Mechanical Energy and Its Types - Kinetic Energy (K)



  • Force, Work, Power and Energy
  • Force
    • Force
    • Translational and Rotational Motions
    • Moment (Turning Effect) of a Force Or Torque
    • Couple
    • Equilibrium of Bodies and Its Types
    • Principle of Moments
    • Centre of Gravity
    • Uniform Circular Motion (UCM)
    • Centripetal Force
    • Centrifugal Forces
  • Work, Energy and Power
  • Light
  • Sound
  • Machines
    • Machines
    • Simple Machines
    • Technical Terms Related to a Machine
    • Principle of Machine
    • Relationship between efficiency (ղ), mechanical advantage (M.A.) and velocity ratio (VR)
    • Lever
    • Kinds of Levers
    • Examples of Each Class of Levers as Found in the Human Body
    • Pulley
    • Single Fixed Pulley
    • Single Movable Pulley
    • Combination of Pulleys
    • Machines (Numerical)
  • Refraction of Light at Plane Surfaces
    • Refraction of Light
    • Law of Refraction of Light
    • Speed of Light
    • Relationship Between Refractive Index and Speed of Light (µ = C/V)
    • Principle of Reversibility of the Path of Light
    • Experimental Verification of Law of Refraction and Determination of Refractive Index of Glass
    • Refraction of Light Through a Rectangular Glass Slab
    • Multiple Images in a Thick Plane Glass Plate Or Thick Mirror
    • Prism
    • Refraction of Light Through a Prism
    • Real and Apparent Depth
    • Apparent Bending of a Stick Under Water
    • Some Consequences of Refraction of Light
    • Transmission of Light from a Denser Medium (Glass Or Water) to a Rarer Medium (Air) at Different Angles of Incidence
    • Critical Angle
    • Relationship Between the Critical Angle and the Refractive Index (µ = 1/ Sin C)
    • Total Internal Reflection
    • Total Internal Reflection in a Prism
    • Use of a Total Internal Reflecting Prism in Place of a Plane Mirror
    • Consequences of Total Internal Refraction
  • Electricity and Magnetism
  • Heat
  • Refraction Through a Lense
  • Modern Physics
  • Spectrum
    • Deviation Produced by a Triangular Prism
    • Colour in White Light with Their Wavelength and Frequency Range
    • Dispersion of Light Through Prism and Formation of Spectrum
    • Electromagnetic Spectrum
    • Different Radiation of Electromagnetic Spectrum
    • Gamma Rays
    • X rays
    • Ultraviolet Radiations
    • Visible Light
    • Infrared Radiations
    • Micro Waves
    • Radio Waves
    • Scattering of Light and Its Types
    • Applications of Scattering of Light
  • Sound
    • Sound
    • Difference Between the Sound and Light Waves
    • Reflection of Sound
    • Echoes
    • Determination of Speed of Sound by the Method of Echo
    • Use of Echoes
    • Natural Vibrations
    • Damped Vibrations
    • Forced Vibrations
    • Resonance
    • Demonstration of Resonance
    • Some Examples of Resonance
    • Properties of Sounds
    • Loudness and Intensity
    • Pitch (or shrillness) and frequency
    • Audibility and Range
    • Quality (Or Timbre) and Wave Form
    • Noise Pollution
    • Noise and Music
    • Sound (Numerical)
  • Current Electricity
  • Household Circuits
    • Transmission of Power from the Power Generating Station to the Consumer
    • Power Distribution to a House
    • House Wiring (Ring System)
    • Electric Fuse
    • Miniature Circuit Breaker (MCB)
    • Electric Switch
    • Circuits with Dual Control Switches (Staircase Wire)
    • Earthing (Grounding)
    • Three-pin Plug and Socket
    • Colour Coding of Live, Neutral, and Earth Wires
    • High Tension Wires
    • Precautions to Be Taken While Using Electricity
  • Electro Magnetism
  • Calorimetry
    • Heat and Its Unit
    • Temperatures
    • Factors Affecting the Quantity of Heat Absorbed to Increase the Temperature of a Body
    • Difference Between Heat and Temperature
    • Thermal Capacity (Heat Capacity)
    • Specific Heat Capacity
    • Relationship Between the Heat Capacity and Specfic Heat Capacity
    • Specific Heat Capacity of Some Common Substances
    • Calorimetry and Calorimeter
    • Principle of Method of Mixtures (or Principle of Calorimetry)
    • Natural Phenomena and Consequences of High Specific Heat Capacity of Water
    • Some Examples of High and Low Heat Capacity
    • Change of State of Matter
    • Melting and Freezing
    • Heating Curve of Ice During Melting
    • Change in Volume on Melting
    • Effect of Pressure on the Melting Point
    • Effect of Impurities on the Melting Point
    • Concept of Boiling (Vaporization)
    • Heating Curve for Water
    • Change in Volume on Boiling
    • Effect of Pressure on the Boiling Point
    • Effect of Impurities on the Boiling Point
    • Latent Heat and Specific Latent Heat
    • Specific Latent Heat of Fusion of Ice
    • Explanation of Latent Heat of Melting on the Basis of Kinetic Model
    • Natural Consequences of High Specific Latent Heat of Fusion of Ice
  • Radioactivity
    • Structure of the Atom and Nucleus
    • Atomic Model
    • Isotopes
    • Isobars
    • Isotones or Isoneutronic
    • Radioactivity
    • Radioactivity as Emission of Alpha, Beta, and Gamma Radiations
    • Properties of Alpha Particles
    • Properties of Beta Particles
    • Properties of Gamma Radiations
    • Changes Within the Nucleus in Alpha, Beta and Gamma Emission
    • Alpha Decay (Alpha Emission)
    • Beta Decay (Beta Emission)
    • Gamma Decay (Gamma Emission)
    • Uses of Radioactive Isotopes
    • Sources of Harmful Radiations
    • Hazards of Radioactive Substances and Radiation
    • Safety Precautions While Using Nuclear Energy
    • Background Radiations
    • Nuclear Energy
    • Nuclear Fission
    • Distinction Between the Radioactive Decay and Nuclear Fission
    • Nuclear Fusion
    • Distinction Between the Nuclear Fission and Nuclear Fusion
  • Kinetic Energy
  • Expression for the Kinetic Energy `(K = 1/2"mv"^2)` 
  • Factors affecting the kinetic energy of a moving body
  • Relationship between kinetic energy and momentum
  • Work-energy theorem


Formula for Kinetic Energy:

 Work done →  W = F x s     ...(i)

due to force, the velocity changes to 'v', and the acceleration produced is 'a' 

`therefore` relationship between v, u, a and s= v2 - u2 =2as

`therefore` `"s" = ("v"^2 - "u"^2)/"2a"`     ...(ii)

F = ma     ...(iii)

substitute (ii) and (iii) in (i) we get

W = F x s

`= "ma" xx ("v"^2 - "u"^2)/"2a"`

`"W" = 1/2 "m"("v"^2 - "u"^2)`

if    u = 0, (object starts at rest)

`therefore`   `"W" = 1/2"mv"^2`

Work done = Change in kinetic energy 

`therefore`    `"E"_"k" = 1/2"mv"^2`

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