relativistic mechanics
DESCRIPTION
Relativistic Mechanics. Momentum and energy. Momentum. p = g mv Momentum is conserved in all interactions. Total Energy. E = g mc 2 Total energy is conserved in all interactions. Rest Energy. E = g mc 2 If v = 0 then g = 1, E = mc 2 Rest energy is mc 2 - PowerPoint PPT PresentationTRANSCRIPT
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Relativistic Mechanics
Momentum and energy
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Momentum
p = mvMomentum is conserved in all interactions.
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Total Energy
E = mc2
Total energy is conserved in all interactions.
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Rest Energy
• E = mc2
• If v = 0 then = 1, E = mc2
• Rest energy is mc2
• Kinetic energy is (–1)mc2
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Mass is Energy
• Or, E = K + mc2
• Particle masses often given as energies– More correctly, as rest energy/c2
• Customary unit: eV = electron·Volt– 1 elementary charge pushed through 1 V– Just like 1 J = (1 C)(1 V)– e = 1.60×10–19 C, so 1 eV = 1.60×10–19 J
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Particle Masses
• Electron 511 keV/c2
• Proton 983.3 MeV/c2
• Neutron 939.6 MeV/c2
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Correspondence
At small :
Momentum mv mv
Energy mc2 = (1–2)–1/2 mc2
Binomal approximation (1+x)n 1+nx for small x
So (1–2)–1/2 1 + (–1/2)(–2) = 1 + 2/2
mc2 mc2 + 1/2 mv2
Is this true? Let’s check:
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Convenient Formula
E2 = (mc2)2 + (pc)2
• Derivation: show R side = (mc2)2
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A massless photon
• p = h/• E = hf = hc/• h = 6.62610–36 J·s (Planck constant)
• mc2 incalculable: = and m = 0
• But E2 = (mc2)2 + (pc)2 works:– E2 = 0 + (hc/)2 = (hf)2
– E = hf