Kinetic Energy Contents: Rest Energy /Moving energy.

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Presentation transcript:

Kinetic Energy Contents: Rest Energy /Moving energy

Kinetic Energy TOC Mass increase is energy Example: What is the kinetic energy of a 10.0 kg object going.60 c?

Dilated mass is 10.0/√( ) = 12.5 kg So its mass has increased by 2.5 kg, this mass is energy. 2.5 kg represents (2.5 kg)(3.00E8 m/s) 2 = 2.25E17 J 12.5 kg 10.0 kg = rest mass 2.5 kg = energy mass What does this diagram look like for a 6.5 TeV proton? m o ≈ 1 GeV KE = 6,500 GeV

Kinetic Energy TOC Example – A kg baseball has 2.0x10 15 J of kinetic energy. What is its mass, what is its velocity?

Well – the increase of mass is (2.0E15 J)/(3E8) 2 = kg so the new mass is kg and v = c √(1-small 2 /big 2 ) = c √( / ) ≈.50c

Kinetic Energy TOC Example – An electron (rest mass MeV) is accelerated through MV, What is its velocity?

Example – An electron (rest mass MeV) is accelerated through MeV, What is its velocity? Well – the new mass is = MeV v = c √(1-small 2 /big 2 ) = c √( / ) =.64c

Whiteboards: Kinetic Energy 11 | 2 | 3 | 423 TOC

W 3.84 kg, 2.4E+17 J A 1.2 kg object (rest mass) is moving at 2.85x10 8 m/s. What is its new mass, and what is its kinetic energy? So the new mass is 1.2/√(1-(2.85E8) 2 /(3E8) 2 ) = kg So the “energy mass” is kg – 1.2 kg = kg and that represents ( kg)(3E8) 2 = 2.4E+17 J

W.800 c What velocity must an electron have when it is accelerated through 340. kV? m o = 9.11E-31 kg = MeV So the new mass is MeV MeV = MeV v = c √(1-small 2 /big 2 ) = c √( / ) = c about.800 c

W 2.97E+13 J,.32 c A kg (rest mass) bullet is going so fast it has a (dilated) mass of kg. What is its kinetic energy, and what is its velocity The increase in mass is kg kg = kg and that represents ( kg )(3E8) 2 = 2.97E+13 J v = c √(1-small 2 /big 2 ) = c √( /645 2 ) = c about.32 c

W Your Mother The LHC will accelerate protons to about 7 TeV. If a proton has a rest mass of 938 MeV, what is the velocity of the protons in the LHC? So the new mass is 938 MeV + 7,000,000 MeV = 7,000,938 MeV v = c √(1-small 2 /big 2 ) = c √(1-(938) 2 /( ) 2 ) = c about 1 c