energy

Conservation of energy and energy degradation

Energy degradation The gradual decrease of useful energy due to radiation loss, frictional loss etc is called degradation of energy

Law of conservation of energy

Energy can neither be created or destroyed

Chapter 3 Machines

3.1 Formula and quick reference card: Load The resistive or opposive force to be

overcome by a machine is called load

Effort The force applied on the machine to overcome the load is called Effort

Mechanical Advantage Ratio of Load to effort

Mechanical Advantage MA MA = ( )

( )

Velocity Ratio VR VR =

The ratio of the velocity of

effort to the velocity of load

Velocity of Load VL =

dL is the distance moved by

the Load in time t

Velocity of Effort VE = ⁄ dE is the distance moved by



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the Effort in time t

Velocity Ratio VR VR = ⁄ Note velocity ratio has no unit as it’s a ratio

Work input The work done on the machine by the effort

Work Output The work done by the machine on the load

Efficiency (ƞ) The ratio of the useful work done by the machine to the work put into the machine by the effort

Efficiency (ƞ) = ⁄

Ideal machine A machine in which there is no loss of energy in any manner

The efficiency of an ideal machine is 100%

Actual Machine An actual machine has an efficiency always less than 100% because the moving parts are neither weightless or frictionless Strings are not perfectly elastic and the different parts are not rigid

Relationship between efficiency mechanical advantage and velocity ratio

MA = VR X ƞ

Class 1 Lever Fulcrum is in between the effort and load Effort and Load are in the same direction MA can be <1 = 1 or >1

See Saw, Plier, crow bar, scissors

Class 2 Lever Mechanical advantage of the lever is

always > 1 Bottle opener, Nut cracker

Class 3 Lever Effort is in between the fulcrum and the load MA is always < 1

Sugar tongs, Knife spade

3.2 Inclined plane and gear Inclined plane A sloping surface that behaves

like a simple machine whose MA is always greater than 1



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MA and VR of an inclined plane VR = MA =

This is true in the absence of friction

Gear A wheel with teeth around its rim

Gear Ratio Gear Ratio =

Where Na is the number of teeth in the

driving and Nb is the number of teeth in the driven

Relationship between number of teeth, radius and the speed of rotation

=

=

Pulley Single Fixed Pulley A pulley which has its axis of

rotation fixed in position is called fixed pulley

MA =

=

= 1

Single Movable pulley A pulley whose axis of

rotation is not fixed in position is called a movable pulley. It is also called as a force multiplier

MA =

=

= 2



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Combination Pulleys One fixed and other movable Pulley’s MA =VR = 2n

Block and Tackle pulley MA =

=

= n

VR =

= n

Chapter 4 Refraction of Light Refraction of Light Change in direction of the path of light

when it passes from one transparent medium to another transparent medium

Refractive Index µ =

=

Snells law

Refraction of Light through a prism Prism A transparent refracting medium bounded by 5 surface inclined at the

same angle



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Chapter 5 Refraction of Light through a Lens

Lens A transparent refracting medium bounded by two curved surface which are generally spherical

Convex lens or converging lens

Thicker in the middle and thinner in the periphery

Concave Lens Thicker in the periphery and thinner in the middle

Chapter 7 Sound Longitudinal waves The vibration of the medium is along the direction of propagation



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They can travel in solids liquids or gases

Transverse wave The vibration of the medium is perpendicular to the direction of propagation They can only travel in solids or liquids

Echo The sound heard after reflection from a distant obstacle after the original sound has ceased is called an echo. An echo is heard only if the distance between the person producing the sound and the rigid obstacle is long enough to allow the reflected sound to reach the person at least 0.1 second later

Distance D =

Relations between velocity and frequency

V = f λ

Frequency of vibration f =

(

)

Chapter 8 Current electricity

8.1 Formula and quick reference card: Current Rate of flow of charge

Unit of current Ampere

-1

Unit of charge Coulomb

Flow of current If n electrons pass through a cross section of a conductor in time t, then the total charge passed through the conductor is given as

Potential Direction of flow of charge when two conductors are placed in contact.

Potential at a point It is the amount of work done in bringing a unit positive charge from infinity to that point

Potential at a point

Unit is volts

-

1

Potential difference Pd between two points is the work done in moving a unit positive charge from one point to the other

Resistance and its relation with length and area of cross section

Ohms law Current flowing in a conductor is directly proportional to the potential difference across its ends provided



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the physical conditions and the temperature of the conductor remain constant

Specific resistance or resistivity

Where is the specific resistance

8.2 Electro-Motive force, Terminal voltage and internal resistance of a cell Electro motive force (EMF)

When no current is drawn from a cell that is the cell is open, the potential difference between the terminal o the cell is called electro motive force (ε)

The EMF of a cell is defined as the energy spent per unit charge in taking a positive charge around the complete circuit

ε =

Terminal voltage of a cell

When current is drawn from a cell when the cell is In closed circuit. The potential difference between the electrodes is called terminal voltage

V =

Voltage drop in a cell ε = V +v or V = ε - v

Representation of a cell with internal resistance

Resistors in series Effective resistance R = R1 + R2 + .. Rn



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Resistors in Parallel Effective resistance Formula

=

+

+

+ ….

Chapter 9 Electrical Power and Household Circuits Electrical Energy W = Q V or W = VI t or W = I2Rt or

V2t/R Unit Joules

Charge Q = I X t Columb

Electrical Power P = VI or I2R or V2/R or W/t Unit Watt

Commercial unit of electrical energy

W = power X time 1 Wh = 3600 Joules

Unit Watt second

Remember Fuse is made up of an alloy of Lead and Tin

Remember A bulb (incandescent lamp) filament is made up of tungsten

Chapter 10 Calorimetry Heat The kinetic energy due to random motion of molecules of a

substance.

Temperature of a substance

The average internal kinetic energy of molecules of a substance

One calorie One calorie of heat is the heat energy required to raise the temperature of 1g of water from 14.50C to 15.50C

One Kilo calorie One Kilo calorie of heat is the heat energy required to raise the temperature of 1Kg of water from 14.50C to 15.50C

Heat capacity The heat capacity of a body is the amount of heat energy required to raise its temperature by 10c or 1K

C =

Specific heat capacity c =

Joules/ kelvin

Principle of calorimetry

Heat energy lost by A is equal to the heat energy gained by B m1c1 (t1 – t) = m2 c2 (t – t2)

Melting Change of state from solid to liquid. The temperature at which this state change happens is called melting point

Boiling Change of state from liquid to gas. The temperature at which this state change happens is called boiling point

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Physics formula ICSE_Standard 10