Chapter2_2 - ) / 1 /( 2 2 2 2 c v m m = and 2 2 2 2 ) / 1 (...

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PHY3063 R. D. Field Department of Physics Chapter2_2.doc University of Florida Relativistic Kinetic Energy ( derivation ) Relativistic Force: The force is equal to the rate of chance of the (relativistic) momentum as follows: v dt dm dt v d m dt v m d dt p d F r r r r r + = = = ) ( where 0 m m γ = is the relativistic mass. Relativistic Kinetic Energy: The kinetic energy of a particle is (as classical) the total work done in moving particle from rest to the speed v as follows: RME E c m mc dm c dm v dm v c dm v mvdv mv vd dx dt mv d Fdx KE m m m m = = = + = + = = = = 2 0 2 2 2 2 2 2 0 0 ) ) (( ) ( ) ( ) ( where I used ) / 1 ( 2 2 0 2 2 m m c v = and dm v c mvdv ) ( 2 2 = . Energy Momentum Connection:
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Unformatted text preview: ) / 1 /( 2 2 2 2 c v m m = and 2 2 2 2 ) / 1 ( m c v m = which implies that 2 2 2 2 2 / m c v m m = and 4 2 2 2 2 4 2 c m c v m c m = thus 2 2 2 2 ) ( ) ( c m cp E + = . Speed of a particle: Since mv p = and 2 / c E m = we get 2 / c Ev p = and thus 2 2 2 ) ( ) ( c m cp cp E cp c v + = = = . Classically this term is zero and F = ma Time t = 0 F Particle at rest: v = 0, m = m Later time t v Particle moving at speed v, m = m...
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This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.

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