Math Problem Statement
Bestäm arbetet som krävs för att accelerera ett objekt med massa 7,8 kg från hastigheten 0,47c till hastigheten 0,60c. Arbetet ges av skillnaden i kinetisk energi mellan slut- och starthastigheten.
Svaret ska anges i enheten PJ (petajoule, 1 PJ = 1015 J) och vara korrekt inom en felmarginal på 5%.
Använd c = 299 792 458 m/s.
Solution
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Math Problem Analysis
Mathematical Concepts
Relativistic Mechanics
Kinetic Energy
Work-Energy Principle
Formulas
Relativistic kinetic energy: E_k = (γ - 1)mc^2
Lorentz factor: γ = 1 / √(1 - (v/c)^2)
Work: W = ΔE_k = E_k(final) - E_k(initial)
Theorems
Work-Energy Theorem
Special Theory of Relativity
Suitable Grade Level
Undergraduate Physics
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